Av(1234, 2341, 4123)
Generating Function
\(\displaystyle \frac{4 \left(x -1\right)^{6} \left(x -\frac{1}{2}\right)^{2} \left(x +1\right) \sqrt{1-4 x}-40 x^{9}+168 x^{8}-361 x^{7}+445 x^{6}-305 x^{5}+87 x^{4}+25 x^{3}-29 x^{2}+9 x -1}{2 x \left(2 x -1\right)^{2} \left(x -1\right)^{7}}\)
Counting Sequence
1, 1, 2, 6, 21, 76, 270, 929, 3118, 10354, 34472, 116097, 397167, 1380884, 4872188, ...
Implicit Equation for the Generating Function
\(\displaystyle x \left(2 x -1\right)^{4} \left(x -1\right)^{14} F \left(x
\right)^{2}+\left(40 x^{9}-168 x^{8}+361 x^{7}-445 x^{6}+305 x^{5}-87 x^{4}-25 x^{3}+29 x^{2}-9 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{7} F \! \left(x \right)+16 x^{18}+204 x^{17}-2280 x^{16}+10794 x^{15}-32169 x^{14}+67520 x^{13}-104127 x^{12}+118822 x^{11}-97614 x^{10}+51735 x^{9}-8432 x^{8}-13598 x^{7}+15600 x^{6}-9327 x^{5}+3702 x^{4}-1009 x^{3}+183 x^{2}-20 x +1 = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 21\)
\(\displaystyle a \! \left(5\right) = 76\)
\(\displaystyle a \! \left(6\right) = 270\)
\(\displaystyle a \! \left(7\right) = 929\)
\(\displaystyle a \! \left(8\right) = 3118\)
\(\displaystyle a \! \left(9\right) = 10354\)
\(\displaystyle a \! \left(10\right) = 34472\)
\(\displaystyle a \! \left(11\right) = 116097\)
\(\displaystyle a \! \left(12\right) = 397167\)
\(\displaystyle a \! \left(n +6\right) = \frac{16 \left(2 n +1\right) a \! \left(n \right)}{7+n}-\frac{8 \left(7 n +3\right) a \! \left(1+n \right)}{7+n}+\frac{4 \left(n -24\right) a \! \left(n +2\right)}{7+n}+\frac{2 \left(23 n +117\right) a \! \left(n +3\right)}{7+n}-\frac{\left(183+35 n \right) a \! \left(n +4\right)}{7+n}+\frac{10 \left(n +6\right) a \! \left(n +5\right)}{7+n}+\frac{6 n^{6}-187 n^{5}+1565 n^{4}-2875 n^{3}-851 n^{2}-7858 n -3720}{120 n +840}, \quad n \geq 13\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 21\)
\(\displaystyle a \! \left(5\right) = 76\)
\(\displaystyle a \! \left(6\right) = 270\)
\(\displaystyle a \! \left(7\right) = 929\)
\(\displaystyle a \! \left(8\right) = 3118\)
\(\displaystyle a \! \left(9\right) = 10354\)
\(\displaystyle a \! \left(10\right) = 34472\)
\(\displaystyle a \! \left(11\right) = 116097\)
\(\displaystyle a \! \left(12\right) = 397167\)
\(\displaystyle a \! \left(n +6\right) = \frac{16 \left(2 n +1\right) a \! \left(n \right)}{7+n}-\frac{8 \left(7 n +3\right) a \! \left(1+n \right)}{7+n}+\frac{4 \left(n -24\right) a \! \left(n +2\right)}{7+n}+\frac{2 \left(23 n +117\right) a \! \left(n +3\right)}{7+n}-\frac{\left(183+35 n \right) a \! \left(n +4\right)}{7+n}+\frac{10 \left(n +6\right) a \! \left(n +5\right)}{7+n}+\frac{6 n^{6}-187 n^{5}+1565 n^{4}-2875 n^{3}-851 n^{2}-7858 n -3720}{120 n +840}, \quad n \geq 13\)
This specification was found using the strategy pack "Row And Col Placements Req Corrob Expand Verified" and has 225 rules.
Found on January 21, 2022.Finding the specification took 227 seconds.
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Copy 225 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{13}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{13}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{41}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{11}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{13}\! \left(x \right) &= x\\
F_{14}\! \left(x \right) &= F_{13}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x , 1\right)\\
F_{16}\! \left(x , y\right) &= \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , 1\right)}{-1+y}\\
F_{17}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= y x\\
F_{20}\! \left(x , y\right) &= F_{13}\! \left(x \right) F_{16}\! \left(x , y\right)\\
F_{21}\! \left(x \right) &= F_{13}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{23}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{32}\! \left(x \right) &= 0\\
F_{33}\! \left(x \right) &= F_{13}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{13}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{13}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{13}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{13}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{42}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{45}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{44}\! \left(x \right) &= -F_{1}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{13}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{13}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{13}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{71}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{54}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{13}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{13}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{13}\! \left(x \right) F_{23}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{61}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{62}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{13}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{13}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{64}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{29} \left(x \right)^{2} F_{13}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{13}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{13}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{13}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{13}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{29} \left(x \right)^{2}\\
F_{76}\! \left(x \right) &= F_{23}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{13}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{3}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{13}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{222}\! \left(x \right)+F_{29}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{13}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{83}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{191}\! \left(x \right)-F_{69}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{13}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{181}\! \left(x \right)+F_{90}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{68}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{9}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{13}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{100}\! \left(x \right) &= \frac{F_{101}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= -F_{107}\! \left(x \right)-F_{150}\! \left(x \right)-F_{90}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{117}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{107}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{13}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{109}\! \left(x \right) &= \frac{F_{110}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= -F_{115}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= \frac{F_{113}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{113}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{114}\! \left(x \right)+F_{3}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{13}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{115}\! \left(x \right) &= \frac{F_{116}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{116}\! \left(x \right) &= -F_{1}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{121}\! \left(x \right) &= -F_{131}\! \left(x \right)-F_{132}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{124}\! \left(x \right) &= -F_{9}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{13}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{29} \left(x \right)^{2} F_{13}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{23}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{13}\! \left(x \right) F_{134}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{23} \left(x \right)^{2} F_{13}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{23} \left(x \right)^{2} F_{98} \left(x \right)^{2} F_{13}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{13}\! \left(x \right) F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{144}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{13}\! \left(x \right) F_{23}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{13}\! \left(x \right) F_{146}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{98} \left(x \right)^{2}\\
F_{148}\! \left(x \right) &= F_{23}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{13}\! \left(x \right) F_{140}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{13}\! \left(x \right) F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)+F_{165}\! \left(x \right)+F_{178}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{158}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{13}\! \left(x \right) F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{13}\! \left(x \right) F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{13}\! \left(x \right) F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{13}\! \left(x \right) F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{23} \left(x \right)^{2} F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{172}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{13}\! \left(x \right) F_{169}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{13}\! \left(x \right) F_{169}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{13}\! \left(x \right) F_{175}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{176}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{23} \left(x \right)^{2} F_{169}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{29}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{13}\! \left(x \right) F_{151}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{23} \left(x \right)^{2} F_{13}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{13}\! \left(x \right) F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{184}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{23} \left(x \right)^{2}\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{23} \left(x \right)^{2} F_{13}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{13}\! \left(x \right) F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{29} \left(x \right)^{2} F_{13}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{13}\! \left(x \right) F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= \frac{F_{193}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{193}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{194}\! \left(x \right)-F_{42}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{13}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{13}\! \left(x \right) F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= \frac{F_{198}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{215}\! \left(x \right)+F_{217}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{13}\! \left(x \right) F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{204}\! \left(x \right)+F_{207}\! \left(x \right)+F_{212}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{13}\! \left(x \right) F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{155}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= 2 F_{32}\! \left(x \right)+F_{207}\! \left(x \right)+F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{13}\! \left(x \right) F_{211}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{209}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{13}\! \left(x \right) F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= 2 F_{32}\! \left(x \right)+F_{163}\! \left(x \right)+F_{212}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{13}\! \left(x \right) F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{13}\! \left(x \right) F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= 2 F_{32}\! \left(x \right)+F_{217}\! \left(x \right)+F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{13}\! \left(x \right) F_{221}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{222}\! \left(x \right) &= -F_{223}\! \left(x \right)-F_{29}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{29} \left(x \right)^{2} F_{13}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Expand Verified" and has 309 rules.
Found on January 21, 2022.Finding the specification took 666 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{7}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{230}\! \left(x \right)\\
F_{21}\! \left(x \right) &= -F_{212}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{35}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{43}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{42}\! \left(x \right) &= 0\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x , 1\right)\\
F_{45}\! \left(x , y\right) &= -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}\\
F_{46}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{42}\! \left(x \right)+F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{45}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{35}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{54}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{59}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{35}\! \left(x \right) F_{73}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{35}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{75}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= -F_{53}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{90}\! \left(x \right) &= -F_{142}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= \frac{F_{92}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{89}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{9}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{35}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{54}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104} \left(x \right)^{2} F_{35}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{108}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{111}\! \left(x \right) &= \frac{F_{112}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= \frac{F_{115}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{115}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{116}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= -F_{118}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{118}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{35}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{128}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{125}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{125}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{138}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{136}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{135}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{140}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{139}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{144}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{143}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{211}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{150}\! \left(x \right) &= -F_{33}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= -F_{152}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= -F_{161}\! \left(x \right)+F_{159}\! \left(x \right)\\
F_{159}\! \left(x \right) &= \frac{F_{160}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{160}\! \left(x \right) &= F_{117}\! \left(x \right)\\
F_{161}\! \left(x \right) &= \frac{F_{162}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= -F_{7}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{168}\! \left(x \right) &= \frac{F_{169}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= -F_{7}\! \left(x \right)+F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{174}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{35}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{176}\! \left(x \right) &= -F_{177}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{143}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{178}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= \frac{F_{180}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right)\\
F_{181}\! \left(x \right) &= -F_{184}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= \frac{F_{183}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{183}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{189}\! \left(x \right) &= \frac{F_{190}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{190}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{194}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{35}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{196}\! \left(x \right) &= \frac{F_{197}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= -F_{185}\! \left(x \right)+F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= -F_{200}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{35}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{75}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{35}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{53} \left(x \right)^{2} F_{35}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)+F_{217}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{225}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right)+F_{224}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{222}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{146}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{35}\! \left(x \right) F_{53}\! \left(x \right) F_{54}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{108}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)+F_{229}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{135}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{78} \left(x \right)^{2}\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{236}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{104}\! \left(x \right) F_{35}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{25}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{36}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{35}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right) F_{35}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{252}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)+F_{294}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{262}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{257}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{257}\! \left(x \right) &= -F_{189}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= \frac{F_{259}\! \left(x \right)}{F_{35}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= -F_{261}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{35}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{262}\! \left(x \right) &= -F_{274}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= \frac{F_{264}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)\\
F_{265}\! \left(x \right) &= -F_{273}\! \left(x \right)+F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{271}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{252}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{35}\! \left(x \right) F_{54}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{276}\! \left(x \right) &= \frac{F_{277}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{280}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{281}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{282}\! \left(x \right) F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{189}\! \left(x \right)+F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{284}\! \left(x \right)+F_{288}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{287}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{289}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{289}\! \left(x \right) &= 2 F_{42}\! \left(x \right)+F_{290}\! \left(x \right)+F_{292}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{289}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{292}\! \left(x \right)+F_{298}\! \left(x \right)+F_{300}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{301}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{302}\! \left(x \right)+F_{305}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{304}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{302}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{305}\! \left(x \right) &= 2 F_{42}\! \left(x \right)+F_{300}\! \left(x \right)+F_{306}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{307}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{308}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{306}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob Expand Verified" and has 370 rules.
Found on January 21, 2022.Finding the specification took 318 seconds.
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Copy 370 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{361}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{348}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{343}\! \left(x \right)\\
F_{27}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{33}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{41}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{4}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{49}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{48}\! \left(x \right) &= 0\\
F_{49}\! \left(x \right) &= F_{4}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x , 1\right)\\
F_{51}\! \left(x , y\right) &= -\frac{-y F_{52}\! \left(x , y\right)+F_{52}\! \left(x , 1\right)}{-1+y}\\
F_{52}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{48}\! \left(x \right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{4}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{41}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{62}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{4}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{4}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{105}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{4}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{23}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{42}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{75}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{4}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{4}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{4}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{4}\! \left(x \right) F_{41}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{4}\! \left(x \right) F_{41}\! \left(x \right)}\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{4}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{4}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= -F_{92}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{102}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{103}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{42}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{107}\! \left(x \right) &= \frac{F_{108}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{108}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{109}\! \left(x \right) &= -F_{341}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= \frac{F_{111}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= -F_{337}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{114}\! \left(x \right) &= -F_{122}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= \frac{F_{116}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{35}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{41}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{133}\! \left(x \right) &= \frac{F_{134}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{141}\! \left(x \right) &= -F_{144}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= \frac{F_{143}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{143}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{144}\! \left(x \right) &= \frac{F_{145}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= \frac{F_{148}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{148}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{42}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)+F_{319}\! \left(x \right)\\
F_{153}\! \left(x \right) &= -F_{316}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= \frac{F_{155}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= -F_{314}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{311}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{157}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{163}\! \left(x \right) &= -F_{175}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{164}\! \left(x \right) &= \frac{F_{165}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{168}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{170}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{42}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{188}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{23}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{182}\! \left(x \right) &= -F_{187}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= -F_{147}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{184}\! \left(x \right) &= \frac{F_{185}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{42}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{42}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{189}\! \left(x \right) &= -F_{310}\! \left(x \right)+F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= -F_{308}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= \frac{F_{192}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{192}\! \left(x \right) &= F_{193}\! \left(x \right)\\
F_{193}\! \left(x \right) &= -F_{307}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= -F_{306}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{284}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= -F_{271}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{203}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{23}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{203}\! \left(x \right) &= -F_{251}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= -F_{241}\! \left(x \right)+F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= \frac{F_{206}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{209}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{240}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{23}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{213}\! \left(x \right) &= -F_{238}\! \left(x \right)+F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{221}\! \left(x \right)+F_{229}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{226}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{225}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{226}\! \left(x \right) &= 2 F_{48}\! \left(x \right)+F_{221}\! \left(x \right)+F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{234}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{234}\! \left(x \right) &= 2 F_{48}\! \left(x \right)+F_{229}\! \left(x \right)+F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{235}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{42}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{42}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{250}\! \left(x \right)\\
F_{242}\! \left(x \right) &= -F_{247}\! \left(x \right)+F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{23}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{249}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{42}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{41}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{243}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{254}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{4}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{256}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= -F_{104}\! \left(x \right)+F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= -F_{266}\! \left(x \right)+F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= \frac{F_{261}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= \frac{F_{265}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{265}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{266}\! \left(x \right) &= -F_{269}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= \frac{F_{268}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{268}\! \left(x \right) &= F_{263}\! \left(x \right)\\
F_{269}\! \left(x \right) &= \frac{F_{270}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{270}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{271}\! \left(x \right) &= -F_{277}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{272}\! \left(x \right) &= -F_{275}\! \left(x \right)+F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= \frac{F_{274}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{274}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{269}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{282}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{279}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{280}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{281}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{279}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{277}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)+F_{296}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{175}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= -F_{292}\! \left(x \right)+F_{287}\! \left(x \right)\\
F_{287}\! \left(x \right) &= -F_{290}\! \left(x \right)+F_{288}\! \left(x \right)\\
F_{288}\! \left(x \right) &= \frac{F_{289}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{289}\! \left(x \right) &= F_{182}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{144}\! \left(x \right)+F_{287}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{294}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{279}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{292}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{297}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right)+F_{302}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{300}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{301}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{299}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{302}\! \left(x \right) &= 2 F_{48}\! \left(x \right)+F_{303}\! \left(x \right)+F_{305}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{304}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{302}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{298}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{23}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{309}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{200}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{175}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)+F_{313}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{100}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{60} \left(x \right)^{2}\\
F_{314}\! \left(x \right) &= F_{315}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{42}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{317}\! \left(x \right)+F_{318}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{100}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{60}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{319}\! \left(x \right) &= \frac{F_{320}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{320}\! \left(x \right) &= F_{321}\! \left(x \right)\\
F_{321}\! \left(x \right) &= -F_{123}\! \left(x \right)+F_{322}\! \left(x \right)\\
F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)\\
F_{323}\! \left(x \right) &= F_{324}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{324}\! \left(x \right) &= \frac{F_{325}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{325}\! \left(x \right) &= F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{327}\! \left(x \right)\\
F_{327}\! \left(x \right) &= -F_{100}\! \left(x \right)+F_{328}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{329}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{330}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{330}\! \left(x \right) &= \frac{F_{331}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{211}\! \left(x \right)+F_{333}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{334}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{336}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{238}\! \left(x \right)+F_{333}\! \left(x \right)\\
F_{337}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{338}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)+F_{340}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{23}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{42}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{342}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{343}\! \left(x \right) &= -F_{346}\! \left(x \right)+F_{344}\! \left(x \right)\\
F_{344}\! \left(x \right) &= \frac{F_{345}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{345}\! \left(x \right) &= F_{150}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{347}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{76} \left(x \right)^{2}\\
F_{348}\! \left(x \right) &= F_{349}\! \left(x \right)\\
F_{349}\! \left(x \right) &= F_{350}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{350}\! \left(x \right) &= F_{351}\! \left(x \right)+F_{353}\! \left(x \right)\\
F_{351}\! \left(x \right) &= F_{352}\! \left(x \right)\\
F_{352}\! \left(x \right) &= F_{41}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{353}\! \left(x \right) &= F_{354}\! \left(x \right)\\
F_{354}\! \left(x \right) &= F_{355}\! \left(x \right) F_{4}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{355}\! \left(x \right) &= F_{356}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{357}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{358}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{358}\! \left(x \right) &= F_{359}\! \left(x \right)+F_{360}\! \left(x \right)\\
F_{359}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{360}\! \left(x \right) &= F_{226}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{361}\! \left(x \right) &= F_{362}\! \left(x \right)+F_{364}\! \left(x \right)\\
F_{362}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{363}\! \left(x \right)\\
F_{363}\! \left(x \right) &= F_{176}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{364}\! \left(x \right) &= F_{365}\! \left(x \right)\\
F_{365}\! \left(x \right) &= F_{366}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{366}\! \left(x \right) &= F_{367}\! \left(x \right)+F_{369}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{368}\! \left(x \right)\\
F_{368}\! \left(x \right) &= F_{133}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{369}\! \left(x \right) &= F_{76} \left(x \right)^{2} F_{41}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Insertion Point Placements Expand Verified" and has 509 rules.
Found on January 21, 2022.Finding the specification took 125 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
F_{14}\! \left(x , y\right) &= -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{474}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{24}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{25}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{46}\! \left(x \right) &= 0\\
F_{47}\! \left(x \right) &= F_{4}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{4}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{61}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= -F_{60}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= -F_{8}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{7}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{24}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{25}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{64}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{64}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{4}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{25} \left(x \right)^{2}\\
F_{80}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{25}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{25}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{85}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{4}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{4}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{88}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{34}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{4}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{25} \left(x \right)^{2}\\
F_{97}\! \left(x \right) &= -F_{101}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{100}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{25}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{331}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{25}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{123}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x , 1\right)\\
F_{125}\! \left(x , y\right) &= -\frac{-y F_{126}\! \left(x , y\right)+F_{126}\! \left(x , 1\right)}{-1+y}\\
F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{46}\! \left(x \right)\\
F_{127}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{223}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= -F_{222}\! \left(x \right)+F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= \frac{F_{131}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{138}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{25}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{25}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{45} \left(x \right)^{2}\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{143}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= -F_{147}\! \left(x \right)+F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= \frac{F_{146}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{146}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= 2 F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= -F_{221}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= -F_{208}\! \left(x \right)+F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= -F_{205}\! \left(x \right)+F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= \frac{F_{155}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{25}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)+F_{184}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{165}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{25}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{166}\! \left(x \right)\\
F_{166}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= -F_{164}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= -F_{161}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= -F_{180}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{170}\! \left(x \right) &= \frac{F_{171}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{172}\! \left(x \right) &= -F_{84}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= -F_{176}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= \frac{F_{175}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{175}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{178}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{179}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{181}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{182}\! \left(x \right)+F_{183}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{24}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{168}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{188}\! \left(x \right)+F_{196}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{185}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{189}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{193}\! \left(x \right)\\
F_{190}\! \left(x \right) &= F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= F_{192}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{192}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{193}\! \left(x \right) &= 2 F_{46}\! \left(x \right)+F_{188}\! \left(x \right)+F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{195}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{193}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)+F_{201}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{198}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{201}\! \left(x \right) &= 2 F_{46}\! \left(x \right)+F_{196}\! \left(x \right)+F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{160}\! \left(x \right)+F_{207}\! \left(x \right)\\
F_{207}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{208}\! \left(x \right) &= -F_{221}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= -F_{220}\! \left(x \right)+F_{210}\! \left(x \right)\\
F_{210}\! \left(x \right) &= -F_{213}\! \left(x \right)+F_{211}\! \left(x \right)\\
F_{211}\! \left(x \right) &= \frac{F_{212}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{212}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{217}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{25}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{219}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{25}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{193}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{34}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{25}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{44}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{223}\! \left(x \right) &= -F_{321}\! \left(x \right)+F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= -F_{307}\! \left(x \right)+F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= \frac{F_{226}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{274}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{266}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right)+F_{236}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{239}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{239}\! \left(x \right) &= -F_{235}\! \left(x \right)+F_{240}\! \left(x \right)\\
F_{240}\! \left(x \right) &= -F_{247}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{241}\! \left(x \right) &= \frac{F_{242}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)\\
F_{243}\! \left(x \right) &= -F_{8}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{244}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{245}\! \left(x \right) &= \frac{F_{246}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{246}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{247}\! \left(x \right) &= -F_{254}\! \left(x \right)+F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= \frac{F_{249}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= -F_{8}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{251}\! \left(x \right) &= -F_{6}\! \left(x \right)+F_{252}\! \left(x \right)\\
F_{252}\! \left(x \right) &= \frac{F_{253}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{253}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{254}\! \left(x \right) &= -F_{258}\! \left(x \right)+F_{255}\! \left(x \right)\\
F_{255}\! \left(x \right) &= -F_{236}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= \frac{F_{257}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{257}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{25}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{261}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{262}\! \left(x \right)+F_{263}\! \left(x \right)+F_{264}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{261}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{237}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{265}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{24}\! \left(x \right) F_{261}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= -F_{198}\! \left(x \right)+F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= -F_{112}\! \left(x \right)+F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= -F_{149}\! \left(x \right)+F_{270}\! \left(x \right)\\
F_{270}\! \left(x \right) &= \frac{F_{271}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{271}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{25}\! \left(x \right) F_{273}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{277}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{231}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{278}\! \left(x \right)\\
F_{278}\! \left(x \right) &= -F_{284}\! \left(x \right)+F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{280}\! \left(x \right)\\
F_{280}\! \left(x \right) &= -F_{283}\! \left(x \right)+F_{281}\! \left(x \right)\\
F_{281}\! \left(x \right) &= \frac{F_{282}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{282}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{24}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{25}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{288}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{84} \left(x \right)^{2}\\
F_{288}\! \left(x \right) &= F_{289}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{25}\! \left(x \right) F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{291}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{25}\! \left(x \right) F_{292}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{293}\! \left(x \right)+F_{306}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)\\
F_{294}\! \left(x \right) &= F_{295}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{296}\! \left(x \right)+F_{305}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{297}\! \left(x \right)+F_{301}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{298}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{299}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{299}\! \left(x \right) &= F_{296}\! \left(x \right)+F_{300}\! \left(x \right)\\
F_{300}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{301}\! \left(x \right) &= F_{302}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{46}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{304}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{24}\! \left(x \right) F_{302}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{24}\! \left(x \right) F_{302}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{4}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{308}\! \left(x \right)+F_{310}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{309}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{239}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{311}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{312}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{313}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{315}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{316}\! \left(x \right)+F_{317}\! \left(x \right)+F_{318}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{261}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{317}\! \left(x \right) &= F_{315}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{318}\! \left(x \right) &= F_{319}\! \left(x \right)\\
F_{319}\! \left(x \right) &= F_{24}\! \left(x \right) F_{320}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{320}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{321}\! \left(x \right) &= F_{322}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)\\
F_{323}\! \left(x \right) &= F_{324}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{327}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{230}\! \left(x \right)+F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{25}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{328}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{329}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{330}\! \left(x \right)\\
F_{330}\! \left(x \right) &= -F_{74}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{331}\! \left(x \right) &= F_{332}\! \left(x \right)+F_{338}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{333}\! \left(x \right)\\
F_{333}\! \left(x \right) &= F_{334}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{334}\! \left(x \right) &= F_{335}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{335}\! \left(x \right) &= F_{336}\! \left(x \right)+F_{337}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{332}\! \left(x \right)\\
F_{337}\! \left(x \right) &= F_{237}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{338}\! \left(x \right) &= F_{339}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{340}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{341}\! \left(x \right)+F_{360}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{342}\! \left(x \right)+F_{344}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{25}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{344}\! \left(x \right) &= F_{345}\! \left(x \right)+F_{351}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{346}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{347}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{349}\! \left(x \right)\\
F_{348}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{345}\! \left(x \right)\\
F_{349}\! \left(x \right) &= F_{25}\! \left(x \right) F_{350}\! \left(x \right)\\
F_{350}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{351}\! \left(x \right) &= -F_{357}\! \left(x \right)+F_{352}\! \left(x \right)\\
F_{352}\! \left(x \right) &= -F_{348}\! \left(x \right)+F_{353}\! \left(x \right)\\
F_{353}\! \left(x \right) &= -F_{356}\! \left(x \right)+F_{354}\! \left(x \right)\\
F_{354}\! \left(x \right) &= \frac{F_{355}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{355}\! \left(x \right) &= F_{345}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{111}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{358}\! \left(x \right)\\
F_{358}\! \left(x \right) &= F_{359}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{359}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{357}\! \left(x \right)\\
F_{360}\! \left(x \right) &= F_{361}\! \left(x \right)+F_{363}\! \left(x \right)\\
F_{361}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{362}\! \left(x \right)\\
F_{362}\! \left(x \right) &= F_{25}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{363}\! \left(x \right) &= F_{364}\! \left(x \right)+F_{375}\! \left(x \right)\\
F_{364}\! \left(x \right) &= -F_{332}\! \left(x \right)+F_{365}\! \left(x \right)\\
F_{365}\! \left(x \right) &= -F_{371}\! \left(x \right)+F_{366}\! \left(x \right)\\
F_{366}\! \left(x \right) &= -F_{369}\! \left(x \right)+F_{367}\! \left(x \right)\\
F_{367}\! \left(x \right) &= \frac{F_{368}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{368}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{369}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{370}\! \left(x \right)\\
F_{370}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{371}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{372}\! \left(x \right)\\
F_{372}\! \left(x \right) &= F_{373}\! \left(x \right)+F_{374}\! \left(x \right)\\
F_{373}\! \left(x \right) &= F_{25}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{374}\! \left(x \right) &= F_{120}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{375}\! \left(x \right) &= -F_{473}\! \left(x \right)+F_{376}\! \left(x \right)\\
F_{376}\! \left(x \right) &= -F_{469}\! \left(x \right)+F_{377}\! \left(x \right)\\
F_{377}\! \left(x \right) &= -F_{352}\! \left(x \right)+F_{378}\! \left(x \right)\\
F_{378}\! \left(x \right) &= \frac{F_{379}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{379}\! \left(x \right) &= F_{380}\! \left(x \right)\\
F_{380}\! \left(x \right) &= F_{381}\! \left(x \right)\\
F_{381}\! \left(x \right) &= F_{382}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)+F_{452}\! \left(x \right)\\
F_{383}\! \left(x \right) &= F_{384}\! \left(x \right)\\
F_{384}\! \left(x \right) &= F_{385}\! \left(x \right)+F_{388}\! \left(x \right)\\
F_{385}\! \left(x \right) &= F_{342}\! \left(x \right)+F_{386}\! \left(x \right)\\
F_{386}\! \left(x \right) &= F_{25}\! \left(x \right) F_{387}\! \left(x \right)\\
F_{387}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{389}\! \left(x \right)+F_{394}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{390}\! \left(x \right)\\
F_{390}\! \left(x \right) &= F_{25}\! \left(x \right) F_{391}\! \left(x \right)\\
F_{391}\! \left(x \right) &= F_{392}\! \left(x \right)+F_{393}\! \left(x \right)\\
F_{392}\! \left(x \right) &= F_{25}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{25}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{395}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{25}\! \left(x \right) F_{396}\! \left(x \right)\\
F_{396}\! \left(x \right) &= -F_{451}\! \left(x \right)+F_{397}\! \left(x \right)\\
F_{397}\! \left(x \right) &= -F_{433}\! \left(x \right)+F_{398}\! \left(x \right)\\
F_{398}\! \left(x \right) &= -F_{428}\! \left(x \right)+F_{399}\! \left(x \right)\\
F_{399}\! \left(x \right) &= \frac{F_{400}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{402}\! \left(x \right)\\
F_{402}\! \left(x \right) &= F_{4}\! \left(x \right) F_{403}\! \left(x \right)\\
F_{403}\! \left(x \right) &= F_{404}\! \left(x \right)+F_{410}\! \left(x \right)\\
F_{404}\! \left(x \right) &= F_{405}\! \left(x \right)+F_{406}\! \left(x \right)\\
F_{405}\! \left(x \right) &= F_{235}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{406}\! \left(x \right) &= F_{25}\! \left(x \right) F_{407}\! \left(x \right)\\
F_{407}\! \left(x \right) &= F_{408}\! \left(x \right)+F_{409}\! \left(x \right)\\
F_{408}\! \left(x \right) &= F_{237}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{409}\! \left(x \right) &= F_{24}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{410}\! \left(x \right) &= F_{411}\! \left(x \right)+F_{412}\! \left(x \right)\\
F_{411}\! \left(x \right) &= F_{239}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{412}\! \left(x \right) &= F_{25}\! \left(x \right) F_{413}\! \left(x \right)\\
F_{413}\! \left(x \right) &= F_{414}\! \left(x \right)+F_{427}\! \left(x \right)\\
F_{414}\! \left(x \right) &= F_{415}\! \left(x \right)+F_{416}\! \left(x \right)\\
F_{415}\! \left(x \right) &= F_{216}\! \left(x \right)\\
F_{416}\! \left(x \right) &= F_{417}\! \left(x \right)+F_{425}\! \left(x \right)\\
F_{417}\! \left(x \right) &= 2 F_{46}\! \left(x \right)+F_{418}\! \left(x \right)+F_{420}\! \left(x \right)\\
F_{418}\! \left(x \right) &= F_{4}\! \left(x \right) F_{419}\! \left(x \right)\\
F_{419}\! \left(x \right) &= F_{417}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{420}\! \left(x \right) &= F_{4}\! \left(x \right) F_{421}\! \left(x \right)\\
F_{421}\! \left(x \right) &= F_{417}\! \left(x \right)+F_{422}\! \left(x \right)\\
F_{422}\! \left(x \right) &= F_{423}\! \left(x \right)\\
F_{423}\! \left(x \right) &= F_{4}\! \left(x \right) F_{424}\! \left(x \right)\\
F_{424}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{422}\! \left(x \right)\\
F_{425}\! \left(x \right) &= F_{25}\! \left(x \right) F_{426}\! \left(x \right)\\
F_{426}\! \left(x \right) &= F_{417}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{427}\! \left(x \right) &= F_{25}\! \left(x \right) F_{313}\! \left(x \right)\\
F_{428}\! \left(x \right) &= F_{429}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{429}\! \left(x \right) &= F_{430}\! \left(x \right)\\
F_{430}\! \left(x \right) &= F_{4}\! \left(x \right) F_{431}\! \left(x \right)\\
F_{431}\! \left(x \right) &= F_{406}\! \left(x \right)+F_{432}\! \left(x \right)\\
F_{432}\! \left(x \right) &= F_{25}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{433}\! \left(x \right) &= -F_{450}\! \left(x \right)+F_{434}\! \left(x \right)\\
F_{434}\! \left(x \right) &= -F_{437}\! \left(x \right)+F_{435}\! \left(x \right)\\
F_{435}\! \left(x \right) &= \frac{F_{436}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{436}\! \left(x \right) &= F_{401}\! \left(x \right)\\
F_{437}\! \left(x \right) &= F_{438}\! \left(x \right)+F_{441}\! \left(x \right)\\
F_{438}\! \left(x \right) &= F_{25}\! \left(x \right) F_{439}\! \left(x \right)\\
F_{439}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{440}\! \left(x \right)\\
F_{440}\! \left(x \right) &= F_{24}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{441}\! \left(x \right) &= F_{442}\! \left(x \right)+F_{448}\! \left(x \right)\\
F_{442}\! \left(x \right) &= F_{443}\! \left(x \right)+F_{445}\! \left(x \right)\\
F_{443}\! \left(x \right) &= F_{444}\! \left(x \right)\\
F_{444}\! \left(x \right) &= F_{25} \left(x \right)^{3}\\
F_{445}\! \left(x \right) &= F_{401}\! \left(x \right)+F_{446}\! \left(x \right)\\
F_{446}\! \left(x \right) &= F_{447}\! \left(x \right)\\
F_{447}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{45}\! \left(x \right)\\
F_{448}\! \left(x \right) &= F_{449}\! \left(x \right)\\
F_{449}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{231}\! \left(x \right)\\
F_{450}\! \left(x \right) &= F_{429}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{451}\! \left(x \right) &= F_{392}\! \left(x \right)\\
F_{452}\! \left(x \right) &= F_{453}\! \left(x \right)\\
F_{453}\! \left(x \right) &= F_{454}\! \left(x \right)+F_{457}\! \left(x \right)\\
F_{454}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{455}\! \left(x \right)\\
F_{455}\! \left(x \right) &= F_{456}\! \left(x \right)\\
F_{456}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{83}\! \left(x \right)\\
F_{457}\! \left(x \right) &= F_{458}\! \left(x \right)+F_{467}\! \left(x \right)\\
F_{458}\! \left(x \right) &= F_{25}\! \left(x \right) F_{459}\! \left(x \right)\\
F_{459}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{460}\! \left(x \right)\\
F_{460}\! \left(x \right) &= -F_{463}\! \left(x \right)+F_{461}\! \left(x \right)\\
F_{461}\! \left(x \right) &= \frac{F_{462}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{462}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{463}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{464}\! \left(x \right)\\
F_{464}\! \left(x \right) &= F_{465}\! \left(x \right)+F_{466}\! \left(x \right)\\
F_{465}\! \left(x \right) &= F_{25}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{466}\! \left(x \right) &= F_{24}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{467}\! \left(x \right) &= F_{468}\! \left(x \right)\\
F_{468}\! \left(x \right) &= F_{25}\! \left(x \right) F_{83}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{469}\! \left(x \right) &= F_{223}\! \left(x \right)+F_{470}\! \left(x \right)\\
F_{470}\! \left(x \right) &= F_{310}\! \left(x \right)+F_{471}\! \left(x \right)\\
F_{471}\! \left(x \right) &= F_{472}\! \left(x \right)\\
F_{472}\! \left(x \right) &= F_{25}\! \left(x \right) F_{254}\! \left(x \right)\\
F_{473}\! \left(x \right) &= F_{164}\! \left(x \right)\\
F_{474}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{475}\! \left(x \right)\\
F_{475}\! \left(x \right) &= F_{476}\! \left(x \right)\\
F_{476}\! \left(x \right) &= F_{4}\! \left(x \right) F_{477}\! \left(x \right)\\
F_{477}\! \left(x \right) &= F_{478}\! \left(x \right)+F_{485}\! \left(x \right)\\
F_{478}\! \left(x \right) &= F_{479}\! \left(x \right)\\
F_{479}\! \left(x \right) &= F_{480}\! \left(x \right)+F_{484}\! \left(x \right)\\
F_{480}\! \left(x \right) &= F_{481}\! \left(x \right)+F_{482}\! \left(x \right)\\
F_{481}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{482}\! \left(x \right) &= F_{25}\! \left(x \right) F_{483}\! \left(x \right)\\
F_{483}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{484}\! \left(x \right) &= F_{25}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{485}\! \left(x \right) &= F_{486}\! \left(x \right)+F_{487}\! \left(x \right)\\
F_{486}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{278}\! \left(x \right)\\
F_{487}\! \left(x \right) &= F_{488}\! \left(x \right)+F_{491}\! \left(x \right)\\
F_{488}\! \left(x \right) &= F_{288}\! \left(x \right)+F_{489}\! \left(x \right)\\
F_{489}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{490}\! \left(x \right)\\
F_{490}\! \left(x \right) &= F_{25}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{491}\! \left(x \right) &= -F_{506}\! \left(x \right)+F_{492}\! \left(x \right)\\
F_{492}\! \left(x \right) &= -F_{365}\! \left(x \right)+F_{493}\! \left(x \right)\\
F_{493}\! \left(x \right) &= \frac{F_{494}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{494}\! \left(x \right) &= F_{495}\! \left(x \right)\\
F_{495}\! \left(x \right) &= -F_{505}\! \left(x \right)+F_{496}\! \left(x \right)\\
F_{496}\! \left(x \right) &= -F_{503}\! \left(x \right)+F_{497}\! \left(x \right)\\
F_{497}\! \left(x \right) &= \frac{F_{498}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{498}\! \left(x \right) &= F_{499}\! \left(x \right)\\
F_{499}\! \left(x \right) &= F_{4}\! \left(x \right) F_{500}\! \left(x \right)\\
F_{500}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{501}\! \left(x \right)\\
F_{501}\! \left(x \right) &= F_{365}\! \left(x \right)+F_{502}\! \left(x \right)\\
F_{502}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{321}\! \left(x \right)\\
F_{503}\! \left(x \right) &= F_{345}\! \left(x \right)+F_{504}\! \left(x \right)\\
F_{504}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{505}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{372}\! \left(x \right)\\
F_{506}\! \left(x \right) &= F_{507}\! \left(x \right)+F_{508}\! \left(x \right)\\
F_{507}\! \left(x \right) &= F_{24}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{508}\! \left(x \right) &= F_{83}\! \left(x \right) F_{84}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Insertion Point Row Placements Expand Verified" and has 410 rules.
Found on January 21, 2022.Finding the specification took 105 seconds.
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Copy 410 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{7}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{18}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{23}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{324}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{409}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{24}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{41}\! \left(x \right) &= 0\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{39}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{45}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{24}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{23}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{58}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x , 1\right)\\
F_{60}\! \left(x , y\right) &= -\frac{-y F_{61}\! \left(x , y\right)+F_{61}\! \left(x , 1\right)}{-1+y}\\
F_{61}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{41}\! \left(x \right)+F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{60}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{67}\! \left(x \right) &= 2 F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{23}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{24}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{24}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{355}\! \left(x \right)+F_{41}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{23}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{84}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{24} \left(x \right)^{2}\\
F_{87}\! \left(x \right) &= -F_{92}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= -F_{18}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{23}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{24}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= -F_{350}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= -F_{349}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= -F_{346}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= -F_{200}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= -F_{184}\! \left(x \right)+F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= \frac{F_{101}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{164}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{111}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{24}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{120}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{18}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{24}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{122}\! \left(x \right) &= -F_{163}\! \left(x \right)+F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= -F_{150}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= -F_{141}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= \frac{F_{126}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{139}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right) F_{24}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{135}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{136}\! \left(x \right)+F_{138}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{131}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{24}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{147}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{24}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{23}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{150}\! \left(x \right) &= -F_{162}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= -F_{157}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= \frac{F_{153}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= -F_{155}\! \left(x \right)-F_{41}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{24}\! \left(x \right) F_{45}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{159}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{24} \left(x \right)^{2} F_{23}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{24} \left(x \right)^{2} F_{78}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{24}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{24} \left(x \right)^{2} F_{39}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{182}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{172}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{173}\! \left(x \right)\\
F_{173}\! \left(x \right) &= -F_{176}\! \left(x \right)+F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= \frac{F_{175}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{175}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{179}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{23}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{18}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{23}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{24}\! \left(x \right) F_{39}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{185}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)+F_{189}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{188}\! \left(x \right)\\
F_{188}\! \left(x \right) &= F_{24} \left(x \right)^{3}\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{198}\! \left(x \right)\\
F_{190}\! \left(x \right) &= -F_{195}\! \left(x \right)+F_{191}\! \left(x \right)\\
F_{191}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= \frac{F_{193}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{193}\! \left(x \right) &= -F_{194}\! \left(x \right)-F_{41}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{194}\! \left(x \right) &= F_{48}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{195}\! \left(x \right) &= F_{196}\! \left(x \right)\\
F_{196}\! \left(x \right) &= F_{197}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{24} \left(x \right)^{4}\\
F_{200}\! \left(x \right) &= F_{201}\! \left(x \right)+F_{221}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{203}\! \left(x \right) &= -F_{210}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{204}\! \left(x \right) &= -F_{209}\! \left(x \right)+F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= -F_{208}\! \left(x \right)+F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= \frac{F_{207}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{207}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{177}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{219}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{213}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right) F_{23}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{215}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{216}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{217}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{216}\! \left(x \right) F_{23}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{220}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{217}\! \left(x \right)+F_{219}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{222}\! \left(x \right)+F_{342}\! \left(x \right)\\
F_{222}\! \left(x \right) &= -F_{341}\! \left(x \right)+F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= -F_{246}\! \left(x \right)+F_{224}\! \left(x \right)\\
F_{224}\! \left(x \right) &= -F_{254}\! \left(x \right)+F_{225}\! \left(x \right)\\
F_{225}\! \left(x \right) &= -F_{340}\! \left(x \right)+F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= \frac{F_{227}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{227}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{230}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{230}\! \left(x \right) &= F_{231}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)+F_{242}\! \left(x \right)\\
F_{232}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{241}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{235}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{237}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{237}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= -F_{109}\! \left(x \right)+F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= \frac{F_{240}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{240}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{24}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{244}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{233}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{244}\! \left(x \right) &= F_{40} \left(x \right)^{2}\\
F_{245}\! \left(x \right) &= F_{246}\! \left(x \right)+F_{254}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{228}\! \left(x \right)+F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{251}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{177}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{252}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{210}\! \left(x \right)+F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{247}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{265}\! \left(x \right)\\
F_{255}\! \left(x \right) &= -F_{233}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{256}\! \left(x \right) &= -F_{261}\! \left(x \right)+F_{257}\! \left(x \right)\\
F_{257}\! \left(x \right) &= -F_{260}\! \left(x \right)+F_{258}\! \left(x \right)\\
F_{258}\! \left(x \right) &= \frac{F_{259}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{259}\! \left(x \right) &= F_{233}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{24}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{261}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{262}\! \left(x \right)\\
F_{262}\! \left(x \right) &= F_{263}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{262}\! \left(x \right)\\
F_{265}\! \left(x \right) &= -F_{316}\! \left(x \right)+F_{266}\! \left(x \right)\\
F_{266}\! \left(x \right) &= -F_{313}\! \left(x \right)+F_{267}\! \left(x \right)\\
F_{267}\! \left(x \right) &= -F_{299}\! \left(x \right)+F_{268}\! \left(x \right)\\
F_{268}\! \left(x \right) &= \frac{F_{269}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{269}\! \left(x \right) &= F_{270}\! \left(x \right)\\
F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{295}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{271}\! \left(x \right) &= F_{272}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{273}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{274}\! \left(x \right)+F_{277}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)+F_{276}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{24}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{24}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)+F_{289}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{24}\! \left(x \right) F_{279}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{280}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{281}\! \left(x \right)+F_{283}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{282}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{280}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{284}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{285}\! \left(x \right)\\
F_{285}\! \left(x \right) &= 2 F_{41}\! \left(x \right)+F_{283}\! \left(x \right)+F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{287}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{288}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{286}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= -F_{172}\! \left(x \right)+F_{291}\! \left(x \right)\\
F_{291}\! \left(x \right) &= -F_{298}\! \left(x \right)+F_{292}\! \left(x \right)\\
F_{292}\! \left(x \right) &= -F_{297}\! \left(x \right)+F_{293}\! \left(x \right)\\
F_{293}\! \left(x \right) &= \frac{F_{294}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{294}\! \left(x \right) &= -F_{295}\! \left(x \right)-F_{41}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{295}\! \left(x \right) &= F_{296}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{296}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{297}\! \left(x \right) &= F_{24}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{298}\! \left(x \right) &= F_{24}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{299}\! \left(x \right) &= -F_{302}\! \left(x \right)+F_{300}\! \left(x \right)\\
F_{300}\! \left(x \right) &= \frac{F_{301}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{301}\! \left(x \right) &= F_{172}\! \left(x \right)\\
F_{302}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{312}\! \left(x \right)\\
F_{303}\! \left(x \right) &= F_{304}\! \left(x \right)+F_{311}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{304}\! \left(x \right) &= F_{305}\! \left(x \right)\\
F_{305}\! \left(x \right) &= F_{306}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{306}\! \left(x \right) &= F_{303}\! \left(x \right)+F_{307}\! \left(x \right)\\
F_{307}\! \left(x \right) &= F_{23}\! \left(x \right) F_{308}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{308}\! \left(x \right) &= F_{215}\! \left(x \right)+F_{309}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)\\
F_{310}\! \left(x \right) &= F_{23}\! \left(x \right) F_{308}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{311}\! \left(x \right) &= F_{214}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{312}\! \left(x \right) &= F_{214}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)\\
F_{314}\! \left(x \right) &= F_{24}\! \left(x \right) F_{315}\! \left(x \right)\\
F_{315}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{316}\! \left(x \right) &= F_{317}\! \left(x \right)+F_{338}\! \left(x \right)\\
F_{317}\! \left(x \right) &= -F_{337}\! \left(x \right)+F_{318}\! \left(x \right)\\
F_{318}\! \left(x \right) &= -F_{333}\! \left(x \right)+F_{319}\! \left(x \right)\\
F_{319}\! \left(x \right) &= -F_{332}\! \left(x \right)+F_{320}\! \left(x \right)\\
F_{320}\! \left(x \right) &= \frac{F_{321}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{321}\! \left(x \right) &= F_{322}\! \left(x \right)\\
F_{322}\! \left(x \right) &= -F_{323}\! \left(x \right)-F_{41}\! \left(x \right)+F_{270}\! \left(x \right)\\
F_{323}\! \left(x \right) &= F_{324}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{324}\! \left(x \right) &= F_{270}\! \left(x \right)+F_{325}\! \left(x \right)\\
F_{325}\! \left(x \right) &= F_{326}\! \left(x \right)\\
F_{326}\! \left(x \right) &= F_{327}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{329}\! \left(x \right)\\
F_{328}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{330}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{331}\! \left(x \right)\\
F_{331}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{332}\! \left(x \right) &= F_{131}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{333}\! \left(x \right) &= -F_{303}\! \left(x \right)+F_{334}\! \left(x \right)\\
F_{334}\! \left(x \right) &= \frac{F_{335}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{335}\! \left(x \right) &= -F_{336}\! \left(x \right)-F_{41}\! \left(x \right)+F_{172}\! \left(x \right)\\
F_{336}\! \left(x \right) &= F_{296}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{337}\! \left(x \right) &= F_{24} \left(x \right)^{2}\\
F_{338}\! \left(x \right) &= F_{24}\! \left(x \right) F_{339}\! \left(x \right)\\
F_{339}\! \left(x \right) &= F_{233}\! \left(x \right)+F_{317}\! \left(x \right)\\
F_{340}\! \left(x \right) &= F_{23}\! \left(x \right) F_{233}\! \left(x \right)\\
F_{341}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)\\
F_{343}\! \left(x \right) &= F_{24} \left(x \right)^{2} F_{344}\! \left(x \right)\\
F_{344}\! \left(x \right) &= F_{304}\! \left(x \right)+F_{345}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{345}\! \left(x \right) &= F_{211}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{346}\! \left(x \right) &= F_{347}\! \left(x \right)+F_{348}\! \left(x \right)\\
F_{347}\! \left(x \right) &= F_{111}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{348}\! \left(x \right) &= F_{46} \left(x \right)^{2}\\
F_{349}\! \left(x \right) &= F_{24}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{350}\! \left(x \right) &= -F_{64}\! \left(x \right)+F_{351}\! \left(x \right)\\
F_{351}\! \left(x \right) &= -F_{354}\! \left(x \right)+F_{352}\! \left(x \right)\\
F_{352}\! \left(x \right) &= \frac{F_{353}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{353}\! \left(x \right) &= -F_{41}\! \left(x \right)-F_{49}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{354}\! \left(x \right) &= F_{195}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{355}\! \left(x \right) &= F_{356}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{356}\! \left(x \right) &= F_{357}\! \left(x \right)+F_{359}\! \left(x \right)\\
F_{357}\! \left(x \right) &= F_{24}\! \left(x \right) F_{358}\! \left(x \right)\\
F_{358}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{359}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{360}\! \left(x \right)\\
F_{360}\! \left(x \right) &= F_{361}\! \left(x \right)+F_{362}\! \left(x \right)\\
F_{361}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{362}\! \left(x \right) &= -F_{167}\! \left(x \right)+F_{363}\! \left(x \right)\\
F_{363}\! \left(x \right) &= -F_{374}\! \left(x \right)+F_{364}\! \left(x \right)\\
F_{364}\! \left(x \right) &= -F_{368}\! \left(x \right)+F_{365}\! \left(x \right)\\
F_{365}\! \left(x \right) &= \frac{F_{366}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{366}\! \left(x \right) &= -F_{367}\! \left(x \right)-F_{41}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{367}\! \left(x \right) &= F_{224}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{368}\! \left(x \right) &= F_{369}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{369}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{370}\! \left(x \right)\\
F_{370}\! \left(x \right) &= -F_{92}\! \left(x \right)+F_{371}\! \left(x \right)\\
F_{371}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{372}\! \left(x \right)\\
F_{372}\! \left(x \right) &= \frac{F_{373}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{373}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{374}\! \left(x \right) &= F_{24}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{375}\! \left(x \right) &= -F_{378}\! \left(x \right)+F_{376}\! \left(x \right)\\
F_{376}\! \left(x \right) &= \frac{F_{377}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{377}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{378}\! \left(x \right) &= F_{379}\! \left(x \right)+F_{382}\! \left(x \right)\\
F_{379}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{381}\! \left(x \right)\\
F_{380}\! \left(x \right) &= F_{23}\! \left(x \right) F_{247}\! \left(x \right)\\
F_{381}\! \left(x \right) &= F_{39}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{382}\! \left(x \right) &= -F_{380}\! \left(x \right)+F_{383}\! \left(x \right)\\
F_{383}\! \left(x \right) &= -F_{386}\! \left(x \right)+F_{384}\! \left(x \right)\\
F_{384}\! \left(x \right) &= \frac{F_{385}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{385}\! \left(x \right) &= F_{228}\! \left(x \right)\\
F_{386}\! \left(x \right) &= \frac{F_{387}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{387}\! \left(x \right) &= -F_{388}\! \left(x \right)-F_{41}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{388}\! \left(x \right) &= F_{389}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{389}\! \left(x \right) &= F_{390}\! \left(x \right)+F_{396}\! \left(x \right)\\
F_{390}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{391}\! \left(x \right)\\
F_{391}\! \left(x \right) &= F_{392}\! \left(x \right)\\
F_{392}\! \left(x \right) &= F_{393}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{393}\! \left(x \right) &= F_{394}\! \left(x \right)+F_{395}\! \left(x \right)\\
F_{394}\! \left(x \right) &= F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{395}\! \left(x \right) &= F_{23}\! \left(x \right) F_{24}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{396}\! \left(x \right) &= F_{397}\! \left(x \right)+F_{398}\! \left(x \right)\\
F_{397}\! \left(x \right) &= F_{112}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{398}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{399}\! \left(x \right)\\
F_{399}\! \left(x \right) &= F_{400}\! \left(x \right)+F_{401}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{400}\! \left(x \right) &= F_{46}\! \left(x \right) F_{48}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{401}\! \left(x \right) &= F_{402}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{402}\! \left(x \right) &= F_{399}\! \left(x \right)+F_{403}\! \left(x \right)\\
F_{403}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{404}\! \left(x \right)\\
F_{404}\! \left(x \right) &= -F_{112}\! \left(x \right)+F_{405}\! \left(x \right)\\
F_{405}\! \left(x \right) &= -F_{408}\! \left(x \right)+F_{406}\! \left(x \right)\\
F_{406}\! \left(x \right) &= \frac{F_{407}\! \left(x \right)}{F_{9}\! \left(x \right)}\\
F_{407}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{408}\! \left(x \right) &= F_{18}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{409}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{91}\! \left(x \right)\\
\end{align*}\)