Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C

Average Error: 26.1 → 0.5

Time: 7.7s

Precision: 64

Math

\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -1.36994683509101684 \cdot 10^{54} \lor \neg \left(x \le 8.13570962149231836 \cdot 10^{42}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(\frac{\sqrt[3]{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

C

double code(double x, double y, double z) {
	return (((x - 2.0) * ((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z)) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606));
}

↓

double code(double x, double y, double z) {
	double VAR;
	if (((x <= -1.3699468350910168e+54) || !(x <= 8.135709621492318e+42))) {
		VAR = (((y / pow(x, 2.0)) + (4.16438922228 * x)) - 110.1139242984811);
	} else {
		VAR = ((x - 2.0) * ((((((((((cbrt((cbrt((pow((x * 4.16438922228), 3.0) + pow(78.6994924154, 3.0))) * cbrt((((x * 4.16438922228) * (x * 4.16438922228)) - (78.6994924154 * 78.6994924154))))) * cbrt((cbrt((((x * 4.16438922228) * (x * 4.16438922228)) - (78.6994924154 * 78.6994924154))) * cbrt(((x * 4.16438922228) + 78.6994924154))))) / (cbrt((cbrt(((x * 4.16438922228) - 78.6994924154)) * cbrt((((x * 4.16438922228) * (x * 4.16438922228)) + ((78.6994924154 * 78.6994924154) - ((x * 4.16438922228) * 78.6994924154)))))) * cbrt(cbrt(((x * 4.16438922228) - 78.6994924154))))) * cbrt((cbrt(((x * 4.16438922228) + 78.6994924154)) * cbrt(((x * 4.16438922228) + 78.6994924154))))) * (cbrt(((x * 4.16438922228) + 78.6994924154)) * x)) + 137.519416416) * x) + y) * x) + z) / (((((((x + 43.3400022514) * x) + 263.505074721) * x) + 313.399215894) * x) + 47.066876606)));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	26.1
Target	0.4
Herbie	0.5

\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if x < -1.3699468350910168e+54 or 8.135709621492318e+42 < x

   1. Initial program 61.4

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   2. Taylor expanded around inf 0.7

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]

   if -1.3699468350910168e+54 < x < 8.135709621492318e+42

   1. Initial program 1.0

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
   2. Using strategy rm

   3. Applied *-un-lft-identity 1.0

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right)}}\]

   4. Applied times-frac 0.4

      \[\leadsto \color{blue}{\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}\]

   5. Simplified 0.4

      \[\leadsto \color{blue}{\left(x - 2\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
   6. Using strategy rm

   7. Applied add-cube-cbrt 0.4

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\color{blue}{\left(\left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}\right) \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}\right)} \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   8. Applied associate-*l* 0.4

      \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right)} + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
   9. Using strategy rm

   10. Applied add-cube-cbrt 0.5

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right)} \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
   11. Using strategy rm

   12. Applied flip-+ 0.5

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\color{blue}{\frac{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}{x \cdot 4.16438922227999964 - 78.6994924154000017}}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   13. Applied cbrt-div 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \color{blue}{\frac{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   14. Applied associate-*r/ 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   15. Applied cbrt-div 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}} \cdot \color{blue}{\frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   16. Applied flip-+ 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\color{blue}{\frac{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}{x \cdot 4.16438922227999964 - 78.6994924154000017}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   17. Applied cbrt-div 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \color{blue}{\frac{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   18. Applied flip3-+ 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}}{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)}}} \cdot \frac{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   19. Applied cbrt-div 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\color{blue}{\frac{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}}}{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)}}} \cdot \frac{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   20. Applied frac-times 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\sqrt[3]{\color{blue}{\frac{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)} \cdot \sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   21. Applied cbrt-div 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\left(\color{blue}{\frac{\sqrt[3]{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)} \cdot \sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}\right) \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   22. Applied frac-times 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\color{blue}{\frac{\sqrt[3]{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)} \cdot \sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   23. Simplified 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\frac{\color{blue}{\sqrt[3]{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}}}{\sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)} \cdot \sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

   24. Simplified 0.4

       \[\leadsto \left(x - 2\right) \cdot \frac{\left(\left(\left(\frac{\sqrt[3]{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}}{\color{blue}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.36994683509101684 \cdot 10^{54} \lor \neg \left(x \le 8.13570962149231836 \cdot 10^{42}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{\left(\left(\left(\frac{\sqrt[3]{\sqrt[3]{{\left(x \cdot 4.16438922227999964\right)}^{3} + {78.6994924154000017}^{3}} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017}} \cdot \sqrt[3]{\sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) - 78.6994924154000017 \cdot 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}}{\sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017} \cdot \sqrt[3]{\left(x \cdot 4.16438922227999964\right) \cdot \left(x \cdot 4.16438922227999964\right) + \left(78.6994924154000017 \cdot 78.6994924154000017 - \left(x \cdot 4.16438922227999964\right) \cdot 78.6994924154000017\right)}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 - 78.6994924154000017}}} \cdot \sqrt[3]{\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot \sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017}}\right) \cdot \left(\sqrt[3]{x \cdot 4.16438922227999964 + 78.6994924154000017} \cdot x\right) + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))