Average Error: 26.8 → 0.6
Time: 5.7s
Precision: binary64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -1.6570490193562163 \cdot 10^{+61} \lor \neg \left(x \leq 2.82367765051812 \cdot 10^{+37}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 + \left(\frac{y}{{x}^{3}} - \frac{101.7851458539211}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{x \cdot \left(y + \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right)\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -1.6570490193562163 \cdot 10^{+61} \lor \neg \left(x \leq 2.82367765051812 \cdot 10^{+37}\right):\\
\;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 + \left(\frac{y}{{x}^{3}} - \frac{101.7851458539211}{x}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \cdot \frac{x \cdot \left(y + \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right)\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\

\end{array}
double code(double x, double y, double z) {
	return (((double) (((double) (x - 2.0)) * ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * 4.16438922228)) + 78.6994924154)) * x)) + 137.519416416)) * x)) + y)) * x)) + z)))) / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (x + 43.3400022514)) * x)) + 263.505074721)) * x)) + 313.399215894)) * x)) + 47.066876606)));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((x <= -1.6570490193562163e+61) || !(x <= 2.82367765051812e+37))) {
		VAR = ((double) (((double) (x - 2.0)) * ((double) (4.16438922228 + ((double) ((y / ((double) pow(x, 3.0))) - (101.7851458539211 / x)))))));
	} else {
		VAR = ((double) (((double) (x - 2.0)) * (((double) (((double) (x * ((double) (y + ((double) (((double) (((double) cbrt(x)) * ((double) cbrt(x)))) * ((double) (((double) cbrt(x)) * ((double) (((double) (x * ((double) (((double) (x * 4.16438922228)) + 78.6994924154)))) + 137.519416416)))))))))) + z)) / ((double) (((double) (x * ((double) (((double) (x * ((double) (((double) (x * ((double) (x + 43.3400022514)))) + 263.505074721)))) + 313.399215894)))) + 47.066876606)))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.8
Target0.5
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.65704901935621632e61 or 2.8236776505181202e37 < x

    1. Initial program 61.6

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]

    2. Simplified57.5

      \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}\]

    3. Taylor expanded around inf 0.7

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(\frac{y}{{x}^{3}} + 4.16438922228\right) - 101.7851458539211 \cdot \frac{1}{x}\right)}\]

    4. Simplified0.7

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(4.16438922228 + \left(\frac{y}{{x}^{3}} - \frac{101.7851458539211}{x}\right)\right)}\]

    if -1.65704901935621632e61 < x < 2.8236776505181202e37

    1. Initial program 1.1

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\]

    2. Simplified0.5

      \[\leadsto \color{blue}{\left(x - 2\right) \cdot \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}}\]
    3. Using strategy rm

    4. Applied add-cube-cbrt0.6

      \[\leadsto \left(x - 2\right) \cdot \frac{x \cdot \left(\color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\]

    5. Applied associate-*l*0.6

      \[\leadsto \left(x - 2\right) \cdot \frac{x \cdot \left(\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right)} + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\]

    6. Simplified0.6

      \[\leadsto \left(x - 2\right) \cdot \frac{x \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \color{blue}{\left(\left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) \cdot \sqrt[3]{x}\right)} + y\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6570490193562163 \cdot 10^{+61} \lor \neg \left(x \leq 2.82367765051812 \cdot 10^{+37}\right):\\ \;\;\;\;\left(x - 2\right) \cdot \left(4.16438922228 + \left(\frac{y}{{x}^{3}} - \frac{101.7851458539211}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \frac{x \cdot \left(y + \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right)\right) + z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* 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 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))