Average Error: 19.6 → 0.1
Time: 4.2s
Precision: binary64
\[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.120362690310111 \cdot 10^{+22} \lor \neg \left(z \leq 458236.22514243907\right):\\ \;\;\;\;x + \left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.40462203869992125}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \left(z \cdot \left(\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}\right)\right) + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array}\]
x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.120362690310111 \cdot 10^{+22} \lor \neg \left(z \leq 458236.22514243907\right):\\
\;\;\;\;x + \left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.40462203869992125}{z}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \left(z \cdot \left(\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}\right)\right) + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (x + (((double) (y * ((double) (((double) (((double) (((double) (z * 0.0692910599291889)) + 0.4917317610505968)) * z)) + 0.279195317918525)))) / ((double) (((double) (((double) (z + 6.012459259764103)) * z)) + 3.350343815022304)))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.120362690310111e+22) || !(z <= 458236.22514243907))) {
		VAR = ((double) (x + ((double) (((double) (0.0692910599291889 * y)) + ((double) ((y / z) * ((double) (0.07512208616047561 - (0.40462203869992125 / z)))))))));
	} else {
		VAR = ((double) (x + ((double) (y * (((double) (((double) (((double) cbrt(((double) (((double) (z * 0.0692910599291889)) + 0.4917317610505968)))) * ((double) (z * ((double) (((double) cbrt(((double) (((double) (z * 0.0692910599291889)) + 0.4917317610505968)))) * ((double) cbrt(((double) (((double) (z * 0.0692910599291889)) + 0.4917317610505968)))))))))) + 0.279195317918525)) / ((double) (((double) (z * ((double) (z + 6.012459259764103)))) + 3.350343815022304)))))));
	}
	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

Original19.6
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z < -8120153.652456675:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \mathbf{elif}\;z < 6.576118972787377 \cdot 10^{+20}:\\ \;\;\;\;x + \left(y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)\right) \cdot \frac{1}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{0.07512208616047561}{z} + 0.0692910599291889\right) \cdot y - \left(\frac{0.40462203869992125 \cdot y}{z \cdot z} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.12036269031011092e22 or 458236.225142439071 < z

    1. Initial program 41.8

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    2. Simplified33.0

      \[\leadsto \color{blue}{x + y \cdot \frac{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}}\]

    3. Taylor expanded around inf 0.0

      \[\leadsto x + \color{blue}{\left(\left(0.07512208616047561 \cdot \frac{y}{z} + 0.0692910599291889 \cdot y\right) - 0.40462203869992125 \cdot \frac{y}{{z}^{2}}\right)}\]

    4. Simplified0.0

      \[\leadsto x + \color{blue}{\left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.40462203869992125}{z}\right)\right)}\]

    if -1.12036269031011092e22 < z < 458236.225142439071

    1. Initial program 0.2

      \[x + \frac{y \cdot \left(\left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) \cdot z + 0.279195317918525\right)}{\left(z + 6.012459259764103\right) \cdot z + 3.350343815022304}\]

    2. Simplified0.1

      \[\leadsto \color{blue}{x + y \cdot \frac{z \cdot \left(z \cdot 0.0692910599291889 + 0.4917317610505968\right) + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}}\]
    3. Using strategy rm

    4. Applied add-cube-cbrt0.1

      \[\leadsto x + y \cdot \frac{z \cdot \color{blue}{\left(\left(\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}\right) \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}\right)} + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\]

    5. Applied associate-*r*0.1

      \[\leadsto x + y \cdot \frac{\color{blue}{\left(z \cdot \left(\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}\right)\right) \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}} + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.120362690310111 \cdot 10^{+22} \lor \neg \left(z \leq 458236.22514243907\right):\\ \;\;\;\;x + \left(0.0692910599291889 \cdot y + \frac{y}{z} \cdot \left(0.07512208616047561 - \frac{0.40462203869992125}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \left(z \cdot \left(\sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968} \cdot \sqrt[3]{z \cdot 0.0692910599291889 + 0.4917317610505968}\right)\right) + 0.279195317918525}{z \cdot \left(z + 6.012459259764103\right) + 3.350343815022304}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (if (< z -8120153.652456675) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x)) (if (< z 6.576118972787377e+20) (+ x (* (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (/ 1.0 (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))) (- (* (+ (/ 0.07512208616047561 z) 0.0692910599291889) y) (- (/ (* 0.40462203869992125 y) (* z z)) x))))

  (+ x (/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))