Average Error: 5.8 → 1.0
Time: 19.9s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[\frac{e^{y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right)\right)}}{y} + x\]
x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}
↓
\frac{e^{y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right)\right)}}{y} + x
double f(double x, double y, double z) {
        double r24218897 = x;
        double r24218898 = y;
        double r24218899 = z;
        double r24218900 = r24218899 + r24218898;
        double r24218901 = r24218898 / r24218900;
        double r24218902 = log(r24218901);
        double r24218903 = r24218898 * r24218902;
        double r24218904 = exp(r24218903);
        double r24218905 = r24218904 / r24218898;
        double r24218906 = r24218897 + r24218905;
        return r24218906;
}
↓
double f(double x, double y, double z) {
        double r24218907 = y;
        double r24218908 = cbrt(r24218907);
        double r24218909 = z;
        double r24218910 = r24218907 + r24218909;
        double r24218911 = cbrt(r24218910);
        double r24218912 = r24218908 / r24218911;
        double r24218913 = log(r24218912);
        double r24218914 = r24218913 + r24218913;
        double r24218915 = r24218913 + r24218914;
        double r24218916 = r24218907 * r24218915;
        double r24218917 = exp(r24218916);
        double r24218918 = r24218917 / r24218907;
        double r24218919 = x;
        double r24218920 = r24218918 + r24218919;
        return r24218920;
}

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

Original5.8
Target1.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.1154157597908 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 5.8

    \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt18.9

    \[\leadsto x + \frac{e^{y \cdot \log \left(\frac{y}{\color{blue}{\left(\sqrt[3]{z + y} \cdot \sqrt[3]{z + y}\right) \cdot \sqrt[3]{z + y}}}\right)}}{y}\]

  4. Applied add-cube-cbrt5.8

    \[\leadsto x + \frac{e^{y \cdot \log \left(\frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\left(\sqrt[3]{z + y} \cdot \sqrt[3]{z + y}\right) \cdot \sqrt[3]{z + y}}\right)}}{y}\]

  5. Applied times-frac5.8

    \[\leadsto x + \frac{e^{y \cdot \log \color{blue}{\left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z + y} \cdot \sqrt[3]{z + y}} \cdot \frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right)}}}{y}\]

  6. Applied log-prod1.9

    \[\leadsto x + \frac{e^{y \cdot \color{blue}{\left(\log \left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{z + y} \cdot \sqrt[3]{z + y}}\right) + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right)\right)}}}{y}\]

  7. Simplified1.0

    \[\leadsto x + \frac{e^{y \cdot \left(\color{blue}{\left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right) + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right)\right)} + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right)\right)}}{y}\]

  8. Final simplification1.0

    \[\leadsto \frac{e^{y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right)\right)}}{y} + x\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"

  :herbie-target
  (if (< (/ y (+ z y)) 7.1154157597908e-315) (+ x (/ (exp (/ -1 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y)))

  (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))