Average Error: 5.9 → 1.2
Time: 13.4s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[\frac{e^{\left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + 2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right) \cdot y}}{y} + x\]
x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}
↓
\frac{e^{\left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + 2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right) \cdot y}}{y} + x
double f(double x, double y, double z) {
        double r336849 = x;
        double r336850 = y;
        double r336851 = z;
        double r336852 = r336851 + r336850;
        double r336853 = r336850 / r336852;
        double r336854 = log(r336853);
        double r336855 = r336850 * r336854;
        double r336856 = exp(r336855);
        double r336857 = r336856 / r336850;
        double r336858 = r336849 + r336857;
        return r336858;
}
↓
double f(double x, double y, double z) {
        double r336859 = y;
        double r336860 = cbrt(r336859);
        double r336861 = z;
        double r336862 = r336859 + r336861;
        double r336863 = cbrt(r336862);
        double r336864 = r336860 / r336863;
        double r336865 = log(r336864);
        double r336866 = 2.0;
        double r336867 = r336866 * r336865;
        double r336868 = r336865 + r336867;
        double r336869 = r336868 * r336859;
        double r336870 = exp(r336869);
        double r336871 = r336870 / r336859;
        double r336872 = x;
        double r336873 = r336871 + r336872;
        return r336873;
}

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

Original5.9
Target1.2
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.115415759790762719541517221498726780517 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 5.9

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

  3. Applied add-cube-cbrt19.3

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

  4. Applied add-cube-cbrt5.9

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

  5. Applied times-frac5.9

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

  6. Applied log-prod2.2

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

  7. Simplified1.2

    \[\leadsto x + \frac{e^{y \cdot \left(\color{blue}{2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)} + \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right)\right)}}{y}\]

  8. Simplified1.2

    \[\leadsto x + \frac{e^{y \cdot \left(2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \color{blue}{\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)}\right)}}{y}\]

  9. Final simplification1.2

    \[\leadsto \frac{e^{\left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + 2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right) \cdot y}}{y} + x\]

Reproduce

herbie shell --seed 2019196 
(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 (/ -1.0 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y)))

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