Average Error: 5.9 → 1.2
Time: 13.3s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[\frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) \cdot 2\right)}}{y} + x\]
x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}
↓
\frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) \cdot 2\right)}}{y} + x
double f(double x, double y, double z) {
        double r257984 = x;
        double r257985 = y;
        double r257986 = z;
        double r257987 = r257986 + r257985;
        double r257988 = r257985 / r257987;
        double r257989 = log(r257988);
        double r257990 = r257985 * r257989;
        double r257991 = exp(r257990);
        double r257992 = r257991 / r257985;
        double r257993 = r257984 + r257992;
        return r257993;
}
↓
double f(double x, double y, double z) {
        double r257994 = y;
        double r257995 = cbrt(r257994);
        double r257996 = z;
        double r257997 = r257994 + r257996;
        double r257998 = cbrt(r257997);
        double r257999 = r257995 / r257998;
        double r258000 = log(r257999);
        double r258001 = r257994 * r258000;
        double r258002 = 2.0;
        double r258003 = r258000 * r258002;
        double r258004 = r257994 * r258003;
        double r258005 = r258001 + r258004;
        double r258006 = exp(r258005);
        double r258007 = r258006 / r257994;
        double r258008 = x;
        double r258009 = r258007 + r258008;
        return r258009;
}

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. Applied distribute-lft-in2.2

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

  8. Simplified1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(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)))