Average Error: 6.0 → 1.0
Time: 21.0s
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 r17239091 = x;
        double r17239092 = y;
        double r17239093 = z;
        double r17239094 = r17239093 + r17239092;
        double r17239095 = r17239092 / r17239094;
        double r17239096 = log(r17239095);
        double r17239097 = r17239092 * r17239096;
        double r17239098 = exp(r17239097);
        double r17239099 = r17239098 / r17239092;
        double r17239100 = r17239091 + r17239099;
        return r17239100;
}
↓
double f(double x, double y, double z) {
        double r17239101 = y;
        double r17239102 = cbrt(r17239101);
        double r17239103 = z;
        double r17239104 = r17239101 + r17239103;
        double r17239105 = cbrt(r17239104);
        double r17239106 = r17239102 / r17239105;
        double r17239107 = log(r17239106);
        double r17239108 = r17239107 + r17239107;
        double r17239109 = r17239107 + r17239108;
        double r17239110 = r17239101 * r17239109;
        double r17239111 = exp(r17239110);
        double r17239112 = r17239111 / r17239101;
        double r17239113 = x;
        double r17239114 = r17239112 + r17239113;
        return r17239114;
}

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

Original6.0
Target1.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.115415759790762719541517221498726780517 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 6.0

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

  3. Applied add-cube-cbrt19.1

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

  4. Applied add-cube-cbrt6.0

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

  5. Applied times-frac6.0

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

  6. Applied log-prod2.0

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

  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 2019172 
(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)))