Average Error: 6.1 → 1.0
Time: 24.4s
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 r20360785 = x;
        double r20360786 = y;
        double r20360787 = z;
        double r20360788 = r20360787 + r20360786;
        double r20360789 = r20360786 / r20360788;
        double r20360790 = log(r20360789);
        double r20360791 = r20360786 * r20360790;
        double r20360792 = exp(r20360791);
        double r20360793 = r20360792 / r20360786;
        double r20360794 = r20360785 + r20360793;
        return r20360794;
}
↓
double f(double x, double y, double z) {
        double r20360795 = y;
        double r20360796 = cbrt(r20360795);
        double r20360797 = z;
        double r20360798 = r20360795 + r20360797;
        double r20360799 = cbrt(r20360798);
        double r20360800 = r20360796 / r20360799;
        double r20360801 = log(r20360800);
        double r20360802 = r20360801 + r20360801;
        double r20360803 = r20360801 + r20360802;
        double r20360804 = r20360795 * r20360803;
        double r20360805 = exp(r20360804);
        double r20360806 = r20360805 / r20360795;
        double r20360807 = x;
        double r20360808 = r20360806 + r20360807;
        return r20360808;
}

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

Original6.1
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 6.1

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

  3. Applied add-cube-cbrt19.6

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

  4. Applied add-cube-cbrt6.1

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

  5. Applied times-frac6.1

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

  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 2019171 
(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)))