Average Error: 5.9 → 0.9
Time: 20.5s
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 r20613690 = x;
        double r20613691 = y;
        double r20613692 = z;
        double r20613693 = r20613692 + r20613691;
        double r20613694 = r20613691 / r20613693;
        double r20613695 = log(r20613694);
        double r20613696 = r20613691 * r20613695;
        double r20613697 = exp(r20613696);
        double r20613698 = r20613697 / r20613691;
        double r20613699 = r20613690 + r20613698;
        return r20613699;
}
↓
double f(double x, double y, double z) {
        double r20613700 = y;
        double r20613701 = cbrt(r20613700);
        double r20613702 = z;
        double r20613703 = r20613700 + r20613702;
        double r20613704 = cbrt(r20613703);
        double r20613705 = r20613701 / r20613704;
        double r20613706 = log(r20613705);
        double r20613707 = r20613706 + r20613706;
        double r20613708 = r20613706 + r20613707;
        double r20613709 = r20613700 * r20613708;
        double r20613710 = exp(r20613709);
        double r20613711 = r20613710 / r20613700;
        double r20613712 = x;
        double r20613713 = r20613711 + r20613712;
        return r20613713;
}

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
Target0.9
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.115415759790762719541517221498726780517 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

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-cbrt19.5

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

  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-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. Simplified0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019170 
(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)))