Average Error: 5.8 → 1.0
Time: 20.2s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[\frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + \left(y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right)}}{y} + x\]
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) + \left(y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right)}}{y} + x
double f(double x, double y, double z) {
        double r15799405 = x;
        double r15799406 = y;
        double r15799407 = z;
        double r15799408 = r15799407 + r15799406;
        double r15799409 = r15799406 / r15799408;
        double r15799410 = log(r15799409);
        double r15799411 = r15799406 * r15799410;
        double r15799412 = exp(r15799411);
        double r15799413 = r15799412 / r15799406;
        double r15799414 = r15799405 + r15799413;
        return r15799414;
}
↓
double f(double x, double y, double z) {
        double r15799415 = y;
        double r15799416 = cbrt(r15799415);
        double r15799417 = z;
        double r15799418 = r15799415 + r15799417;
        double r15799419 = cbrt(r15799418);
        double r15799420 = r15799416 / r15799419;
        double r15799421 = log(r15799420);
        double r15799422 = r15799415 * r15799421;
        double r15799423 = r15799422 + r15799422;
        double r15799424 = r15799422 + r15799423;
        double r15799425 = exp(r15799424);
        double r15799426 = r15799425 / r15799415;
        double r15799427 = x;
        double r15799428 = r15799426 + r15799427;
        return r15799428;
}

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

Original5.8
Target1.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.1154157597908 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 5.8

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

  3. Applied add-cube-cbrt18.9

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

  4. Applied add-cube-cbrt5.8

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

  5. Applied times-frac5.8

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

  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. Applied distribute-lft-in1.9

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

  8. Simplified1.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2019158 +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 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y)))

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