Average Error: 5.8 → 1.0
Time: 19.2s
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 r21876380 = x;
        double r21876381 = y;
        double r21876382 = z;
        double r21876383 = r21876382 + r21876381;
        double r21876384 = r21876381 / r21876383;
        double r21876385 = log(r21876384);
        double r21876386 = r21876381 * r21876385;
        double r21876387 = exp(r21876386);
        double r21876388 = r21876387 / r21876381;
        double r21876389 = r21876380 + r21876388;
        return r21876389;
}
↓
double f(double x, double y, double z) {
        double r21876390 = y;
        double r21876391 = cbrt(r21876390);
        double r21876392 = z;
        double r21876393 = r21876390 + r21876392;
        double r21876394 = cbrt(r21876393);
        double r21876395 = r21876391 / r21876394;
        double r21876396 = log(r21876395);
        double r21876397 = r21876396 + r21876396;
        double r21876398 = r21876396 + r21876397;
        double r21876399 = r21876390 * r21876398;
        double r21876400 = exp(r21876399);
        double r21876401 = r21876400 / r21876390;
        double r21876402 = x;
        double r21876403 = r21876401 + r21876402;
        return r21876403;
}

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-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-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-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 2019168 
(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)))