Average Error: 5.8 → 1.0
Time: 21.1s
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 r16129285 = x;
        double r16129286 = y;
        double r16129287 = z;
        double r16129288 = r16129287 + r16129286;
        double r16129289 = r16129286 / r16129288;
        double r16129290 = log(r16129289);
        double r16129291 = r16129286 * r16129290;
        double r16129292 = exp(r16129291);
        double r16129293 = r16129292 / r16129286;
        double r16129294 = r16129285 + r16129293;
        return r16129294;
}
↓
double f(double x, double y, double z) {
        double r16129295 = y;
        double r16129296 = cbrt(r16129295);
        double r16129297 = z;
        double r16129298 = r16129295 + r16129297;
        double r16129299 = cbrt(r16129298);
        double r16129300 = r16129296 / r16129299;
        double r16129301 = log(r16129300);
        double r16129302 = r16129295 * r16129301;
        double r16129303 = r16129302 + r16129302;
        double r16129304 = r16129302 + r16129303;
        double r16129305 = exp(r16129304);
        double r16129306 = r16129305 / r16129295;
        double r16129307 = x;
        double r16129308 = r16129306 + r16129307;
        return r16129308;
}

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. Applied distribute-lft-in2.0

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

  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 2019168 +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)))