Average Error: 5.7 → 0.9
Time: 13.5s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[\frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) \cdot 2\right)}}{y} + x\]
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) + y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) \cdot 2\right)}}{y} + x
double f(double x, double y, double z) {
        double r235158 = x;
        double r235159 = y;
        double r235160 = z;
        double r235161 = r235160 + r235159;
        double r235162 = r235159 / r235161;
        double r235163 = log(r235162);
        double r235164 = r235159 * r235163;
        double r235165 = exp(r235164);
        double r235166 = r235165 / r235159;
        double r235167 = r235158 + r235166;
        return r235167;
}
↓
double f(double x, double y, double z) {
        double r235168 = y;
        double r235169 = cbrt(r235168);
        double r235170 = z;
        double r235171 = r235168 + r235170;
        double r235172 = cbrt(r235171);
        double r235173 = r235169 / r235172;
        double r235174 = log(r235173);
        double r235175 = r235168 * r235174;
        double r235176 = 2.0;
        double r235177 = r235174 * r235176;
        double r235178 = r235168 * r235177;
        double r235179 = r235175 + r235178;
        double r235180 = exp(r235179);
        double r235181 = r235180 / r235168;
        double r235182 = x;
        double r235183 = r235181 + r235182;
        return r235183;
}

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

Original5.7
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 5.7

    \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
  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-cbrt5.8

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

  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-prod1.8

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

  7. Applied distribute-lft-in1.8

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

  8. Simplified0.9

    \[\leadsto x + \frac{e^{\color{blue}{\left(2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right) \cdot y} + y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{z + y}}\right)}}{y}\]

  9. Simplified0.9

    \[\leadsto x + \frac{e^{\left(2 \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)\right) \cdot y + \color{blue}{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)}}}{y}\]

  10. Final simplification0.9

    \[\leadsto \frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) + y \cdot \left(\log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right) \cdot 2\right)}}{y} + x\]

Reproduce

herbie shell --seed 2019174 +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 (/ -1.0 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y)))

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