Average Error: 5.8 → 2.1
Time: 18.6s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[\frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{y + z} \cdot \sqrt[3]{y + z}}\right)} \cdot e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)}}{y} + x\]
x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}
↓
\frac{e^{y \cdot \log \left(\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{\sqrt[3]{y + z} \cdot \sqrt[3]{y + z}}\right)} \cdot e^{y \cdot \log \left(\frac{\sqrt[3]{y}}{\sqrt[3]{y + z}}\right)}}{y} + x
double f(double x, double y, double z) {
        double r24049130 = x;
        double r24049131 = y;
        double r24049132 = z;
        double r24049133 = r24049132 + r24049131;
        double r24049134 = r24049131 / r24049133;
        double r24049135 = log(r24049134);
        double r24049136 = r24049131 * r24049135;
        double r24049137 = exp(r24049136);
        double r24049138 = r24049137 / r24049131;
        double r24049139 = r24049130 + r24049138;
        return r24049139;
}
↓
double f(double x, double y, double z) {
        double r24049140 = y;
        double r24049141 = cbrt(r24049140);
        double r24049142 = r24049141 * r24049141;
        double r24049143 = z;
        double r24049144 = r24049140 + r24049143;
        double r24049145 = cbrt(r24049144);
        double r24049146 = r24049145 * r24049145;
        double r24049147 = r24049142 / r24049146;
        double r24049148 = log(r24049147);
        double r24049149 = r24049140 * r24049148;
        double r24049150 = exp(r24049149);
        double r24049151 = r24049141 / r24049145;
        double r24049152 = log(r24049151);
        double r24049153 = r24049140 * r24049152;
        double r24049154 = exp(r24049153);
        double r24049155 = r24049150 * r24049154;
        double r24049156 = r24049155 / r24049140;
        double r24049157 = x;
        double r24049158 = r24049156 + r24049157;
        return r24049158;
}

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
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.115415759790762719541517221498726780517 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 5.8

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

  3. Applied add-cube-cbrt19.1

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

  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-prod2.1

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

  7. Applied distribute-rgt-in2.1

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

  8. Applied exp-sum2.1

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

  9. Final simplification2.1

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

Reproduce

herbie shell --seed 2019179 
(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)))