Average Error: 6.3 → 1.2
Time: 5.7s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[x + \frac{{\left(e^{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)}^{\left(\sqrt[3]{y} \cdot \log \left(\frac{y}{z + y}\right)\right)}}{y}\]
x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}
↓
x + \frac{{\left(e^{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)}^{\left(\sqrt[3]{y} \cdot \log \left(\frac{y}{z + y}\right)\right)}}{y}
double f(double x, double y, double z) {
        double r579304 = x;
        double r579305 = y;
        double r579306 = z;
        double r579307 = r579306 + r579305;
        double r579308 = r579305 / r579307;
        double r579309 = log(r579308);
        double r579310 = r579305 * r579309;
        double r579311 = exp(r579310);
        double r579312 = r579311 / r579305;
        double r579313 = r579304 + r579312;
        return r579313;
}
↓
double f(double x, double y, double z) {
        double r579314 = x;
        double r579315 = y;
        double r579316 = cbrt(r579315);
        double r579317 = r579316 * r579316;
        double r579318 = exp(r579317);
        double r579319 = z;
        double r579320 = r579319 + r579315;
        double r579321 = r579315 / r579320;
        double r579322 = log(r579321);
        double r579323 = r579316 * r579322;
        double r579324 = pow(r579318, r579323);
        double r579325 = r579324 / r579315;
        double r579326 = r579314 + r579325;
        return r579326;
}

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

Original6.3
Target1.2
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.1154157598 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 6.3

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

  3. Applied add-log-exp35.1

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

  4. Applied exp-to-pow1.2

    \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\left(\log \left(\frac{y}{z + y}\right)\right)}}}{y}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.2

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

  7. Applied exp-prod1.2

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

  8. Applied pow-pow1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :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)))