Average Error: 5.8 → 1.3
Time: 40.1s
Precision: 64
\[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}\]
↓
\[x + \frac{{\left(e^{y}\right)}^{\left(\log \left(\frac{y}{y + z}\right)\right)}}{y}\]
x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y}
↓
x + \frac{{\left(e^{y}\right)}^{\left(\log \left(\frac{y}{y + z}\right)\right)}}{y}
double f(double x, double y, double z) {
        double r18283490 = x;
        double r18283491 = y;
        double r18283492 = z;
        double r18283493 = r18283492 + r18283491;
        double r18283494 = r18283491 / r18283493;
        double r18283495 = log(r18283494);
        double r18283496 = r18283491 * r18283495;
        double r18283497 = exp(r18283496);
        double r18283498 = r18283497 / r18283491;
        double r18283499 = r18283490 + r18283498;
        return r18283499;
}
↓
double f(double x, double y, double z) {
        double r18283500 = x;
        double r18283501 = y;
        double r18283502 = exp(r18283501);
        double r18283503 = z;
        double r18283504 = r18283501 + r18283503;
        double r18283505 = r18283501 / r18283504;
        double r18283506 = log(r18283505);
        double r18283507 = pow(r18283502, r18283506);
        double r18283508 = r18283507 / r18283501;
        double r18283509 = r18283500 + r18283508;
        return r18283509;
}

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
Target1.2
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.1154157597908 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1.0}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

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-log-exp35.8

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

  4. Applied exp-to-pow1.3

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

  5. Final simplification1.3

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

Reproduce

herbie shell --seed 2019165 +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)))