Average Error: 5.6 → 1.3
Time: 15.0s
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 r18509357 = x;
        double r18509358 = y;
        double r18509359 = z;
        double r18509360 = r18509359 + r18509358;
        double r18509361 = r18509358 / r18509360;
        double r18509362 = log(r18509361);
        double r18509363 = r18509358 * r18509362;
        double r18509364 = exp(r18509363);
        double r18509365 = r18509364 / r18509358;
        double r18509366 = r18509357 + r18509365;
        return r18509366;
}
↓
double f(double x, double y, double z) {
        double r18509367 = x;
        double r18509368 = y;
        double r18509369 = exp(r18509368);
        double r18509370 = z;
        double r18509371 = r18509368 + r18509370;
        double r18509372 = r18509368 / r18509371;
        double r18509373 = log(r18509372);
        double r18509374 = pow(r18509369, r18509373);
        double r18509375 = r18509374 / r18509368;
        double r18509376 = r18509367 + r18509375;
        return r18509376;
}

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

Original5.6
Target1.2
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z + y} \lt 7.1154157597908 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array}\]

Derivation

  1. Initial program 5.6

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

  3. Applied add-log-exp34.9

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

  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 
(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)))