Average Error: 0.0 → 0.0
Time: 11.2s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\sqrt[3]{{\left(\left(x + y \cdot \log y\right) - z\right)}^{3}}}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\sqrt[3]{{\left(\left(x + y \cdot \log y\right) - z\right)}^{3}}}
double f(double x, double y, double z) {
        double r222155 = x;
        double r222156 = y;
        double r222157 = log(r222156);
        double r222158 = r222156 * r222157;
        double r222159 = r222155 + r222158;
        double r222160 = z;
        double r222161 = r222159 - r222160;
        double r222162 = exp(r222161);
        return r222162;
}
↓
double f(double x, double y, double z) {
        double r222163 = x;
        double r222164 = y;
        double r222165 = log(r222164);
        double r222166 = r222164 * r222165;
        double r222167 = r222163 + r222166;
        double r222168 = z;
        double r222169 = r222167 - r222168;
        double r222170 = 3.0;
        double r222171 = pow(r222169, r222170);
        double r222172 = cbrt(r222171);
        double r222173 = exp(r222172);
        return r222173;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

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Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

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