Average Error: 0.0 → 0.0
Time: 22.1s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(\sqrt[3]{x + y \cdot \log y} \cdot \sqrt[3]{x + y \cdot \log y}\right) \cdot \sqrt[3]{x + y \cdot \log y} - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(\sqrt[3]{x + y \cdot \log y} \cdot \sqrt[3]{x + y \cdot \log y}\right) \cdot \sqrt[3]{x + y \cdot \log y} - z}
double f(double x, double y, double z) {
        double r241138 = x;
        double r241139 = y;
        double r241140 = log(r241139);
        double r241141 = r241139 * r241140;
        double r241142 = r241138 + r241141;
        double r241143 = z;
        double r241144 = r241142 - r241143;
        double r241145 = exp(r241144);
        return r241145;
}
↓
double f(double x, double y, double z) {
        double r241146 = x;
        double r241147 = y;
        double r241148 = log(r241147);
        double r241149 = r241147 * r241148;
        double r241150 = r241146 + r241149;
        double r241151 = cbrt(r241150);
        double r241152 = r241151 * r241151;
        double r241153 = r241152 * r241151;
        double r241154 = z;
        double r241155 = r241153 - r241154;
        double r241156 = exp(r241155);
        return r241156;
}

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-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 
(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)))