Average Error: 0.0 → 0.0
Time: 15.8s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\left(x + y \cdot \log y\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\left(x + y \cdot \log y\right) - z}
double f(double x, double y, double z) {
        double r19413759 = x;
        double r19413760 = y;
        double r19413761 = log(r19413760);
        double r19413762 = r19413760 * r19413761;
        double r19413763 = r19413759 + r19413762;
        double r19413764 = z;
        double r19413765 = r19413763 - r19413764;
        double r19413766 = exp(r19413765);
        return r19413766;
}
↓
double f(double x, double y, double z) {
        double r19413767 = x;
        double r19413768 = y;
        double r19413769 = log(r19413768);
        double r19413770 = r19413768 * r19413769;
        double r19413771 = r19413767 + r19413770;
        double r19413772 = z;
        double r19413773 = r19413771 - r19413772;
        double r19413774 = exp(r19413773);
        return r19413774;
}

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. Taylor expanded around inf 0.0

    \[\leadsto e^{\color{blue}{\left(x - y \cdot \log \left(\frac{1}{y}\right)\right)} - z}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"

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

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