Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[{\left(e^{y}\right)}^{y} \cdot x\]
x \cdot e^{y \cdot y}
↓
{\left(e^{y}\right)}^{y} \cdot x
double f(double x, double y) {
        double r687654 = x;
        double r687655 = y;
        double r687656 = r687655 * r687655;
        double r687657 = exp(r687656);
        double r687658 = r687654 * r687657;
        return r687658;
}
↓
double f(double x, double y) {
        double r687659 = y;
        double r687660 = exp(r687659);
        double r687661 = pow(r687660, r687659);
        double r687662 = x;
        double r687663 = r687661 * r687662;
        return r687663;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto {\left(e^{y}\right)}^{y} \cdot x\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))