Average Error: 0.0 → 0.0
Time: 11.8s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[e^{x \cdot \left(y \cdot y\right)}\]
e^{\left(x \cdot y\right) \cdot y}
↓
e^{x \cdot \left(y \cdot y\right)}
double f(double x, double y) {
        double r12106678 = x;
        double r12106679 = y;
        double r12106680 = r12106678 * r12106679;
        double r12106681 = r12106680 * r12106679;
        double r12106682 = exp(r12106681);
        return r12106682;
}
↓
double f(double x, double y) {
        double r12106683 = x;
        double r12106684 = y;
        double r12106685 = r12106684 * r12106684;
        double r12106686 = r12106683 * r12106685;
        double r12106687 = exp(r12106686);
        return r12106687;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-exp-log0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  (exp (* (* x y) y)))