Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[e^{x \cdot {y}^{2}}\]
e^{\left(x \cdot y\right) \cdot y}
↓
e^{x \cdot {y}^{2}}
double f(double x, double y) {
        double r257499 = x;
        double r257500 = y;
        double r257501 = r257499 * r257500;
        double r257502 = r257501 * r257500;
        double r257503 = exp(r257502);
        return r257503;
}
↓
double f(double x, double y) {
        double r257504 = x;
        double r257505 = y;
        double r257506 = 2.0;
        double r257507 = pow(r257505, r257506);
        double r257508 = r257504 * r257507;
        double r257509 = exp(r257508);
        return r257509;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied associate-*l*0.0

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

  4. Simplified0.0

    \[\leadsto e^{x \cdot \color{blue}{{y}^{2}}}\]

  5. Final simplification0.0

    \[\leadsto e^{x \cdot {y}^{2}}\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))