Average Error: 0.0 → 0.1
Time: 8.7s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(e^{\left(x \cdot y\right) \cdot y}\right)\right)\]
e^{\left(x \cdot y\right) \cdot y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(e^{\left(x \cdot y\right) \cdot y}\right)\right)
double f(double x, double y) {
        double r242579 = x;
        double r242580 = y;
        double r242581 = r242579 * r242580;
        double r242582 = r242581 * r242580;
        double r242583 = exp(r242582);
        return r242583;
}
↓
double f(double x, double y) {
        double r242584 = x;
        double r242585 = y;
        double r242586 = r242584 * r242585;
        double r242587 = r242586 * r242585;
        double r242588 = exp(r242587);
        double r242589 = expm1(r242588);
        double r242590 = log1p(r242589);
        return r242590;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

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 log1p-expm1-u0.1

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(e^{\left(x \cdot y\right) \cdot y}\right)\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(e^{\left(x \cdot y\right) \cdot y}\right)\right)\]

Reproduce

herbie shell --seed 2020046 +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)))