Average Error: 0.0 → 0.0
Time: 9.0s
Precision: 64
\[e^{\left(x \cdot y\right) \cdot y}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\left(x \cdot y\right) \cdot y}\right)\right)\]
e^{\left(x \cdot y\right) \cdot y}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\left(x \cdot y\right) \cdot y}\right)\right)
double f(double x, double y) {
        double r12639452 = x;
        double r12639453 = y;
        double r12639454 = r12639452 * r12639453;
        double r12639455 = r12639454 * r12639453;
        double r12639456 = exp(r12639455);
        return r12639456;
}
↓
double f(double x, double y) {
        double r12639457 = x;
        double r12639458 = y;
        double r12639459 = r12639457 * r12639458;
        double r12639460 = r12639459 * r12639458;
        double r12639461 = exp(r12639460);
        double r12639462 = log1p(r12639461);
        double r12639463 = expm1(r12639462);
        return r12639463;
}

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 expm1-log1p-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  (exp (* (* x y) y)))