Average Error: 0.0 → 0.0
Time: 5.0s
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 r128116 = x;
        double r128117 = y;
        double r128118 = r128116 * r128117;
        double r128119 = r128118 * r128117;
        double r128120 = exp(r128119);
        return r128120;
}
↓
double f(double x, double y) {
        double r128121 = x;
        double r128122 = y;
        double r128123 = r128121 * r128122;
        double r128124 = r128123 * r128122;
        double r128125 = exp(r128124);
        double r128126 = log1p(r128125);
        double r128127 = expm1(r128126);
        return r128127;
}

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 2019208 +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)))