Average Error: 0.0 → 0.0
Time: 1.1s
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 r179140 = x;
        double r179141 = y;
        double r179142 = r179140 * r179141;
        double r179143 = r179142 * r179141;
        double r179144 = exp(r179143);
        return r179144;
}
↓
double f(double x, double y) {
        double r179145 = x;
        double r179146 = y;
        double r179147 = r179145 * r179146;
        double r179148 = r179147 * r179146;
        double r179149 = exp(r179148);
        double r179150 = log1p(r179149);
        double r179151 = expm1(r179150);
        return r179151;
}

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 2020020 +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)))