Average Error: 0.0 → 0.0
Time: 3.4s
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 r182488 = x;
        double r182489 = y;
        double r182490 = r182488 * r182489;
        double r182491 = r182490 * r182489;
        double r182492 = exp(r182491);
        return r182492;
}
↓
double f(double x, double y) {
        double r182493 = x;
        double r182494 = y;
        double r182495 = 2.0;
        double r182496 = pow(r182494, r182495);
        double r182497 = r182493 * r182496;
        double r182498 = exp(r182497);
        return r182498;
}

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 add-log-exp0.0

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

  4. Simplified0.0

    \[\leadsto e^{\log \color{blue}{\left(e^{x \cdot {y}^{2}}\right)}}\]

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2"
  :precision binary64
  (exp (* (* x y) y)))