Average Error: 0.0 → 0.0
Time: 2.5s
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 r213196 = x;
        double r213197 = y;
        double r213198 = r213196 * r213197;
        double r213199 = r213198 * r213197;
        double r213200 = exp(r213199);
        return r213200;
}
↓
double f(double x, double y) {
        double r213201 = x;
        double r213202 = y;
        double r213203 = 2.0;
        double r213204 = pow(r213202, r213203);
        double r213205 = r213201 * r213204;
        double r213206 = exp(r213205);
        return r213206;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[e^{\left(x \cdot y\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-*l*0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +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)))