Average Error: 0.3 → 0.2
Time: 8.4s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(\left(y \cdot x\right) \cdot 3\right) \cdot y\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(\left(y \cdot x\right) \cdot 3\right) \cdot y
double f(double x, double y) {
        double r31577211 = x;
        double r31577212 = 3.0;
        double r31577213 = r31577211 * r31577212;
        double r31577214 = y;
        double r31577215 = r31577213 * r31577214;
        double r31577216 = r31577215 * r31577214;
        return r31577216;
}
↓
double f(double x, double y) {
        double r31577217 = y;
        double r31577218 = x;
        double r31577219 = r31577217 * r31577218;
        double r31577220 = 3.0;
        double r31577221 = r31577219 * r31577220;
        double r31577222 = r31577221 * r31577217;
        return r31577222;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.3
Herbie0.2
\[\left(x \cdot \left(3 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(3 \cdot \left(x \cdot y\right)\right)} \cdot y\]

  3. Final simplification0.2

    \[\leadsto \left(\left(y \cdot x\right) \cdot 3\right) \cdot y\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (* (* x (* 3.0 y)) y)

  (* (* (* x 3.0) y) y))