Average Error: 0.3 → 0.3
Time: 7.6s
Precision: 64
\[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
↓
\[\left(\left(y \cdot x\right) \cdot y\right) \cdot 3\]
\left(\left(x \cdot 3\right) \cdot y\right) \cdot y
↓
\left(\left(y \cdot x\right) \cdot y\right) \cdot 3
double f(double x, double y) {
        double r564532 = x;
        double r564533 = 3.0;
        double r564534 = r564532 * r564533;
        double r564535 = y;
        double r564536 = r564534 * r564535;
        double r564537 = r564536 * r564535;
        return r564537;
}
↓
double f(double x, double y) {
        double r564538 = y;
        double r564539 = x;
        double r564540 = r564538 * r564539;
        double r564541 = r564540 * r564538;
        double r564542 = 3.0;
        double r564543 = r564541 * r564542;
        return r564543;
}

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

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\]
  2. Using strategy rm

  3. Applied pow10.3

    \[\leadsto \left(\left(x \cdot 3\right) \cdot y\right) \cdot \color{blue}{{y}^{1}}\]

  4. Applied pow10.3

    \[\leadsto \left(\left(x \cdot 3\right) \cdot \color{blue}{{y}^{1}}\right) \cdot {y}^{1}\]

  5. Applied pow10.3

    \[\leadsto \left(\left(x \cdot \color{blue}{{3}^{1}}\right) \cdot {y}^{1}\right) \cdot {y}^{1}\]

  6. Applied pow10.3

    \[\leadsto \left(\left(\color{blue}{{x}^{1}} \cdot {3}^{1}\right) \cdot {y}^{1}\right) \cdot {y}^{1}\]

  7. Applied pow-prod-down0.3

    \[\leadsto \left(\color{blue}{{\left(x \cdot 3\right)}^{1}} \cdot {y}^{1}\right) \cdot {y}^{1}\]

  8. Applied pow-prod-down0.3

    \[\leadsto \color{blue}{{\left(\left(x \cdot 3\right) \cdot y\right)}^{1}} \cdot {y}^{1}\]

  9. Applied pow-prod-down0.3

    \[\leadsto \color{blue}{{\left(\left(\left(x \cdot 3\right) \cdot y\right) \cdot y\right)}^{1}}\]

  10. Simplified0.2

    \[\leadsto {\color{blue}{\left(\left(y \cdot x\right) \cdot \left(y \cdot 3\right)\right)}}^{1}\]
  11. Using strategy rm

  12. Applied associate-*r*0.3

    \[\leadsto {\color{blue}{\left(\left(\left(y \cdot x\right) \cdot y\right) \cdot 3\right)}}^{1}\]

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (* (* x (* 3 y)) y)

  (* (* (* x 3) y) y))