Average Error: 0.0 → 0.1
Time: 4.7s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[\left(\left(x - y\right) \cdot 2\right) \cdot x\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
\left(\left(x - y\right) \cdot 2\right) \cdot x
double f(double x, double y) {
        double r464653 = 2.0;
        double r464654 = x;
        double r464655 = r464654 * r464654;
        double r464656 = y;
        double r464657 = r464654 * r464656;
        double r464658 = r464655 - r464657;
        double r464659 = r464653 * r464658;
        return r464659;
}
↓
double f(double x, double y) {
        double r464660 = x;
        double r464661 = y;
        double r464662 = r464660 - r464661;
        double r464663 = 2.0;
        double r464664 = r464662 * r464663;
        double r464665 = r464664 * r464660;
        return r464665;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.1
\[\left(x \cdot 2\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x - x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x - y\right)\right) \cdot 2}\]
  3. Using strategy rm

  4. Applied pow10.0

    \[\leadsto \left(x \cdot \left(x - y\right)\right) \cdot \color{blue}{{2}^{1}}\]

  5. Applied pow10.0

    \[\leadsto \left(x \cdot \color{blue}{{\left(x - y\right)}^{1}}\right) \cdot {2}^{1}\]

  6. Applied pow10.0

    \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {\left(x - y\right)}^{1}\right) \cdot {2}^{1}\]

  7. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(x \cdot \left(x - y\right)\right)}^{1}} \cdot {2}^{1}\]

  8. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(\left(x \cdot \left(x - y\right)\right) \cdot 2\right)}^{1}}\]

  9. Simplified0.1

    \[\leadsto {\color{blue}{\left(x \cdot \left(\left(x - y\right) \cdot 2\right)\right)}}^{1}\]

  10. Final simplification0.1

    \[\leadsto \left(\left(x - y\right) \cdot 2\right) \cdot x\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2) (- x y))

  (* 2 (- (* x x) (* x y))))