Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[\left(2 \cdot x\right) \cdot \left(x - y\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
\left(2 \cdot x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r370366 = 2.0;
        double r370367 = x;
        double r370368 = r370367 * r370367;
        double r370369 = y;
        double r370370 = r370367 * r370369;
        double r370371 = r370368 - r370370;
        double r370372 = r370366 * r370371;
        return r370372;
}
↓
double f(double x, double y) {
        double r370373 = 2.0;
        double r370374 = x;
        double r370375 = r370373 * r370374;
        double r370376 = y;
        double r370377 = r370374 - r370376;
        double r370378 = r370375 * r370377;
        return r370378;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"

  :herbie-target
  (* (* x 2.0) (- x y))

  (* 2.0 (- (* x x) (* x y))))