Average Error: 0.0 → 0.0
Time: 1.7s
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 r521647 = 2.0;
        double r521648 = x;
        double r521649 = r521648 * r521648;
        double r521650 = y;
        double r521651 = r521648 * r521650;
        double r521652 = r521649 - r521651;
        double r521653 = r521647 * r521652;
        return r521653;
}
↓
double f(double x, double y) {
        double r521654 = 2.0;
        double r521655 = x;
        double r521656 = r521654 * r521655;
        double r521657 = y;
        double r521658 = r521655 - r521657;
        double r521659 = r521656 * r521658;
        return r521659;
}

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. Using strategy rm

  3. Applied distribute-lft-out--0.0

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

  4. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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))))