Average Error: 0.0 → 0.0
Time: 1.2s
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 r2022370 = 2.0;
        double r2022371 = x;
        double r2022372 = r2022371 * r2022371;
        double r2022373 = y;
        double r2022374 = r2022371 * r2022373;
        double r2022375 = r2022372 - r2022374;
        double r2022376 = r2022370 * r2022375;
        return r2022376;
}
↓
double f(double x, double y) {
        double r2022377 = 2.0;
        double r2022378 = x;
        double r2022379 = r2022377 * r2022378;
        double r2022380 = y;
        double r2022381 = r2022378 - r2022380;
        double r2022382 = r2022379 * r2022381;
        return r2022382;
}

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 2020018 +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))))