Average Error: 0.0 → 0.1
Time: 3.4s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[x \cdot \left(\left(x - y\right) \cdot 2\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
x \cdot \left(\left(x - y\right) \cdot 2\right)
double f(double x, double y) {
        double r507134 = 2.0;
        double r507135 = x;
        double r507136 = r507135 * r507135;
        double r507137 = y;
        double r507138 = r507135 * r507137;
        double r507139 = r507136 - r507138;
        double r507140 = r507134 * r507139;
        return r507140;
}
↓
double f(double x, double y) {
        double r507141 = x;
        double r507142 = y;
        double r507143 = r507141 - r507142;
        double r507144 = 2.0;
        double r507145 = r507143 * r507144;
        double r507146 = r507141 * r507145;
        return r507146;
}

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

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 associate-*l*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 +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))))