Average Error: 0.0 → 0.1
Time: 5.8s
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 r542368 = 2.0;
        double r542369 = x;
        double r542370 = r542369 * r542369;
        double r542371 = y;
        double r542372 = r542369 * r542371;
        double r542373 = r542370 + r542372;
        double r542374 = r542368 * r542373;
        return r542374;
}
↓
double f(double x, double y) {
        double r542375 = x;
        double r542376 = y;
        double r542377 = r542375 + r542376;
        double r542378 = 2.0;
        double r542379 = r542377 * r542378;
        double r542380 = r542375 * r542379;
        return r542380;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

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

  (* 2 (+ (* x x) (* x y))))