Average Error: 0.0 → 0.0
Time: 1.1s
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 r487399 = 2.0;
        double r487400 = x;
        double r487401 = r487400 * r487400;
        double r487402 = y;
        double r487403 = r487400 * r487402;
        double r487404 = r487401 + r487403;
        double r487405 = r487399 * r487404;
        return r487405;
}
↓
double f(double x, double y) {
        double r487406 = x;
        double r487407 = y;
        double r487408 = r487406 + r487407;
        double r487409 = 2.0;
        double r487410 = r487408 * r487409;
        double r487411 = r487406 * r487410;
        return r487411;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, x \cdot y\right) \cdot 2}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

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

  5. Simplified0.0

    \[\leadsto \left(\color{blue}{{x}^{2}} + x \cdot y\right) \cdot 2\]
  6. Using strategy rm

  7. Applied unpow20.0

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

  8. Applied distribute-lft-out0.0

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

  9. Applied associate-*l*0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +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))))