Average Error: 0.0 → 0.0
Time: 14.1s
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 r407585 = 2.0;
        double r407586 = x;
        double r407587 = r407586 * r407586;
        double r407588 = y;
        double r407589 = r407586 * r407588;
        double r407590 = r407587 + r407589;
        double r407591 = r407585 * r407590;
        return r407591;
}
↓
double f(double x, double y) {
        double r407592 = x;
        double r407593 = y;
        double r407594 = r407592 + r407593;
        double r407595 = 2.0;
        double r407596 = r407594 * r407595;
        double r407597 = r407592 * r407596;
        return r407597;
}

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

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

  4. Applied pow10.0

    \[\leadsto \left(x \cdot \left(x + y\right)\right) \cdot \color{blue}{{2}^{1}}\]

  5. Applied pow10.0

    \[\leadsto \left(x \cdot \color{blue}{{\left(x + y\right)}^{1}}\right) \cdot {2}^{1}\]

  6. Applied pow10.0

    \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {\left(x + y\right)}^{1}\right) \cdot {2}^{1}\]

  7. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(x \cdot \left(x + y\right)\right)}^{1}} \cdot {2}^{1}\]

  8. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(\left(x \cdot \left(x + y\right)\right) \cdot 2\right)}^{1}}\]

  9. Simplified0.0

    \[\leadsto {\color{blue}{\left(x \cdot \left(\left(x + y\right) \cdot 2\right)\right)}}^{1}\]

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(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))))