Average Error: 0.0 → 0.0
Time: 12.0s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot y + x \cdot \left(x + y \cdot 2\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot y + x \cdot \left(x + y \cdot 2\right)
double f(double x, double y) {
        double r384624 = x;
        double r384625 = y;
        double r384626 = r384624 + r384625;
        double r384627 = r384626 * r384626;
        return r384627;
}
↓
double f(double x, double y) {
        double r384628 = y;
        double r384629 = r384628 * r384628;
        double r384630 = x;
        double r384631 = 2.0;
        double r384632 = r384628 * r384631;
        double r384633 = r384630 + r384632;
        double r384634 = r384630 * r384633;
        double r384635 = r384629 + r384634;
        return r384635;
}

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

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(x + y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Taylor expanded around 0 0.0

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

  5. Simplified0.0

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

  7. Applied distribute-lft-in0.0

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

  8. Applied associate-+l+0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

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