Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left({x}^{2} + {y}^{2}\right) + 2 \cdot \left(x \cdot y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left({x}^{2} + {y}^{2}\right) + 2 \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r849620 = x;
        double r849621 = y;
        double r849622 = r849620 + r849621;
        double r849623 = r849622 * r849622;
        return r849623;
}
↓
double f(double x, double y) {
        double r849624 = x;
        double r849625 = 2.0;
        double r849626 = pow(r849624, r849625);
        double r849627 = y;
        double r849628 = pow(r849627, r849625);
        double r849629 = r849626 + r849628;
        double r849630 = r849624 * r849627;
        double r849631 = r849625 * r849630;
        double r849632 = r849629 + r849631;
        return r849632;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  6. Taylor expanded around 0 0.0

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

  8. Applied associate-+r+0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(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)))