Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(y \cdot 2 + x\right) + {y}^{2}\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(y \cdot 2 + x\right) + {y}^{2}
double f(double x, double y) {
        double r473639 = x;
        double r473640 = y;
        double r473641 = r473639 + r473640;
        double r473642 = r473641 * r473641;
        return r473642;
}
↓
double f(double x, double y) {
        double r473643 = x;
        double r473644 = y;
        double r473645 = 2.0;
        double r473646 = r473644 * r473645;
        double r473647 = r473646 + r473643;
        double r473648 = r473643 * r473647;
        double r473649 = pow(r473644, r473645);
        double r473650 = r473648 + r473649;
        return r473650;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 1978988140 
(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)))