Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[{x}^{2} + \left({y}^{2} + 2 \cdot \left(x \cdot y\right)\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
{x}^{2} + \left({y}^{2} + 2 \cdot \left(x \cdot y\right)\right)
double f(double x, double y) {
        double r770030 = x;
        double r770031 = y;
        double r770032 = r770030 + r770031;
        double r770033 = r770032 * r770032;
        return r770033;
}
↓
double f(double x, double y) {
        double r770034 = x;
        double r770035 = 2.0;
        double r770036 = pow(r770034, r770035);
        double r770037 = y;
        double r770038 = pow(r770037, r770035);
        double r770039 = r770034 * r770037;
        double r770040 = r770035 * r770039;
        double r770041 = r770038 + r770040;
        double r770042 = r770036 + r770041;
        return r770042;
}

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 flip-+0.0

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

  4. Applied flip-+0.1

    \[\leadsto \color{blue}{\frac{x \cdot x - y \cdot y}{x - y}} \cdot \frac{x \cdot x - y \cdot y}{x - y}\]

  5. Applied frac-times34.6

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

  6. Taylor expanded around 0 0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(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)))