Average Error: 0.0 → 0.0
Time: 3.0s
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 r630367 = x;
        double r630368 = y;
        double r630369 = r630367 + r630368;
        double r630370 = r630369 * r630369;
        return r630370;
}
↓
double f(double x, double y) {
        double r630371 = x;
        double r630372 = 2.0;
        double r630373 = pow(r630371, r630372);
        double r630374 = y;
        double r630375 = pow(r630374, r630372);
        double r630376 = r630371 * r630374;
        double r630377 = r630372 * r630376;
        double r630378 = r630375 + r630377;
        double r630379 = r630373 + r630378;
        return r630379;
}

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)))