Average Error: 0.0 → 0.0
Time: 2.6s
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 r661918 = x;
        double r661919 = y;
        double r661920 = r661918 + r661919;
        double r661921 = r661920 * r661920;
        return r661921;
}
↓
double f(double x, double y) {
        double r661922 = x;
        double r661923 = 2.0;
        double r661924 = pow(r661922, r661923);
        double r661925 = y;
        double r661926 = pow(r661925, r661923);
        double r661927 = r661922 * r661925;
        double r661928 = r661923 * r661927;
        double r661929 = r661926 + r661928;
        double r661930 = r661924 + r661929;
        return r661930;
}

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 associate-*r/18.6

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

  5. Simplified18.6

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

  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 2020036 
(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)))