Average Error: 0.0 → 0.0
Time: 2.8s
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 r382813 = x;
        double r382814 = y;
        double r382815 = r382813 + r382814;
        double r382816 = r382815 * r382815;
        return r382816;
}
↓
double f(double x, double y) {
        double r382817 = x;
        double r382818 = y;
        double r382819 = 2.0;
        double r382820 = r382818 * r382819;
        double r382821 = r382820 + r382817;
        double r382822 = r382817 * r382821;
        double r382823 = pow(r382818, r382819);
        double r382824 = r382822 + r382823;
        return r382824;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 
(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)))