Average Error: 0.0 → 0.0
Time: 5.2s
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 r467032 = x;
        double r467033 = y;
        double r467034 = r467032 + r467033;
        double r467035 = r467034 * r467034;
        return r467035;
}
↓
double f(double x, double y) {
        double r467036 = x;
        double r467037 = y;
        double r467038 = 2.0;
        double r467039 = r467037 * r467038;
        double r467040 = r467039 + r467036;
        double r467041 = r467036 * r467040;
        double r467042 = pow(r467037, r467038);
        double r467043 = r467041 + r467042;
        return r467043;
}

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 add-sqr-sqrt32.6

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

  4. Applied associate-*l*32.6

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

  5. Simplified32.8

    \[\leadsto \sqrt{x + y} \cdot \color{blue}{{\left(\sqrt{x + y}\right)}^{3}}\]

  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 2019297 
(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)))