Average Error: 0.0 → 0.0
Time: 7.6s
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 r459550 = x;
        double r459551 = y;
        double r459552 = r459550 + r459551;
        double r459553 = r459552 * r459552;
        return r459553;
}
↓
double f(double x, double y) {
        double r459554 = x;
        double r459555 = y;
        double r459556 = 2.0;
        double r459557 = r459555 * r459556;
        double r459558 = r459557 + r459554;
        double r459559 = r459554 * r459558;
        double r459560 = pow(r459555, r459556);
        double r459561 = r459559 + r459560;
        return r459561;
}

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

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

  5. Simplified0.0

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

  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 2019291 
(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)))