Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[{x}^{2} + y \cdot \left(2 \cdot x + y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
{x}^{2} + y \cdot \left(2 \cdot x + y\right)
double f(double x, double y) {
        double r693576 = x;
        double r693577 = y;
        double r693578 = r693576 + r693577;
        double r693579 = r693578 * r693578;
        return r693579;
}
↓
double f(double x, double y) {
        double r693580 = x;
        double r693581 = 2.0;
        double r693582 = pow(r693580, r693581);
        double r693583 = y;
        double r693584 = r693581 * r693580;
        double r693585 = r693584 + r693583;
        double r693586 = r693583 * r693585;
        double r693587 = r693582 + r693586;
        return r693587;
}

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. Taylor expanded around 0 0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 
(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)))