Average Error: 0.0 → 0.0
Time: 1.4s
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 r823664 = x;
        double r823665 = y;
        double r823666 = r823664 + r823665;
        double r823667 = r823666 * r823666;
        return r823667;
}
↓
double f(double x, double y) {
        double r823668 = x;
        double r823669 = 2.0;
        double r823670 = pow(r823668, r823669);
        double r823671 = y;
        double r823672 = r823669 * r823668;
        double r823673 = r823672 + r823671;
        double r823674 = r823671 * r823673;
        double r823675 = r823670 + r823674;
        return r823675;
}

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 2020046 
(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)))