Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(2 \cdot y + x\right) + {y}^{2}\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(2 \cdot y + x\right) + {y}^{2}
double f(double x, double y) {
        double r626595 = x;
        double r626596 = y;
        double r626597 = r626595 + r626596;
        double r626598 = r626597 * r626597;
        return r626598;
}
↓
double f(double x, double y) {
        double r626599 = x;
        double r626600 = 2.0;
        double r626601 = y;
        double r626602 = r626600 * r626601;
        double r626603 = r626602 + r626599;
        double r626604 = r626599 * r626603;
        double r626605 = pow(r626601, r626600);
        double r626606 = r626604 + r626605;
        return r626606;
}

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. Using strategy rm

  8. Applied *-un-lft-identity0.0

    \[\leadsto {x}^{2} + \color{blue}{1 \cdot \left({y}^{2} + 2 \cdot \left(x \cdot y\right)\right)}\]

  9. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot {x}^{2}} + 1 \cdot \left({y}^{2} + 2 \cdot \left(x \cdot y\right)\right)\]

  10. Applied distribute-lft-out0.0

    \[\leadsto \color{blue}{1 \cdot \left({x}^{2} + \left({y}^{2} + 2 \cdot \left(x \cdot y\right)\right)\right)}\]

  11. Simplified0.0

    \[\leadsto 1 \cdot \color{blue}{\left(x \cdot \left(2 \cdot y + x\right) + {y}^{2}\right)}\]

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 
(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)))