Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot \left(2 \cdot x + y\right) + x \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot \left(2 \cdot x + y\right) + x \cdot x
double f(double x, double y) {
        double r455459 = x;
        double r455460 = y;
        double r455461 = r455459 + r455460;
        double r455462 = r455461 * r455461;
        return r455462;
}
↓
double f(double x, double y) {
        double r455463 = y;
        double r455464 = 2.0;
        double r455465 = x;
        double r455466 = r455464 * r455465;
        double r455467 = r455466 + r455463;
        double r455468 = r455463 * r455467;
        double r455469 = r455465 * r455465;
        double r455470 = r455468 + r455469;
        return r455470;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(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)))