Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(x + y\right) + y \cdot \left(x + y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(x + y\right) + y \cdot \left(x + y\right)
double f(double x, double y) {
        double r652384 = x;
        double r652385 = y;
        double r652386 = r652384 + r652385;
        double r652387 = r652386 * r652386;
        return r652387;
}
↓
double f(double x, double y) {
        double r652388 = x;
        double r652389 = y;
        double r652390 = r652388 + r652389;
        double r652391 = r652388 * r652390;
        double r652392 = r652389 * r652390;
        double r652393 = r652391 + r652392;
        return r652393;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 
(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)))