Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left(y \cdot \left(2 \cdot x\right) + y \cdot y\right) + x \cdot x\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left(y \cdot \left(2 \cdot x\right) + y \cdot y\right) + x \cdot x
double f(double x, double y) {
        double r552059 = x;
        double r552060 = y;
        double r552061 = r552059 + r552060;
        double r552062 = r552061 * r552061;
        return r552062;
}
↓
double f(double x, double y) {
        double r552063 = y;
        double r552064 = 2.0;
        double r552065 = x;
        double r552066 = r552064 * r552065;
        double r552067 = r552063 * r552066;
        double r552068 = r552063 * r552063;
        double r552069 = r552067 + r552068;
        double r552070 = r552065 * r552065;
        double r552071 = r552069 + r552070;
        return r552071;
}

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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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)))