Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + y \cdot \left(x \cdot 2 + y\right)\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
x \cdot x + y \cdot \left(x \cdot 2 + y\right)
double f(double x, double y) {
        double r755289 = x;
        double r755290 = r755289 * r755289;
        double r755291 = 2.0;
        double r755292 = r755289 * r755291;
        double r755293 = y;
        double r755294 = r755292 * r755293;
        double r755295 = r755290 + r755294;
        double r755296 = r755293 * r755293;
        double r755297 = r755295 + r755296;
        return r755297;
}
↓
double f(double x, double y) {
        double r755298 = x;
        double r755299 = r755298 * r755298;
        double r755300 = y;
        double r755301 = 2.0;
        double r755302 = r755298 * r755301;
        double r755303 = r755302 + r755300;
        double r755304 = r755300 * r755303;
        double r755305 = r755299 + r755304;
        return r755305;
}

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

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
  2. Using strategy rm

  3. Applied associate-+l+0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2)))

  (+ (+ (* x x) (* (* x 2) y)) (* y y)))