Average Error: 0.0 → 0.0
Time: 3.8s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
double f(double x, double y) {
        double r702346 = x;
        double r702347 = r702346 * r702346;
        double r702348 = 2.0;
        double r702349 = r702346 * r702348;
        double r702350 = y;
        double r702351 = r702349 * r702350;
        double r702352 = r702347 + r702351;
        double r702353 = r702350 * r702350;
        double r702354 = r702352 + r702353;
        return r702354;
}
↓
double f(double x, double y) {
        double r702355 = x;
        double r702356 = r702355 * r702355;
        double r702357 = 2.0;
        double r702358 = r702355 * r702357;
        double r702359 = y;
        double r702360 = r702358 * r702359;
        double r702361 = r702356 + r702360;
        double r702362 = r702359 * r702359;
        double r702363 = r702361 + r702362;
        return r702363;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020024 
(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)))