Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[x \cdot \left(2 \cdot y + x\right) + y \cdot y\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
x \cdot \left(2 \cdot y + x\right) + y \cdot y
double f(double x, double y) {
        double r737347 = x;
        double r737348 = r737347 * r737347;
        double r737349 = 2.0;
        double r737350 = r737347 * r737349;
        double r737351 = y;
        double r737352 = r737350 * r737351;
        double r737353 = r737348 + r737352;
        double r737354 = r737351 * r737351;
        double r737355 = r737353 + r737354;
        return r737355;
}
↓
double f(double x, double y) {
        double r737356 = x;
        double r737357 = 2.0;
        double r737358 = y;
        double r737359 = r737357 * r737358;
        double r737360 = r737359 + r737356;
        double r737361 = r737356 * r737360;
        double r737362 = r737358 * r737358;
        double r737363 = r737361 + r737362;
        return r737363;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(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)))