Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2.0\right) \cdot y\right) + y \cdot y\]
↓
\[y \cdot y + x \cdot \left(x + 2.0 \cdot y\right)\]
\left(x \cdot x + \left(x \cdot 2.0\right) \cdot y\right) + y \cdot y
↓
y \cdot y + x \cdot \left(x + 2.0 \cdot y\right)
double f(double x, double y) {
        double r30993378 = x;
        double r30993379 = r30993378 * r30993378;
        double r30993380 = 2.0;
        double r30993381 = r30993378 * r30993380;
        double r30993382 = y;
        double r30993383 = r30993381 * r30993382;
        double r30993384 = r30993379 + r30993383;
        double r30993385 = r30993382 * r30993382;
        double r30993386 = r30993384 + r30993385;
        return r30993386;
}
↓
double f(double x, double y) {
        double r30993387 = y;
        double r30993388 = r30993387 * r30993387;
        double r30993389 = x;
        double r30993390 = 2.0;
        double r30993391 = r30993390 * r30993387;
        double r30993392 = r30993389 + r30993391;
        double r30993393 = r30993389 * r30993392;
        double r30993394 = r30993388 + r30993393;
        return r30993394;
}

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
\[x \cdot x + \left(y \cdot y + \left(x \cdot y\right) \cdot 2.0\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + \left(x \cdot 2.0\right) \cdot y\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot y + x \cdot \left(x + y \cdot 2.0\right)}\]

  3. Final simplification0.0

    \[\leadsto y \cdot y + x \cdot \left(x + 2.0 \cdot y\right)\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2.0)))

  (+ (+ (* x x) (* (* x 2.0) y)) (* y y)))