Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
\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 r741384 = x;
        double r741385 = r741384 * r741384;
        double r741386 = 2.0;
        double r741387 = r741384 * r741386;
        double r741388 = y;
        double r741389 = r741387 * r741388;
        double r741390 = r741385 + r741389;
        double r741391 = r741388 * r741388;
        double r741392 = r741390 + r741391;
        return r741392;
}
↓
double f(double x, double y) {
        double r741393 = x;
        double r741394 = r741393 * r741393;
        double r741395 = 2.0;
        double r741396 = r741393 * r741395;
        double r741397 = y;
        double r741398 = r741396 * r741397;
        double r741399 = r741394 + r741398;
        double r741400 = r741397 * r741397;
        double r741401 = r741399 + r741400;
        return r741401;
}

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 2020042 
(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)))