Average Error: 0.0 → 0.0
Time: 2.8s
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 r852297 = x;
        double r852298 = r852297 * r852297;
        double r852299 = 2.0;
        double r852300 = r852297 * r852299;
        double r852301 = y;
        double r852302 = r852300 * r852301;
        double r852303 = r852298 + r852302;
        double r852304 = r852301 * r852301;
        double r852305 = r852303 + r852304;
        return r852305;
}
↓
double f(double x, double y) {
        double r852306 = x;
        double r852307 = r852306 * r852306;
        double r852308 = 2.0;
        double r852309 = r852306 * r852308;
        double r852310 = y;
        double r852311 = r852309 * r852310;
        double r852312 = r852307 + r852311;
        double r852313 = r852310 * r852310;
        double r852314 = r852312 + r852313;
        return r852314;
}

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 2019350 +o rules:numerics
(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)))