Average Error: 0.0 → 0.0
Time: 4.2s
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 r625223 = x;
        double r625224 = r625223 * r625223;
        double r625225 = 2.0;
        double r625226 = r625223 * r625225;
        double r625227 = y;
        double r625228 = r625226 * r625227;
        double r625229 = r625224 + r625228;
        double r625230 = r625227 * r625227;
        double r625231 = r625229 + r625230;
        return r625231;
}
↓
double f(double x, double y) {
        double r625232 = x;
        double r625233 = r625232 * r625232;
        double r625234 = 2.0;
        double r625235 = r625232 * r625234;
        double r625236 = y;
        double r625237 = r625235 * r625236;
        double r625238 = r625233 + r625237;
        double r625239 = r625236 * r625236;
        double r625240 = r625238 + r625239;
        return r625240;
}

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 2020047 +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)))