Average Error: 0.0 → 0.0
Time: 6.0s
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 r468824 = x;
        double r468825 = r468824 * r468824;
        double r468826 = 2.0;
        double r468827 = r468824 * r468826;
        double r468828 = y;
        double r468829 = r468827 * r468828;
        double r468830 = r468825 + r468829;
        double r468831 = r468828 * r468828;
        double r468832 = r468830 + r468831;
        return r468832;
}
↓
double f(double x, double y) {
        double r468833 = x;
        double r468834 = r468833 * r468833;
        double r468835 = 2.0;
        double r468836 = r468833 * r468835;
        double r468837 = y;
        double r468838 = r468836 * r468837;
        double r468839 = r468834 + r468838;
        double r468840 = r468837 * r468837;
        double r468841 = r468839 + r468840;
        return r468841;
}

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 2019326 +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)))