Average Error: 0.0 → 0.0
Time: 6.1s
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 r704888 = x;
        double r704889 = r704888 * r704888;
        double r704890 = 2.0;
        double r704891 = r704888 * r704890;
        double r704892 = y;
        double r704893 = r704891 * r704892;
        double r704894 = r704889 + r704893;
        double r704895 = r704892 * r704892;
        double r704896 = r704894 + r704895;
        return r704896;
}
↓
double f(double x, double y) {
        double r704897 = x;
        double r704898 = r704897 * r704897;
        double r704899 = 2.0;
        double r704900 = r704897 * r704899;
        double r704901 = y;
        double r704902 = r704900 * r704901;
        double r704903 = r704898 + r704902;
        double r704904 = r704901 * r704901;
        double r704905 = r704903 + r704904;
        return r704905;
}

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 
(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)))