Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + x\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r9165885 = x;
        double r9165886 = r9165885 * r9165885;
        double r9165887 = y;
        double r9165888 = r9165887 * r9165887;
        double r9165889 = r9165886 - r9165888;
        return r9165889;
}
↓
double f(double x, double y) {
        double r9165890 = y;
        double r9165891 = x;
        double r9165892 = r9165890 + r9165891;
        double r9165893 = r9165891 - r9165890;
        double r9165894 = r9165892 * r9165893;
        return r9165894;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot x - y \cdot y\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(y + x\right) \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))