Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(x - y\right) \cdot \left(x + y\right)\]
x \cdot x - y \cdot y
↓
\left(x - y\right) \cdot \left(x + y\right)
double f(double x, double y) {
        double r152869 = x;
        double r152870 = r152869 * r152869;
        double r152871 = y;
        double r152872 = r152871 * r152871;
        double r152873 = r152870 - r152872;
        return r152873;
}
↓
double f(double x, double y) {
        double r152874 = x;
        double r152875 = y;
        double r152876 = r152874 - r152875;
        double r152877 = r152874 + r152875;
        double r152878 = r152876 * r152877;
        return r152878;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))