Average Error: 0.0 → 0.0
Time: 825.0ms
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 r160805 = x;
        double r160806 = r160805 * r160805;
        double r160807 = y;
        double r160808 = r160807 * r160807;
        double r160809 = r160806 - r160808;
        return r160809;
}
↓
double f(double x, double y) {
        double r160810 = x;
        double r160811 = y;
        double r160812 = r160810 + r160811;
        double r160813 = r160810 - r160811;
        double r160814 = r160812 * r160813;
        return r160814;
}

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

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

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))