Average Error: 0.0 → 0.0
Time: 1.6s
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 r163519 = x;
        double r163520 = r163519 * r163519;
        double r163521 = y;
        double r163522 = r163521 * r163521;
        double r163523 = r163520 - r163522;
        return r163523;
}
↓
double f(double x, double y) {
        double r163524 = x;
        double r163525 = y;
        double r163526 = r163524 - r163525;
        double r163527 = r163524 + r163525;
        double r163528 = r163526 * r163527;
        return r163528;
}

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)))