Average Error: 0.0 → 0.0
Time: 6.9s
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 r166315 = x;
        double r166316 = r166315 * r166315;
        double r166317 = y;
        double r166318 = r166317 * r166317;
        double r166319 = r166316 - r166318;
        return r166319;
}
↓
double f(double x, double y) {
        double r166320 = x;
        double r166321 = y;
        double r166322 = r166320 - r166321;
        double r166323 = r166320 + r166321;
        double r166324 = r166322 * r166323;
        return r166324;
}

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 2020043 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))