Average Error: 0.0 → 0.0
Time: 15.9s
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 r19516 = x;
        double r19517 = r19516 * r19516;
        double r19518 = y;
        double r19519 = r19518 * r19518;
        double r19520 = r19517 - r19519;
        return r19520;
}
↓
double f(double x, double y) {
        double r19521 = x;
        double r19522 = y;
        double r19523 = r19521 - r19522;
        double r19524 = r19521 + r19522;
        double r19525 = r19523 * r19524;
        return r19525;
}

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 2019315 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))