Average Error: 0.0 → 0.0
Time: 4.9s
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 r103990 = x;
        double r103991 = r103990 * r103990;
        double r103992 = y;
        double r103993 = r103992 * r103992;
        double r103994 = r103991 - r103993;
        return r103994;
}
↓
double f(double x, double y) {
        double r103995 = x;
        double r103996 = y;
        double r103997 = r103995 - r103996;
        double r103998 = r103995 + r103996;
        double r103999 = r103997 * r103998;
        return r103999;
}

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 2019235 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))