Average Error: 0.0 → 0.0
Time: 6.2s
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 r223610 = x;
        double r223611 = r223610 * r223610;
        double r223612 = y;
        double r223613 = r223612 * r223612;
        double r223614 = r223611 - r223613;
        return r223614;
}
↓
double f(double x, double y) {
        double r223615 = x;
        double r223616 = y;
        double r223617 = r223615 - r223616;
        double r223618 = r223615 + r223616;
        double r223619 = r223617 * r223618;
        return r223619;
}

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