Average Error: 0.0 → 0.0
Time: 7.5s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + x\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r102561 = x;
        double r102562 = r102561 * r102561;
        double r102563 = y;
        double r102564 = r102563 * r102563;
        double r102565 = r102562 - r102564;
        return r102565;
}
↓
double f(double x, double y) {
        double r102566 = y;
        double r102567 = x;
        double r102568 = r102566 + r102567;
        double r102569 = r102567 - r102566;
        double r102570 = r102568 * r102569;
        return r102570;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(x - y\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(y + x\right) \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))