Average Error: 0.0 → 0.0
Time: 19.2s
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 r116510 = x;
        double r116511 = r116510 * r116510;
        double r116512 = y;
        double r116513 = r116512 * r116512;
        double r116514 = r116511 - r116513;
        return r116514;
}
↓
double f(double x, double y) {
        double r116515 = x;
        double r116516 = y;
        double r116517 = r116515 + r116516;
        double r116518 = r116515 - r116516;
        double r116519 = r116517 * r116518;
        return r116519;
}

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

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))