Average Error: 0.0 → 0.0
Time: 799.0ms
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 r165379 = x;
        double r165380 = r165379 * r165379;
        double r165381 = y;
        double r165382 = r165381 * r165381;
        double r165383 = r165380 - r165382;
        return r165383;
}
↓
double f(double x, double y) {
        double r165384 = x;
        double r165385 = y;
        double r165386 = r165384 + r165385;
        double r165387 = r165384 - r165385;
        double r165388 = r165386 * r165387;
        return r165388;
}

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 2020036 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))