Average Error: 0.0 → 0.0
Time: 739.0ms
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 r131457 = x;
        double r131458 = r131457 * r131457;
        double r131459 = y;
        double r131460 = r131459 * r131459;
        double r131461 = r131458 - r131460;
        return r131461;
}
↓
double f(double x, double y) {
        double r131462 = x;
        double r131463 = y;
        double r131464 = r131462 + r131463;
        double r131465 = r131462 - r131463;
        double r131466 = r131464 * r131465;
        return r131466;
}

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 2020024 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))