Average Error: 0.0 → 0.0
Time: 1.2s
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 r150012 = x;
        double r150013 = r150012 * r150012;
        double r150014 = y;
        double r150015 = r150014 * r150014;
        double r150016 = r150013 - r150015;
        return r150016;
}
↓
double f(double x, double y) {
        double r150017 = x;
        double r150018 = y;
        double r150019 = r150017 + r150018;
        double r150020 = r150017 - r150018;
        double r150021 = r150019 * r150020;
        return r150021;
}

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)))