Average Error: 0.0 → 0.0
Time: 992.0ms
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 r178070 = x;
        double r178071 = r178070 * r178070;
        double r178072 = y;
        double r178073 = r178072 * r178072;
        double r178074 = r178071 - r178073;
        return r178074;
}
↓
double f(double x, double y) {
        double r178075 = x;
        double r178076 = y;
        double r178077 = r178075 + r178076;
        double r178078 = r178075 - r178076;
        double r178079 = r178077 * r178078;
        return r178079;
}

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 2020025 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))