Average Error: 0.0 → 0.0
Time: 7.7s
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 r136135 = x;
        double r136136 = r136135 * r136135;
        double r136137 = y;
        double r136138 = r136137 * r136137;
        double r136139 = r136136 - r136138;
        return r136139;
}
↓
double f(double x, double y) {
        double r136140 = x;
        double r136141 = y;
        double r136142 = r136140 - r136141;
        double r136143 = r136140 + r136141;
        double r136144 = r136142 * r136143;
        return r136144;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(x + y\right)}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))