Average Error: 0.0 → 0.0
Time: 1.6s
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 r168122 = x;
        double r168123 = r168122 * r168122;
        double r168124 = y;
        double r168125 = r168124 * r168124;
        double r168126 = r168123 - r168125;
        return r168126;
}
↓
double f(double x, double y) {
        double r168127 = x;
        double r168128 = y;
        double r168129 = r168127 - r168128;
        double r168130 = r168127 + r168128;
        double r168131 = r168129 * r168130;
        return r168131;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))