Average Error: 0.0 → 0.0
Time: 1.3s
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 r157130 = x;
        double r157131 = r157130 * r157130;
        double r157132 = y;
        double r157133 = r157132 * r157132;
        double r157134 = r157131 - r157133;
        return r157134;
}
↓
double f(double x, double y) {
        double r157135 = x;
        double r157136 = y;
        double r157137 = r157135 + r157136;
        double r157138 = r157135 - r157136;
        double r157139 = r157137 * r157138;
        return r157139;
}

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 2020035 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))