Average Error: 0.0 → 0.0
Time: 722.0ms
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 r164180 = x;
        double r164181 = r164180 * r164180;
        double r164182 = y;
        double r164183 = r164182 * r164182;
        double r164184 = r164181 - r164183;
        return r164184;
}
↓
double f(double x, double y) {
        double r164185 = x;
        double r164186 = y;
        double r164187 = r164185 + r164186;
        double r164188 = r164185 - r164186;
        double r164189 = r164187 * r164188;
        return r164189;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))