Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + x\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r7717297 = x;
        double r7717298 = r7717297 * r7717297;
        double r7717299 = y;
        double r7717300 = r7717299 * r7717299;
        double r7717301 = r7717298 - r7717300;
        return r7717301;
}
↓
double f(double x, double y) {
        double r7717302 = y;
        double r7717303 = x;
        double r7717304 = r7717302 + r7717303;
        double r7717305 = r7717303 - r7717302;
        double r7717306 = r7717304 * r7717305;
        return r7717306;
}

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

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))