Average Error: 0.0 → 0.0
Time: 9.9s
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 r8698181 = x;
        double r8698182 = r8698181 * r8698181;
        double r8698183 = y;
        double r8698184 = r8698183 * r8698183;
        double r8698185 = r8698182 - r8698184;
        return r8698185;
}
↓
double f(double x, double y) {
        double r8698186 = y;
        double r8698187 = x;
        double r8698188 = r8698186 + r8698187;
        double r8698189 = r8698187 - r8698186;
        double r8698190 = r8698188 * r8698189;
        return r8698190;
}

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 2019158 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))