Average Error: 0.0 → 0.0
Time: 6.1s
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 r164337 = x;
        double r164338 = r164337 * r164337;
        double r164339 = y;
        double r164340 = r164339 * r164339;
        double r164341 = r164338 - r164340;
        return r164341;
}
↓
double f(double x, double y) {
        double r164342 = y;
        double r164343 = x;
        double r164344 = r164342 + r164343;
        double r164345 = r164343 - r164342;
        double r164346 = r164344 * r164345;
        return r164346;
}

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 2019174 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))