Average Error: 0.0 → 0.0
Time: 1.4s
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 r178096 = x;
        double r178097 = r178096 * r178096;
        double r178098 = y;
        double r178099 = r178098 * r178098;
        double r178100 = r178097 - r178099;
        return r178100;
}
↓
double f(double x, double y) {
        double r178101 = x;
        double r178102 = y;
        double r178103 = r178101 - r178102;
        double r178104 = r178101 + r178102;
        double r178105 = r178103 * r178104;
        return r178105;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(x + y\right)}\]

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))