Average Error: 0.0 → 0.0
Time: 763.0ms
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 r221026 = x;
        double r221027 = r221026 * r221026;
        double r221028 = y;
        double r221029 = r221028 * r221028;
        double r221030 = r221027 - r221029;
        return r221030;
}
↓
double f(double x, double y) {
        double r221031 = x;
        double r221032 = y;
        double r221033 = r221031 + r221032;
        double r221034 = r221031 - r221032;
        double r221035 = r221033 * r221034;
        return r221035;
}

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 2020047 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))