Average Error: 0.0 → 0.0
Time: 1.1s
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 r187954 = x;
        double r187955 = r187954 * r187954;
        double r187956 = y;
        double r187957 = r187956 * r187956;
        double r187958 = r187955 - r187957;
        return r187958;
}
↓
double f(double x, double y) {
        double r187959 = x;
        double r187960 = y;
        double r187961 = r187959 + r187960;
        double r187962 = r187959 - r187960;
        double r187963 = r187961 * r187962;
        return r187963;
}

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 2020034 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))