Average Error: 0.0 → 0.0
Time: 3.1s
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 r163952 = x;
        double r163953 = r163952 * r163952;
        double r163954 = y;
        double r163955 = r163954 * r163954;
        double r163956 = r163953 - r163955;
        return r163956;
}
↓
double f(double x, double y) {
        double r163957 = x;
        double r163958 = y;
        double r163959 = r163957 - r163958;
        double r163960 = r163957 + r163958;
        double r163961 = r163959 * r163960;
        return r163961;
}

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