Average Error: 0.0 → 0.0
Time: 737.0ms
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 r146073 = x;
        double r146074 = r146073 * r146073;
        double r146075 = y;
        double r146076 = r146075 * r146075;
        double r146077 = r146074 - r146076;
        return r146077;
}
↓
double f(double x, double y) {
        double r146078 = x;
        double r146079 = y;
        double r146080 = r146078 + r146079;
        double r146081 = r146078 - r146079;
        double r146082 = r146080 * r146081;
        return r146082;
}

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