Average Error: 0.0 → 0.0
Time: 9.9s
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\left(y + x\right) \cdot \left(x - y\right)\]
x \cdot x - y \cdot y
↓
\left(y + x\right) \cdot \left(x - y\right)
double f(double x, double y) {
        double r7041876 = x;
        double r7041877 = r7041876 * r7041876;
        double r7041878 = y;
        double r7041879 = r7041878 * r7041878;
        double r7041880 = r7041877 - r7041879;
        return r7041880;
}
↓
double f(double x, double y) {
        double r7041881 = y;
        double r7041882 = x;
        double r7041883 = r7041881 + r7041882;
        double r7041884 = r7041882 - r7041881;
        double r7041885 = r7041883 * r7041884;
        return r7041885;
}

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

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))