Average Error: 0.0 → 0.0
Time: 11.5s
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 r9804372 = x;
        double r9804373 = r9804372 * r9804372;
        double r9804374 = y;
        double r9804375 = r9804374 * r9804374;
        double r9804376 = r9804373 - r9804375;
        return r9804376;
}
↓
double f(double x, double y) {
        double r9804377 = y;
        double r9804378 = x;
        double r9804379 = r9804377 + r9804378;
        double r9804380 = r9804378 - r9804377;
        double r9804381 = r9804379 * r9804380;
        return r9804381;
}

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))