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 r7004804 = x;
        double r7004805 = r7004804 * r7004804;
        double r7004806 = y;
        double r7004807 = r7004806 * r7004806;
        double r7004808 = r7004805 - r7004807;
        return r7004808;
}
↓
double f(double x, double y) {
        double r7004809 = y;
        double r7004810 = x;
        double r7004811 = r7004809 + r7004810;
        double r7004812 = r7004810 - r7004809;
        double r7004813 = r7004811 * r7004812;
        return r7004813;
}

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)))