Average Error: 0.0 → 0.0
Time: 1.1s
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 r145818 = x;
        double r145819 = r145818 * r145818;
        double r145820 = y;
        double r145821 = r145820 * r145820;
        double r145822 = r145819 - r145821;
        return r145822;
}
↓
double f(double x, double y) {
        double r145823 = x;
        double r145824 = y;
        double r145825 = r145823 + r145824;
        double r145826 = r145823 - r145824;
        double r145827 = r145825 * r145826;
        return r145827;
}

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 2020034 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))