Average Error: 0.0 → 0.0
Time: 5.0s
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 r195080 = x;
        double r195081 = r195080 * r195080;
        double r195082 = y;
        double r195083 = r195082 * r195082;
        double r195084 = r195081 - r195083;
        return r195084;
}
↓
double f(double x, double y) {
        double r195085 = x;
        double r195086 = y;
        double r195087 = r195085 - r195086;
        double r195088 = r195085 + r195086;
        double r195089 = r195087 * r195088;
        return r195089;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(x - y\right) \cdot \left(x + y\right)}\]

  3. 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)))