Average Error: 0.0 → 0.0
Time: 736.0ms
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 r161773 = x;
        double r161774 = r161773 * r161773;
        double r161775 = y;
        double r161776 = r161775 * r161775;
        double r161777 = r161774 - r161776;
        return r161777;
}
↓
double f(double x, double y) {
        double r161778 = x;
        double r161779 = y;
        double r161780 = r161778 + r161779;
        double r161781 = r161778 - r161779;
        double r161782 = r161780 * r161781;
        return r161782;
}

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 2020039 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))