Average Error: 0.0 → 0.0
Time: 2.9s
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 r3684228 = x;
        double r3684229 = r3684228 * r3684228;
        double r3684230 = y;
        double r3684231 = r3684230 * r3684230;
        double r3684232 = r3684229 - r3684231;
        return r3684232;
}
↓
double f(double x, double y) {
        double r3684233 = x;
        double r3684234 = y;
        double r3684235 = r3684233 + r3684234;
        double r3684236 = r3684233 - r3684234;
        double r3684237 = r3684235 * r3684236;
        return r3684237;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} - {y}^{2}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto \left(x + y\right) \cdot \left(x - y\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))