Average Error: 0.0 → 0.0
Time: 11.5s
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 r8891738 = x;
        double r8891739 = r8891738 * r8891738;
        double r8891740 = y;
        double r8891741 = r8891740 * r8891740;
        double r8891742 = r8891739 - r8891741;
        return r8891742;
}
↓
double f(double x, double y) {
        double r8891743 = y;
        double r8891744 = x;
        double r8891745 = r8891743 + r8891744;
        double r8891746 = r8891744 - r8891743;
        double r8891747 = r8891745 * r8891746;
        return r8891747;
}

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 2019162 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))