Average Error: 0.0 → 0.0
Time: 6.3s
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 r7066717 = x;
        double r7066718 = r7066717 * r7066717;
        double r7066719 = y;
        double r7066720 = r7066719 * r7066719;
        double r7066721 = r7066718 - r7066720;
        return r7066721;
}
↓
double f(double x, double y) {
        double r7066722 = y;
        double r7066723 = x;
        double r7066724 = r7066722 + r7066723;
        double r7066725 = r7066723 - r7066722;
        double r7066726 = r7066724 * r7066725;
        return r7066726;
}

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 2019192 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))