Average Error: 0.0 → 0.0
Time: 12.5s
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 r9025197 = x;
        double r9025198 = r9025197 * r9025197;
        double r9025199 = y;
        double r9025200 = r9025199 * r9025199;
        double r9025201 = r9025198 - r9025200;
        return r9025201;
}
↓
double f(double x, double y) {
        double r9025202 = y;
        double r9025203 = x;
        double r9025204 = r9025202 + r9025203;
        double r9025205 = r9025203 - r9025202;
        double r9025206 = r9025204 * r9025205;
        return r9025206;
}

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))