Average Error: 0.0 → 0.0
Time: 21.3s
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 r10277019 = x;
        double r10277020 = r10277019 * r10277019;
        double r10277021 = y;
        double r10277022 = r10277021 * r10277021;
        double r10277023 = r10277020 - r10277022;
        return r10277023;
}
↓
double f(double x, double y) {
        double r10277024 = y;
        double r10277025 = x;
        double r10277026 = r10277024 + r10277025;
        double r10277027 = r10277025 - r10277024;
        double r10277028 = r10277026 * r10277027;
        return r10277028;
}

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 2019168 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))