Average Error: 0.0 → 0.0
Time: 6.9s
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 r8195571 = x;
        double r8195572 = r8195571 * r8195571;
        double r8195573 = y;
        double r8195574 = r8195573 * r8195573;
        double r8195575 = r8195572 - r8195574;
        return r8195575;
}
↓
double f(double x, double y) {
        double r8195576 = y;
        double r8195577 = x;
        double r8195578 = r8195576 + r8195577;
        double r8195579 = r8195577 - r8195576;
        double r8195580 = r8195578 * r8195579;
        return r8195580;
}

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 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  (- (* x x) (* y y)))