Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
\[\left(x + y\right) \cdot \left(x - y\right)\]
↓
\[x \cdot x - y \cdot y\]
\left(x + y\right) \cdot \left(x - y\right)
↓
x \cdot x - y \cdot y
double f(double x, double y) {
        double r148673 = x;
        double r148674 = y;
        double r148675 = r148673 + r148674;
        double r148676 = r148673 - r148674;
        double r148677 = r148675 * r148676;
        return r148677;
}
↓
double f(double x, double y) {
        double r148678 = x;
        double r148679 = r148678 * r148678;
        double r148680 = y;
        double r148681 = r148680 * r148680;
        double r148682 = r148679 - r148681;
        return r148682;
}

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

    \[\left(x + y\right) \cdot \left(x - y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot x - y \cdot y}\]

  3. Final simplification0.0

    \[\leadsto x \cdot x - y \cdot y\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f1 from sbv-4.4"
  :precision binary64
  (* (+ x y) (- x y)))