Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[x \cdot x - 1\]
↓
\[\left(x + \sqrt{1}\right) \cdot \left(x - \sqrt{1}\right)\]
x \cdot x - 1
↓
\left(x + \sqrt{1}\right) \cdot \left(x - \sqrt{1}\right)
double f(double x) {
        double r289733 = x;
        double r289734 = r289733 * r289733;
        double r289735 = 1.0;
        double r289736 = r289734 - r289735;
        return r289736;
}
↓
double f(double x) {
        double r289737 = x;
        double r289738 = 1.0;
        double r289739 = sqrt(r289738);
        double r289740 = r289737 + r289739;
        double r289741 = r289737 - r289739;
        double r289742 = r289740 * r289741;
        return r289742;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[x \cdot x - 1\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto x \cdot x - \color{blue}{\sqrt{1} \cdot \sqrt{1}}\]

  4. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(x + \sqrt{1}\right) \cdot \left(x - \sqrt{1}\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(x + \sqrt{1}\right) \cdot \left(x - \sqrt{1}\right)\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))