Average Error: 0.0 → 0.0
Time: 2.9s
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 r157489 = x;
        double r157490 = r157489 * r157489;
        double r157491 = 1.0;
        double r157492 = r157490 - r157491;
        return r157492;
}
↓
double f(double x) {
        double r157493 = x;
        double r157494 = 1.0;
        double r157495 = sqrt(r157494);
        double r157496 = r157493 + r157495;
        double r157497 = r157493 - r157495;
        double r157498 = r157496 * r157497;
        return r157498;
}

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 
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))