Data.Random.Dice:roll from dice-0.1

Average Error: 0.0 → 0.0

Time: 2.5s

Precision: 64

Math

\[x \cdot x - 1\]

↓

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

C

double f(double x) {
        double r12635937 = x;
        double r12635938 = r12635937 * r12635937;
        double r12635939 = 1.0;
        double r12635940 = r12635938 - r12635939;
        return r12635940;
}

↓

double f(double x) {
        double r12635941 = x;
        double r12635942 = 1.0;
        double r12635943 = sqrt(r12635942);
        double r12635944 = r12635941 + r12635943;
        double r12635945 = r12635941 - r12635943;
        double r12635946 = r12635944 * r12635945;
        return r12635946;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

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

3. Applied add-sqr-sqrt 0.0

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

4. Applied difference-of-squares 0.0

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

5. Final simplification 0.0

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  (- (* x x) 1.0))