Data.Random.Dice:roll from dice-0.1

Average Error: 0.0 → 0

Time: 2.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x \cdot x - 1\]

↓

\[\mathsf{fma}\left(x, x, -1\right)\]

C

double f(double x) {
        double r224399 = x;
        double r224400 = r224399 * r224399;
        double r224401 = 1.0;
        double r224402 = r224400 - r224401;
        return r224402;
}

↓

double f(double x) {
        double r224403 = x;
        double r224404 = 1.0;
        double r224405 = -r224404;
        double r224406 = fma(r224403, r224403, r224405);
        return r224406;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

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

3. Applied fma-neg 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -1\right)}\]

4. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, x, -1\right)\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))