Data.Random.Dice:roll from dice-0.1

Average Error: 0.0 → 0

Time: 875.0ms

Precision: 64

Math

\[x \cdot x - 1\]

↓

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

C

double f(double x) {
        double r109511 = x;
        double r109512 = r109511 * r109511;
        double r109513 = 1.0;
        double r109514 = r109512 - r109513;
        return r109514;
}

↓

double f(double x) {
        double r109515 = x;
        double r109516 = 1.0;
        double r109517 = -r109516;
        double r109518 = fma(r109515, r109515, r109517);
        return r109518;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x \cdot x - 1\]

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  (- (* x x) 1.0))