Average Error: 0.0 → 0
Time: 4.2s
Precision: 64
\[x \cdot x - 1\]
↓
\[\mathsf{fma}\left(x, x, -1\right)\]
x \cdot x - 1
↓
\mathsf{fma}\left(x, x, -1\right)
double f(double x) {
        double r140719 = x;
        double r140720 = r140719 * r140719;
        double r140721 = 1.0;
        double r140722 = r140720 - r140721;
        return r140722;
}
↓
double f(double x) {
        double r140723 = x;
        double r140724 = 1.0;
        double r140725 = -r140724;
        double r140726 = fma(r140723, r140723, r140725);
        return r140726;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied fma-neg0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))