Average Error: 0.0 → 0
Time: 3.9s
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 r8928896 = x;
        double r8928897 = r8928896 * r8928896;
        double r8928898 = 1.0;
        double r8928899 = r8928897 - r8928898;
        return r8928899;
}
↓
double f(double x) {
        double r8928900 = x;
        double r8928901 = 1.0;
        double r8928902 = -r8928901;
        double r8928903 = fma(r8928900, r8928900, r8928902);
        return r8928903;
}

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 2019192 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  (- (* x x) 1.0))