Average Error: 0.0 → 0
Time: 499.0ms
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 r205367 = x;
        double r205368 = r205367 * r205367;
        double r205369 = 1.0;
        double r205370 = r205368 - r205369;
        return r205370;
}
↓
double f(double x) {
        double r205371 = x;
        double r205372 = 1.0;
        double r205373 = -r205372;
        double r205374 = fma(r205371, r205371, r205373);
        return r205374;
}

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 2020025 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))