Average Error: 0.0 → 0
Time: 517.0ms
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 r209487 = x;
        double r209488 = r209487 * r209487;
        double r209489 = 1.0;
        double r209490 = r209488 - r209489;
        return r209490;
}
↓
double f(double x) {
        double r209491 = x;
        double r209492 = 1.0;
        double r209493 = -r209492;
        double r209494 = fma(r209491, r209491, r209493);
        return r209494;
}

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 2020065 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))