Average Error: 0.0 → 0
Time: 4.5s
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 r175414 = x;
        double r175415 = r175414 * r175414;
        double r175416 = 1.0;
        double r175417 = r175415 - r175416;
        return r175417;
}
↓
double f(double x) {
        double r175418 = x;
        double r175419 = 1.0;
        double r175420 = -r175419;
        double r175421 = fma(r175418, r175418, r175420);
        return r175421;
}

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 2019323 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  :precision binary64
  (- (* x x) 1))