Average Error: 0.0 → 0
Time: 4.3s
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 r15492955 = x;
        double r15492956 = r15492955 * r15492955;
        double r15492957 = 1.0;
        double r15492958 = r15492956 - r15492957;
        return r15492958;
}
↓
double f(double x) {
        double r15492959 = x;
        double r15492960 = 1.0;
        double r15492961 = -r15492960;
        double r15492962 = fma(r15492959, r15492959, r15492961);
        return r15492962;
}

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 2019170 +o rules:numerics
(FPCore (x)
  :name "Data.Random.Dice:roll from dice-0.1"
  (- (* x x) 1.0))