Average Error: 0.0 → 0.0
Time: 13.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{\mathsf{fma}\left(x, x, -1\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{\mathsf{fma}\left(x, x, -1\right)}
double f(double x) {
        double r1484427 = 1.0;
        double r1484428 = x;
        double r1484429 = r1484428 * r1484428;
        double r1484430 = r1484427 - r1484429;
        double r1484431 = -r1484430;
        double r1484432 = exp(r1484431);
        return r1484432;
}
↓
double f(double x) {
        double r1484433 = x;
        double r1484434 = -1.0;
        double r1484435 = fma(r1484433, r1484433, r1484434);
        double r1484436 = exp(r1484435);
        return r1484436;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(x, x, -1\right)}}\]

  3. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(x, x, -1\right)}\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))