Average Error: 0.0 → 0.0
Time: 11.1s
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 r1331281 = 1.0;
        double r1331282 = x;
        double r1331283 = r1331282 * r1331282;
        double r1331284 = r1331281 - r1331283;
        double r1331285 = -r1331284;
        double r1331286 = exp(r1331285);
        return r1331286;
}
↓
double f(double x) {
        double r1331287 = x;
        double r1331288 = -1.0;
        double r1331289 = fma(r1331287, r1331287, r1331288);
        double r1331290 = exp(r1331289);
        return r1331290;
}

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 2019164 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))