Average Error: 0.0 → 0.0
Time: 13.5s
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 r2544306 = 1.0;
        double r2544307 = x;
        double r2544308 = r2544307 * r2544307;
        double r2544309 = r2544306 - r2544308;
        double r2544310 = -r2544309;
        double r2544311 = exp(r2544310);
        return r2544311;
}
↓
double f(double x) {
        double r2544312 = x;
        double r2544313 = -1.0;
        double r2544314 = fma(r2544312, r2544312, r2544313);
        double r2544315 = exp(r2544314);
        return r2544315;
}

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)))))