Average Error: 0.0 → 0.0
Time: 15.1s
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 r1406325 = 1.0;
        double r1406326 = x;
        double r1406327 = r1406326 * r1406326;
        double r1406328 = r1406325 - r1406327;
        double r1406329 = -r1406328;
        double r1406330 = exp(r1406329);
        return r1406330;
}
↓
double f(double x) {
        double r1406331 = x;
        double r1406332 = -1.0;
        double r1406333 = fma(r1406331, r1406331, r1406332);
        double r1406334 = exp(r1406333);
        return r1406334;
}

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 2019124 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))