Average Error: 0.0 → 0.0
Time: 12.8s
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 r1069924 = 1.0;
        double r1069925 = x;
        double r1069926 = r1069925 * r1069925;
        double r1069927 = r1069924 - r1069926;
        double r1069928 = -r1069927;
        double r1069929 = exp(r1069928);
        return r1069929;
}
↓
double f(double x) {
        double r1069930 = x;
        double r1069931 = -1.0;
        double r1069932 = fma(r1069930, r1069930, r1069931);
        double r1069933 = exp(r1069932);
        return r1069933;
}

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 2019151 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))