Average Error: 0.0 → 0.0
Time: 14.1s
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 r1611750 = 1.0;
        double r1611751 = x;
        double r1611752 = r1611751 * r1611751;
        double r1611753 = r1611750 - r1611752;
        double r1611754 = -r1611753;
        double r1611755 = exp(r1611754);
        return r1611755;
}
↓
double f(double x) {
        double r1611756 = x;
        double r1611757 = -1.0;
        double r1611758 = fma(r1611756, r1611756, r1611757);
        double r1611759 = exp(r1611758);
        return r1611759;
}

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 2019163 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))