Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
\[e^{(x \cdot x + -1)_*}\]
double f(double x) {
        double r858192 = 1.0;
        double r858193 = x;
        double r858194 = r858193 * r858193;
        double r858195 = r858192 - r858194;
        double r858196 = -r858195;
        double r858197 = exp(r858196);
        return r858197;
}

double f(double x) {
        double r858198 = x;
        double r858199 = -1.0;
        double r858200 = fma(r858198, r858198, r858199);
        double r858201 = exp(r858200);
        return r858201;
}

e^{-\left(1 - x \cdot x\right)}
e^{(x \cdot x + -1)_*}

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]
  2. Simplified0.0

    \[\leadsto \color{blue}{e^{(x \cdot x + -1)_*}}\]
  3. Final simplification0.0

    \[\leadsto e^{(x \cdot x + -1)_*}\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))