Average Error: 0.0 → 0.0
Time: 24.3s
Precision: 64
\[e^{-\left(1.0 - x \cdot x\right)}\]
↓
\[e^{x \cdot x - 1.0}\]
e^{-\left(1.0 - x \cdot x\right)}
↓
e^{x \cdot x - 1.0}
double f(double x) {
        double r1373878 = 1.0;
        double r1373879 = x;
        double r1373880 = r1373879 * r1373879;
        double r1373881 = r1373878 - r1373880;
        double r1373882 = -r1373881;
        double r1373883 = exp(r1373882);
        return r1373883;
}
↓
double f(double x) {
        double r1373884 = x;
        double r1373885 = r1373884 * r1373884;
        double r1373886 = 1.0;
        double r1373887 = r1373885 - r1373886;
        double r1373888 = exp(r1373887);
        return r1373888;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{-\left(1.0 - x \cdot x\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1.0}}\]

  3. Final simplification0.0

    \[\leadsto e^{x \cdot x - 1.0}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))