Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{1}{e^{1 - x \cdot x}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{1}{e^{1 - x \cdot x}}
double f(double x) {
        double r18135 = 1.0;
        double r18136 = x;
        double r18137 = r18136 * r18136;
        double r18138 = r18135 - r18137;
        double r18139 = -r18138;
        double r18140 = exp(r18139);
        return r18140;
}
↓
double f(double x) {
        double r18141 = 1.0;
        double r18142 = 1.0;
        double r18143 = x;
        double r18144 = r18143 * r18143;
        double r18145 = r18142 - r18144;
        double r18146 = exp(r18145);
        double r18147 = r18141 / r18146;
        return r18147;
}

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

    \[e^{-\left(1 - x \cdot x\right)}\]
  2. Using strategy rm

  3. Applied exp-neg0.0

    \[\leadsto \color{blue}{\frac{1}{e^{1 - x \cdot x}}}\]

  4. Final simplification0.0

    \[\leadsto \frac{1}{e^{1 - x \cdot x}}\]

Reproduce

herbie shell --seed 2020033 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))