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 r19636 = 1.0;
        double r19637 = x;
        double r19638 = r19637 * r19637;
        double r19639 = r19636 - r19638;
        double r19640 = -r19639;
        double r19641 = exp(r19640);
        return r19641;
}
↓
double f(double x) {
        double r19642 = 1.0;
        double r19643 = 1.0;
        double r19644 = x;
        double r19645 = r19644 * r19644;
        double r19646 = r19643 - r19645;
        double r19647 = exp(r19646);
        double r19648 = r19642 / r19647;
        return r19648;
}

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 2019356 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))