Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)} \cdot {\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)} \cdot {\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}
double f(double x) {
        double r35675 = 1.0;
        double r35676 = x;
        double r35677 = r35676 * r35676;
        double r35678 = r35675 - r35677;
        double r35679 = -r35678;
        double r35680 = exp(r35679);
        return r35680;
}
↓
double f(double x) {
        double r35681 = x;
        double r35682 = 1.0;
        double r35683 = sqrt(r35682);
        double r35684 = r35681 + r35683;
        double r35685 = exp(r35684);
        double r35686 = r35681 - r35683;
        double r35687 = 2.0;
        double r35688 = r35686 / r35687;
        double r35689 = pow(r35685, r35688);
        double r35690 = r35689 * r35689;
        return r35690;
}

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. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.0

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

  5. Applied difference-of-squares0.0

    \[\leadsto e^{\color{blue}{\left(x + \sqrt{1}\right) \cdot \left(x - \sqrt{1}\right)}}\]

  6. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}}\]
  7. Using strategy rm

  8. Applied sqr-pow0.0

    \[\leadsto \color{blue}{{\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)} \cdot {\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}}\]

  9. Final simplification0.0

    \[\leadsto {\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)} \cdot {\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))