Average Error: 0.0 → 0.0
Time: 13.2s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot \left(\sqrt{{\left(e^{x}\right)}^{x}} \cdot \sqrt{{\left(e^{x}\right)}^{x}}\right)\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot \left(\sqrt{{\left(e^{x}\right)}^{x}} \cdot \sqrt{{\left(e^{x}\right)}^{x}}\right)
double f(double x) {
        double r21350 = 1.0;
        double r21351 = x;
        double r21352 = r21351 * r21351;
        double r21353 = r21350 - r21352;
        double r21354 = -r21353;
        double r21355 = exp(r21354);
        return r21355;
}
↓
double f(double x) {
        double r21356 = 1.0;
        double r21357 = -r21356;
        double r21358 = exp(r21357);
        double r21359 = x;
        double r21360 = exp(r21359);
        double r21361 = pow(r21360, r21359);
        double r21362 = sqrt(r21361);
        double r21363 = r21362 * r21362;
        double r21364 = r21358 * r21363;
        return r21364;
}

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 sub-neg0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

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

  8. Applied add-sqr-sqrt0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))