Average Error: 0.0 → 0.0
Time: 52.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\sqrt{{\left(e^{-x}\right)}^{\left(1 - x\right)} \cdot {\left(e^{-1}\right)}^{\left(1 - x\right)}} \cdot \sqrt{{\left(e^{-x}\right)}^{\left(1 - x\right)} \cdot {\left(e^{-1}\right)}^{\left(1 - x\right)}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\sqrt{{\left(e^{-x}\right)}^{\left(1 - x\right)} \cdot {\left(e^{-1}\right)}^{\left(1 - x\right)}} \cdot \sqrt{{\left(e^{-x}\right)}^{\left(1 - x\right)} \cdot {\left(e^{-1}\right)}^{\left(1 - x\right)}}
double f(double x) {
        double r6199625 = 1.0;
        double r6199626 = x;
        double r6199627 = r6199626 * r6199626;
        double r6199628 = r6199625 - r6199627;
        double r6199629 = -r6199628;
        double r6199630 = exp(r6199629);
        return r6199630;
}
↓
double f(double x) {
        double r6199631 = x;
        double r6199632 = -r6199631;
        double r6199633 = exp(r6199632);
        double r6199634 = 1.0;
        double r6199635 = r6199634 - r6199631;
        double r6199636 = pow(r6199633, r6199635);
        double r6199637 = -1.0;
        double r6199638 = exp(r6199637);
        double r6199639 = pow(r6199638, r6199635);
        double r6199640 = r6199636 * r6199639;
        double r6199641 = sqrt(r6199640);
        double r6199642 = r6199641 * r6199641;
        return r6199642;
}

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 *-un-lft-identity0.0

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

  4. Applied difference-of-squares0.0

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

  5. Applied distribute-lft-neg-in0.0

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

  6. Applied exp-prod0.0

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

  7. Simplified0.0

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

  9. Applied sub-neg0.0

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

  10. Applied exp-sum0.0

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

  11. Applied unpow-prod-down0.0

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

  13. Applied add-sqr-sqrt0.0

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

  14. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))