Average Error: 0.0 → 0.0
Time: 11.7s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\left(\sqrt{e^{-1}} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right) \cdot \left(\sqrt{e^{-1}} \cdot {\left(e^{x}\right)}^{\left(\frac{x}{2}\right)}\right)\]
e^{-\left(1 - x \cdot x\right)}
↓
\left(\sqrt{e^{-1}} \cdot {\left(\sqrt{e^{x}}\right)}^{x}\right) \cdot \left(\sqrt{e^{-1}} \cdot {\left(e^{x}\right)}^{\left(\frac{x}{2}\right)}\right)
double f(double x) {
        double r40876 = 1.0;
        double r40877 = x;
        double r40878 = r40877 * r40877;
        double r40879 = r40876 - r40878;
        double r40880 = -r40879;
        double r40881 = exp(r40880);
        return r40881;
}
↓
double f(double x) {
        double r40882 = 1.0;
        double r40883 = -r40882;
        double r40884 = exp(r40883);
        double r40885 = sqrt(r40884);
        double r40886 = x;
        double r40887 = exp(r40886);
        double r40888 = sqrt(r40887);
        double r40889 = pow(r40888, r40886);
        double r40890 = r40885 * r40889;
        double r40891 = 2.0;
        double r40892 = r40886 / r40891;
        double r40893 = pow(r40887, r40892);
        double r40894 = r40885 * r40893;
        double r40895 = r40890 * r40894;
        return r40895;
}

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 sub-neg0.0

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

  4. Applied distribute-neg-in0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

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

  8. Applied add-sqr-sqrt0.0

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

  9. Applied unpow-prod-down0.0

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

  10. Applied add-sqr-sqrt0.0

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

  11. Applied unswap-sqr0.0

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

  13. Applied pow1/20.0

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

  14. Applied pow-pow0.0

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

  15. Simplified0.0

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

  16. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))