Average Error: 0.0 → 0.0
Time: 1.7m
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\left(\left(e^{-x} \cdot {\left(e^{-x}\right)}^{\left(-x\right)}\right) \cdot {\left(\frac{1}{\sqrt{e}}\right)}^{\left(1 - x\right)}\right) \cdot {\left(\frac{1}{\sqrt{e}}\right)}^{\left(1 - x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
\left(\left(e^{-x} \cdot {\left(e^{-x}\right)}^{\left(-x\right)}\right) \cdot {\left(\frac{1}{\sqrt{e}}\right)}^{\left(1 - x\right)}\right) \cdot {\left(\frac{1}{\sqrt{e}}\right)}^{\left(1 - x\right)}
double f(double x) {
        double r10937911 = 1.0;
        double r10937912 = x;
        double r10937913 = r10937912 * r10937912;
        double r10937914 = r10937911 - r10937913;
        double r10937915 = -r10937914;
        double r10937916 = exp(r10937915);
        return r10937916;
}
↓
double f(double x) {
        double r10937917 = x;
        double r10937918 = -r10937917;
        double r10937919 = exp(r10937918);
        double r10937920 = pow(r10937919, r10937918);
        double r10937921 = r10937919 * r10937920;
        double r10937922 = 1.0;
        double r10937923 = exp(1.0);
        double r10937924 = sqrt(r10937923);
        double r10937925 = r10937922 / r10937924;
        double r10937926 = r10937922 - r10937917;
        double r10937927 = pow(r10937925, r10937926);
        double r10937928 = r10937921 * r10937927;
        double r10937929 = r10937928 * r10937927;
        return r10937929;
}

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. Using strategy rm

  8. Applied distribute-neg-in0.0

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

  9. Applied exp-sum0.0

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

  10. Applied unpow-prod-down0.0

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

  11. Simplified0.0

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

  13. Applied add-sqr-sqrt1.0

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

  14. Applied *-un-lft-identity1.0

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

  15. Applied times-frac0.0

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

  16. Applied unpow-prod-down0.0

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

  17. Applied associate-*l*0.0

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

  19. Applied sub-neg0.0

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

  20. Applied unpow-prod-up0.0

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

  21. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))