Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{2}\right)}^{\left(\frac{x \cdot x - 1}{2}\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{2}\right)}^{\left(\frac{x \cdot x - 1}{2}\right)}
(FPCore (x) :precision binary64 (exp (- (- 1.0 (* x x)))))
↓
(FPCore (x) :precision binary64 (pow (exp 2.0) (/ (- (* x x) 1.0) 2.0)))
double code(double x) {
	return exp(-(1.0 - (x * x)));
}
↓
double code(double x) {
	return pow(exp(2.0), (((x * x) - 1.0) / 2.0));
}

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-sqrt_binary64_4410.0

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

  6. Applied *-un-lft-identity_binary64_4190.0

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

  7. Applied exp-prod_binary64_4710.0

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

  8. Applied sqrt-pow1_binary64_4370.0

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

  9. Applied *-un-lft-identity_binary64_4190.0

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

  10. Applied exp-prod_binary64_4710.0

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

  11. Applied sqrt-pow1_binary64_4370.0

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

  12. Applied pow-prod-down_binary64_4900.0

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

  13. Simplified0.0

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

  14. Final simplification0.0

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

Reproduce

herbie shell --seed 2020349 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1.0 (* x x)))))