Average Error: 0.3 → 0.3
Time: 12.6s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[e^{-w} \cdot {\left({\ell}^{\left({\left(e^{w}\right)}^{0.25} \cdot \sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
e^{-w} \cdot {\left({\ell}^{\left({\left(e^{w}\right)}^{0.25} \cdot \sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (*
  (exp (- w))
  (pow (pow l (* (pow (exp w) 0.25) (sqrt (exp w)))) (sqrt (sqrt (exp w))))))
double code(double w, double l) {
	return ((double) (((double) exp(((double) -(w)))) * ((double) pow(l, ((double) exp(w))))));
}
↓
double code(double w, double l) {
	return ((double) (((double) exp(((double) -(w)))) * ((double) pow(((double) pow(l, ((double) (((double) pow(((double) exp(w)), 0.25)) * ((double) sqrt(((double) exp(w)))))))), ((double) sqrt(((double) sqrt(((double) exp(w))))))))));
}

Error

Bits error versus w

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.3 bits

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrtError: 0.3 bits

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

  4. Applied pow-unpowError: 0.3 bits

    \[\leadsto e^{-w} \cdot \color{blue}{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{e^{w}}\right)}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrtError: 0.3 bits

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

  7. Applied sqrt-prodError: 0.3 bits

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

  8. Applied pow-unpowError: 0.3 bits

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

  9. Taylor expanded around inf Error: 4.7 bits

    \[\leadsto e^{-w} \cdot {\color{blue}{\left(e^{\left(e^{0.25 \cdot w} \cdot \left(\log 1 - \log \left(\frac{1}{\ell}\right)\right)\right) \cdot \sqrt{e^{w}}}\right)}}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]

  10. SimplifiedError: 0.3 bits

    \[\leadsto e^{-w} \cdot {\color{blue}{\left({\ell}^{\left({\left(e^{w}\right)}^{0.25} \cdot \sqrt{e^{w}}\right)}\right)}}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]

  11. Final simplificationError: 0.3 bits

    \[\leadsto e^{-w} \cdot {\left({\ell}^{\left({\left(e^{w}\right)}^{0.25} \cdot \sqrt{e^{w}}\right)}\right)}^{\left(\sqrt{\sqrt{e^{w}}}\right)}\]

Reproduce

herbie shell --seed 2020204 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))