Average Error: 0.3 → 0.3
Time: 33.1s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\frac{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left({e}^{\left(\frac{w}{2}\right)}\right)}}{e^{w}} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left({e}^{\left(\frac{w}{2}\right)}\right)}}{e^{w}}

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (/ (pow (pow l (sqrt (exp w))) (pow E (/ w 2.0))) (exp w)))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return pow(pow(l, sqrt(exp(w))), pow(((double) M_E), (w / 2.0))) / 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 0.3

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

  2. Simplified0.3

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

  3. Applied add-sqr-sqrt_binary640.3

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

  4. Applied pow-unpow_binary640.3

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

  5. Applied *-un-lft-identity_binary640.3

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

  6. Applied exp-prod_binary640.3

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

  7. Applied sqrt-pow1_binary640.3

    \[\leadsto \frac{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\color{blue}{\left({\left(e^{1}\right)}^{\left(\frac{w}{2}\right)}\right)}}}{e^{w}} \]

  8. Final simplification0.3

    \[\leadsto \frac{{\left({\ell}^{\left(\sqrt{e^{w}}\right)}\right)}^{\left({e}^{\left(\frac{w}{2}\right)}\right)}}{e^{w}} \]

Reproduce

herbie shell --seed 2022024 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))