Average Error: 19.6 → 2.6
Time: 40.6s
Precision: binary64
\[[V, l]=\mathsf{sort}([V, l])\]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 6.480870350222167 \cdot 10^{-120}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right)\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 2.834912887754204 \cdot 10^{+157}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right)\\ \end{array}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;\frac{A}{V \cdot \ell} \leq 6.480870350222167 \cdot 10^{-120}:\\
\;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right)\\

\mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 2.834912887754204 \cdot 10^{+157}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\

\mathbf{else}:\\
\;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right)\\

\end{array}
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (if (<= (/ A (* V l)) 6.480870350222167e-120)
   (*
    (* c0 (fabs (/ (cbrt A) (cbrt V))))
    (*
     (sqrt (/ 1.0 (* (cbrt l) (cbrt l))))
     (sqrt (/ (cbrt A) (* (cbrt V) (cbrt l))))))
   (if (<= (/ A (* V l)) 2.834912887754204e+157)
     (* c0 (sqrt (/ (/ A V) l)))
     (*
      (* c0 (fabs (/ (cbrt A) (cbrt V))))
      (*
       (sqrt (/ (cbrt (* (cbrt A) (cbrt A))) (* (cbrt l) (cbrt l))))
       (sqrt (/ (cbrt (cbrt A)) (* (cbrt V) (cbrt l)))))))))
double code(double c0, double A, double V, double l) {
	return c0 * sqrt(A / (V * l));
}
↓
double code(double c0, double A, double V, double l) {
	double tmp;
	if ((A / (V * l)) <= 6.480870350222167e-120) {
		tmp = (c0 * fabs(cbrt(A) / cbrt(V))) * (sqrt(1.0 / (cbrt(l) * cbrt(l))) * sqrt(cbrt(A) / (cbrt(V) * cbrt(l))));
	} else if ((A / (V * l)) <= 2.834912887754204e+157) {
		tmp = c0 * sqrt((A / V) / l);
	} else {
		tmp = (c0 * fabs(cbrt(A) / cbrt(V))) * (sqrt(cbrt(cbrt(A) * cbrt(A)) / (cbrt(l) * cbrt(l))) * sqrt(cbrt(cbrt(A)) / (cbrt(V) * cbrt(l))));
	}
	return tmp;
}

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 A (*.f64 V l)) < 6.48087035022216712e-120

    1. Initial program 23.3

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt_binary64_113623.5

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{V \cdot \ell}}\]

    4. Applied associate-/l*_binary64_104623.6

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}}\]

    5. Simplified21.6

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\color{blue}{\frac{V}{\frac{\sqrt[3]{A}}{\ell}}}}}\]
    6. Using strategy rm

    7. Applied div-inv_binary64_109821.6

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V}{\color{blue}{\sqrt[3]{A} \cdot \frac{1}{\ell}}}}}\]

    8. Applied add-cube-cbrt_binary64_113621.7

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}{\sqrt[3]{A} \cdot \frac{1}{\ell}}}}\]

    9. Applied times-frac_binary64_110721.1

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\color{blue}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}} \cdot \frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}}\]

    10. Applied times-frac_binary64_110719.8

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}}} \cdot \frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}}\]

    11. Applied sqrt-prod_binary64_11179.4

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}\right)}\]

    12. Applied associate-*r*_binary64_10419.9

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}}}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}}\]

    13. Simplified7.7

      \[\leadsto \color{blue}{\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right)} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}\]
    14. Using strategy rm

    15. Applied add-cube-cbrt_binary64_11367.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}}}\]

    16. Applied add-sqr-sqrt_binary64_11237.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}}\]

    17. Applied times-frac_binary64_11077.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\color{blue}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}}\]

    18. Applied *-un-lft-identity_binary64_11017.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{\color{blue}{1 \cdot V}}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    19. Applied cbrt-prod_binary64_11327.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{V}}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    20. Applied times-frac_binary64_11077.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\color{blue}{\frac{\sqrt[3]{1}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}}\]

    21. Applied *-un-lft-identity_binary64_11017.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{\color{blue}{1 \cdot A}}}{\frac{\sqrt[3]{1}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    22. Applied cbrt-prod_binary64_11327.7

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{A}}}{\frac{\sqrt[3]{1}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    23. Applied times-frac_binary64_11076.0

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{1}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}} \cdot \frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}}\]

    24. Applied sqrt-prod_binary64_11171.6

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{1}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\right)}\]

    25. Simplified1.6

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\color{blue}{\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\right)\]

    26. Simplified1.6

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \color{blue}{\sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}}\right)\]

    if 6.48087035022216712e-120 < (/.f64 A (*.f64 V l)) < 2.834912887754204e157

    1. Initial program 0.4

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied associate-/r*_binary64_10454.4

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}}\]

    if 2.834912887754204e157 < (/.f64 A (*.f64 V l))

    1. Initial program 37.4

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt_binary64_113637.7

      \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{V \cdot \ell}}\]

    4. Applied associate-/l*_binary64_104637.7

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V \cdot \ell}{\sqrt[3]{A}}}}}\]

    5. Simplified35.5

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\color{blue}{\frac{V}{\frac{\sqrt[3]{A}}{\ell}}}}}\]
    6. Using strategy rm

    7. Applied div-inv_binary64_109835.5

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{V}{\color{blue}{\sqrt[3]{A} \cdot \frac{1}{\ell}}}}}\]

    8. Applied add-cube-cbrt_binary64_113635.6

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\frac{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}{\sqrt[3]{A} \cdot \frac{1}{\ell}}}}\]

    9. Applied times-frac_binary64_110733.9

      \[\leadsto c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\color{blue}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}} \cdot \frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}}\]

    10. Applied times-frac_binary64_110732.2

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}}} \cdot \frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}}\]

    11. Applied sqrt-prod_binary64_111716.0

      \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}\right)}\]

    12. Applied associate-*r*_binary64_104116.1

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V} \cdot \sqrt[3]{V}}{\sqrt[3]{A}}}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}}\]

    13. Simplified12.0

      \[\leadsto \color{blue}{\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right)} \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\ell}}}}\]
    14. Using strategy rm

    15. Applied add-cube-cbrt_binary64_113612.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{1}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}}}\]

    16. Applied add-sqr-sqrt_binary64_112312.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}}\]

    17. Applied times-frac_binary64_110712.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\sqrt[3]{V}}{\color{blue}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}}\]

    18. Applied *-un-lft-identity_binary64_110112.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\frac{\color{blue}{1 \cdot \sqrt[3]{V}}}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    19. Applied times-frac_binary64_110712.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\color{blue}{\frac{1}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}}\]

    20. Applied add-cube-cbrt_binary64_113612.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}}{\frac{1}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    21. Applied cbrt-prod_binary64_113212.2

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\color{blue}{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}} \cdot \sqrt[3]{\sqrt[3]{A}}}}{\frac{1}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\]

    22. Applied times-frac_binary64_110710.1

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\frac{1}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}}\]

    23. Applied sqrt-prod_binary64_11171.8

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\frac{1}{\frac{\sqrt{1}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}}} \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\right)}\]

    24. Simplified1.8

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\color{blue}{\sqrt{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}} \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\frac{\sqrt[3]{V}}{\frac{\sqrt{1}}{\sqrt[3]{\ell}}}}}\right)\]

    25. Simplified1.8

      \[\leadsto \left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \color{blue}{\sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V \cdot \ell} \leq 6.480870350222167 \cdot 10^{-120}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right)\\ \mathbf{elif}\;\frac{A}{V \cdot \ell} \leq 2.834912887754204 \cdot 10^{+157}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \left(\sqrt{\frac{\sqrt[3]{\sqrt[3]{A} \cdot \sqrt[3]{A}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{\sqrt[3]{A}}}{\sqrt[3]{V} \cdot \sqrt[3]{\ell}}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021096 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))