Average Error: 18.7 → 12.2
Time: 34.6s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{V \cdot \ell} \le -4.144937970461657 \cdot 10^{+303}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt[3]{\frac{\frac{A}{\ell}}{V}}}\right) \cdot \left|\sqrt[3]{\frac{\frac{A}{\ell}}{V}}\right|\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le -3.542311786339384 \cdot 10^{-284}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 7.889884570616071 \cdot 10^{-304}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]

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 4 regimes

  2. if (/ 1 (* V l)) < -4.144937970461657e+303

    1. Initial program 57.6

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

    3. Applied add-cube-cbrt57.6

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

    4. Applied sqrt-prod57.6

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

    5. Applied associate-*r*57.6

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

    6. Applied simplify57.6

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

    7. Taylor expanded around 0 62.2

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

    8. Applied simplify35.1

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

    if -4.144937970461657e+303 < (/ 1 (* V l)) < -3.542311786339384e-284

    1. Initial program 9.7

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

    if -3.542311786339384e-284 < (/ 1 (* V l)) < 7.889884570616071e-304

    1. Initial program 38.3

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

    3. Applied associate-/r*21.4

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

    if 7.889884570616071e-304 < (/ 1 (* V l))

    1. Initial program 15.2

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

    3. Applied sqrt-div6.5

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

    4. Applied associate-*r/8.6

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}}\]
  3. Recombined 4 regimes into one program.

Runtime

Time bar (total: 34.6s)Debug logProfile

herbie shell --seed 2019053 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))