Average Error: 19.1 → 8.9
Time: 51.0s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.401466221489304 \cdot 10^{+300}:\\ \;\;\;\;\sqrt{\left(\sqrt[3]{\frac{A}{\ell \cdot V}} \cdot \sqrt[3]{\frac{A}{\ell \cdot V}}\right) \cdot \sqrt[3]{\frac{A}{\ell \cdot V}}} \cdot c0\\ \mathbf{if}\;\frac{A}{V} \le -4.46606401392334 \cdot 10^{-309}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{\frac{A}{V}}}{\ell}} \cdot \left|\sqrt[3]{\frac{1}{V}} \cdot \sqrt[3]{A}\right|\right)\\ \mathbf{if}\;\frac{A}{V} \le 8.4649107013579 \cdot 10^{-318} \lor \neg \left(\frac{A}{V} \le 8.309383405127115 \cdot 10^{+303}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\ell}} \cdot \left(\sqrt{\frac{A}{V}} \cdot c0\right)\\ \end{array}\]

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 (/ A V) < -2.401466221489304e+300

    1. Initial program 33.3

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

    3. Applied add-cube-cbrt33.6

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

    if -2.401466221489304e+300 < (/ A V) < -4.46606401392334e-309

    1. Initial program 16.4

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

    3. Applied associate-/r*9.8

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

    5. Applied add-cube-cbrt10.3

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

    6. Applied associate-/l*10.3

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

    8. Applied div-inv10.3

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

    9. Applied times-frac10.3

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

    10. Applied sqrt-prod3.6

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

    11. Applied simplify3.6

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

    13. Applied div-inv3.6

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

    14. Applied cbrt-prod3.7

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

    if -4.46606401392334e-309 < (/ A V) < 8.4649107013579e-318 or 8.309383405127115e+303 < (/ A V)

    1. Initial program 26.7

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

    if 8.4649107013579e-318 < (/ A V) < 8.309383405127115e+303

    1. Initial program 16.5

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

    3. Applied associate-/r*10.2

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

    5. Applied div-inv10.3

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

    6. Applied sqrt-prod0.5

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

    7. Applied associate-*r*2.7

      \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{A}{V}}\right) \cdot \sqrt{\frac{1}{\ell}}}\]
  3. Recombined 4 regimes into one program.

  4. Applied simplify8.9

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.401466221489304 \cdot 10^{+300}:\\ \;\;\;\;\sqrt{\left(\sqrt[3]{\frac{A}{\ell \cdot V}} \cdot \sqrt[3]{\frac{A}{\ell \cdot V}}\right) \cdot \sqrt[3]{\frac{A}{\ell \cdot V}}} \cdot c0\\ \mathbf{if}\;\frac{A}{V} \le -4.46606401392334 \cdot 10^{-309}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{\sqrt[3]{\frac{A}{V}}}{\ell}} \cdot \left|\sqrt[3]{\frac{1}{V}} \cdot \sqrt[3]{A}\right|\right)\\ \mathbf{if}\;\frac{A}{V} \le 8.4649107013579 \cdot 10^{-318} \lor \neg \left(\frac{A}{V} \le 8.309383405127115 \cdot 10^{+303}\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1}{\ell}} \cdot \left(\sqrt{\frac{A}{V}} \cdot c0\right)\\ \end{array}}\]

Runtime

Time bar (total: 51.0s)Debug logProfile

herbie shell --seed 2018207 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))