Average Error: 18.9 → 12.1
Time: 17.3s
Precision: 64
Internal Precision: 128
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.1916098869030572 \cdot 10^{+82}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \le -3.8932537765216586 \cdot 10^{-234}:\\ \;\;\;\;\frac{1}{\frac{\sqrt{\frac{V \cdot \ell}{A}}}{c0}}\\ \mathbf{elif}\;V \cdot \ell \le 4.350192847148013 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{\sqrt{\frac{\ell}{A} \cdot V}}{c0}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right) \cdot c0\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if (* V l) < -1.1916098869030572e+82

    1. Initial program 22.1

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

    3. Applied clear-num22.5

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}\]
    4. Using strategy rm

    5. Applied sqrt-div22.5

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

    6. Applied associate-*r/22.5

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{1}}{\sqrt{\frac{V \cdot \ell}{A}}}}\]
    7. Using strategy rm

    8. Applied associate-/l*17.8

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

    if -1.1916098869030572e+82 < (* V l) < -3.8932537765216586e-234

    1. Initial program 7.8

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

    3. Applied clear-num7.9

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}\]
    4. Using strategy rm

    5. Applied sqrt-div7.1

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

    6. Applied associate-*r/7.0

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{1}}{\sqrt{\frac{V \cdot \ell}{A}}}}\]
    7. Using strategy rm

    8. Applied clear-num7.3

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

    if -3.8932537765216586e-234 < (* V l) < 4.350192847148013e-293

    1. Initial program 48.7

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

    3. Applied clear-num48.7

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}}\]
    4. Using strategy rm

    5. Applied sqrt-div48.4

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

    6. Applied associate-*r/48.4

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{1}}{\sqrt{\frac{V \cdot \ell}{A}}}}\]
    7. Using strategy rm

    8. Applied clear-num48.5

      \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{\frac{V \cdot \ell}{A}}}{c0 \cdot \sqrt{1}}}}\]
    9. Using strategy rm

    10. Applied *-un-lft-identity48.5

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

    11. Applied associate-/r*48.5

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

    12. Simplified29.9

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

    if 4.350192847148013e-293 < (* V l)

    1. Initial program 14.2

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

    3. Applied div-inv14.2

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

    4. Applied sqrt-prod6.7

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

  4. Final simplification12.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.1916098869030572 \cdot 10^{+82}:\\ \;\;\;\;\frac{c0}{\sqrt{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{elif}\;V \cdot \ell \le -3.8932537765216586 \cdot 10^{-234}:\\ \;\;\;\;\frac{1}{\frac{\sqrt{\frac{V \cdot \ell}{A}}}{c0}}\\ \mathbf{elif}\;V \cdot \ell \le 4.350192847148013 \cdot 10^{-293}:\\ \;\;\;\;\frac{1}{\frac{\sqrt{\frac{\ell}{A} \cdot V}}{c0}}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right) \cdot c0\\ \end{array}\]

Runtime

Time bar (total: 17.3s)Debug logProfile

herbie shell --seed 2018336 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))