Average Error: 19.2 → 11.2
Time: 47.9s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{\ell \cdot V} \le -4.575702877914278 \cdot 10^{+299}:\\ \;\;\;\;\sqrt{\frac{1}{\frac{\ell}{\frac{A}{V}}}} \cdot c0\\ \mathbf{if}\;\frac{1}{\ell \cdot V} \le -2.8707985599816365 \cdot 10^{-172}:\\ \;\;\;\;\sqrt{A \cdot \frac{1}{\ell \cdot V}} \cdot c0\\ \mathbf{if}\;\frac{1}{\ell \cdot V} \le 3.1185821779500027 \cdot 10^{-264} \lor \neg \left(\frac{1}{\ell \cdot V} \le 6.46737831082621 \cdot 10^{+280}\right):\\ \;\;\;\;\sqrt{\frac{1}{\frac{\ell}{\frac{A}{V}}}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \end{array}\]

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 3 regimes

  2. if (/ 1 (* V l)) < -4.575702877914278e+299 or -2.8707985599816365e-172 < (/ 1 (* V l)) < 3.1185821779500027e-264 or 6.46737831082621e+280 < (/ 1 (* V l))

    1. Initial program 38.6

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

    3. Applied associate-/r*24.2

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

    5. Applied clear-num24.7

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

    if -4.575702877914278e+299 < (/ 1 (* V l)) < -2.8707985599816365e-172

    1. Initial program 8.8

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

    3. Applied div-inv8.8

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

    if 3.1185821779500027e-264 < (/ 1 (* V l)) < 6.46737831082621e+280

    1. Initial program 9.7

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

    3. Applied div-inv9.8

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

    4. Applied sqrt-prod0.4

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

  4. Applied simplify11.2

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{1}{\ell \cdot V} \le -4.575702877914278 \cdot 10^{+299}:\\ \;\;\;\;\sqrt{\frac{1}{\frac{\ell}{\frac{A}{V}}}} \cdot c0\\ \mathbf{if}\;\frac{1}{\ell \cdot V} \le -2.8707985599816365 \cdot 10^{-172}:\\ \;\;\;\;\sqrt{A \cdot \frac{1}{\ell \cdot V}} \cdot c0\\ \mathbf{if}\;\frac{1}{\ell \cdot V} \le 3.1185821779500027 \cdot 10^{-264} \lor \neg \left(\frac{1}{\ell \cdot V} \le 6.46737831082621 \cdot 10^{+280}\right):\\ \;\;\;\;\sqrt{\frac{1}{\frac{\ell}{\frac{A}{V}}}} \cdot c0\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{\ell \cdot V}}\right)\\ \end{array}}\]

Runtime

Time bar (total: 47.9s)Debug logProfile

herbie shell --seed 2018166 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))