Average Error: 18.5 → 11.3
Time: 56.5s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -1.249767358331218 \cdot 10^{+215}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}}\\ \mathbf{if}\;V \cdot \ell \le -4.524482883968884 \cdot 10^{-298}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{1}}{\sqrt{\frac{V \cdot \ell}{A}}}\\ \mathbf{if}\;V \cdot \ell \le 5.6763202050701 \cdot 10^{-320}:\\ \;\;\;\;c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\\ \mathbf{if}\;V \cdot \ell \le 1.3844248042751056 \cdot 10^{+273}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{1}}{\frac{\sqrt{V \cdot \ell}}{\sqrt{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}}\\ \end{array}\]

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) < -1.249767358331218e+215 or 1.3844248042751056e+273 < (* V l)

    1. Initial program 32.6

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

    3. Applied clear-num32.8

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

    5. Applied associate-/l*21.8

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

    if -1.249767358331218e+215 < (* V l) < -4.524482883968884e-298

    1. Initial program 8.9

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

    3. Applied clear-num9.3

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

    5. Applied sqrt-div9.0

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

    6. Applied associate-*r/9.0

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

    if -4.524482883968884e-298 < (* V l) < 5.6763202050701e-320

    1. Initial program 58.1

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

    3. Applied clear-num58.1

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

    5. Applied associate-/l*35.1

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

    7. Applied associate-/r/35.1

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

    8. Applied sqrt-prod39.5

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

    if 5.6763202050701e-320 < (* V l) < 1.3844248042751056e+273

    1. Initial program 9.4

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

    3. Applied clear-num9.9

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

    5. Applied sqrt-div9.7

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

    6. Applied associate-*r/9.6

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

    8. Applied sqrt-div0.6

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

Runtime

Time bar (total: 56.5s)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))