Average Error: 18.7 → 11.6
Time: 22.7s
Precision: 64
Internal Precision: 320
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -1.114378691831571 \cdot 10^{+295}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{\ell}}}{\sqrt{V}}\\ \mathbf{elif}\;\frac{A}{V} \le -2.9812881782882438 \cdot 10^{-288}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{elif}\;\frac{A}{V} \le 3.5883047723267483 \cdot 10^{-298}:\\ \;\;\;\;\sqrt{\frac{A}{\ell \cdot V}} \cdot c0\\ \mathbf{elif}\;\frac{A}{V} \le 3.511639093455415 \cdot 10^{+256}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

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 5 regimes

  2. if (/ A V) < -1.114378691831571e+295

    1. Initial program 33.2

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

    2. Initial simplification58.3

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

    4. Applied div-inv58.3

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

    6. Applied associate-*l/33.2

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

    7. Applied sqrt-div38.3

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

    8. Simplified38.2

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

    if -1.114378691831571e+295 < (/ A V) < -2.9812881782882438e-288

    1. Initial program 15.8

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

    2. Initial simplification9.7

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

    4. Applied div-inv9.7

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

    if -2.9812881782882438e-288 < (/ A V) < 3.5883047723267483e-298

    1. Initial program 22.7

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

    if 3.5883047723267483e-298 < (/ A V) < 3.511639093455415e+256

    1. Initial program 15.7

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

    2. Initial simplification9.5

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

    4. Applied sqrt-div0.4

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

    if 3.511639093455415e+256 < (/ A V)

    1. Initial program 31.4

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

    2. Initial simplification49.9

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

    4. Applied div-inv49.9

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

    6. Applied frac-times31.4

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

    7. Applied sqrt-div37.4

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

    8. Applied associate-*r/38.6

      \[\leadsto \color{blue}{\frac{c0 \cdot \sqrt{A \cdot 1}}{\sqrt{V \cdot \ell}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification11.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -1.114378691831571 \cdot 10^{+295}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{\ell}}}{\sqrt{V}}\\ \mathbf{elif}\;\frac{A}{V} \le -2.9812881782882438 \cdot 10^{-288}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{elif}\;\frac{A}{V} \le 3.5883047723267483 \cdot 10^{-298}:\\ \;\;\;\;\sqrt{\frac{A}{\ell \cdot V}} \cdot c0\\ \mathbf{elif}\;\frac{A}{V} \le 3.511639093455415 \cdot 10^{+256}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{A}}{\sqrt{\ell \cdot V}}\\ \end{array}\]

Runtime

Time bar (total: 22.7s)Debug logProfile

herbie shell --seed 2018216 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))