Average Error: 18.8 → 12.5
Time: 37.1s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -4.14972561063754 \cdot 10^{+256}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{\ell}} \cdot c0}{\sqrt{V}}\\ \mathbf{if}\;\frac{A}{V} \le -1.4430395126553322 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{if}\;\frac{A}{V} \le 4.9406564584125 \cdot 10^{-323} \lor \neg \left(\frac{A}{V} \le +\infty\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Derivation

  1. Split input into 4 regimes

  2. if (/ A V) < -4.14972561063754e+256

    1. Initial program 33.2

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

    3. Applied associate-/r*50.6

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

    5. Applied div-inv50.6

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

    7. Applied associate-*l/33.2

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

    8. Applied sqrt-div39.3

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

    9. Applied associate-*r/39.6

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

    10. Applied simplify39.7

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

    if -4.14972561063754e+256 < (/ A V) < -1.4430395126553322e-206

    1. Initial program 15.2

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

    3. Applied associate-/r*8.2

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

    5. Applied div-inv8.2

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

    if -1.4430395126553322e-206 < (/ A V) < 4.9406564584125e-323 or +inf.0 < (/ A V)

    1. Initial program 21.2

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

    3. Applied clear-num22.2

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

    if 4.9406564584125e-323 < (/ A V) < +inf.0

    1. Initial program 18.2

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

    3. Applied associate-/r*15.6

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

    5. Applied sqrt-div7.2

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

  4. Applied simplify12.5

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -4.14972561063754 \cdot 10^{+256}:\\ \;\;\;\;\frac{\sqrt{\frac{A}{\ell}} \cdot c0}{\sqrt{V}}\\ \mathbf{if}\;\frac{A}{V} \le -1.4430395126553322 \cdot 10^{-206}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{if}\;\frac{A}{V} \le 4.9406564584125 \cdot 10^{-323} \lor \neg \left(\frac{A}{V} \le +\infty\right):\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{\ell \cdot V}{A}}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}}\]

Runtime

Time bar (total: 37.1s)Debug logProfile

herbie shell --seed '#(1071979731 1496239409 439705970 2863295848 982327776 189749553)' +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))