Average Error: 19.4 → 12.3
Time: 37.1s
Precision: 64
Internal Precision: 384
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{V \cdot \ell} \le -3.2022322594802415 \cdot 10^{+278}:\\ \;\;\;\;\left(c0 \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right) \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le -5.066471781368947 \cdot 10^{-80}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 1.0908688418477978 \cdot 10^{-301}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \end{array}\]

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 (/ 1 (* V l)) < -3.2022322594802415e+278

    1. Initial program 52.3

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

    3. Applied associate-/r*33.2

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

    5. Applied add-sqr-sqrt33.2

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

    6. Applied sqrt-prod33.3

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

    7. Applied associate-*r*33.3

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

    if -3.2022322594802415e+278 < (/ 1 (* V l)) < -5.066471781368947e-80

    1. Initial program 9.1

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

    if -5.066471781368947e-80 < (/ 1 (* V l)) < 1.0908688418477978e-301

    1. Initial program 26.9

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

    3. Applied associate-/r*19.2

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

    if 1.0908688418477978e-301 < (/ 1 (* V l))

    1. Initial program 15.4

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

    3. Applied sqrt-div6.5

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

Runtime

Time bar (total: 37.1s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))