Average Error: 18.2 → 11.4
Time: 34.0s
Precision: 64
Internal Precision: 384
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{V \cdot \ell} \le -3.4242211174656277 \cdot 10^{+274}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le -1.463765466628822 \cdot 10^{-144}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V \cdot \ell}{A}}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 0.0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 9.889523785479379 \cdot 10^{+236}:\\ \;\;\;\;c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

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)) < -3.4242211174656277e+274

    1. Initial program 49.8

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

    3. Applied associate-/r*32.5

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

    5. Applied sqrt-div38.1

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

    if -3.4242211174656277e+274 < (/ 1 (* V l)) < -1.463765466628822e-144

    1. Initial program 7.6

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

    3. Applied clear-num7.8

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

    if -1.463765466628822e-144 < (/ 1 (* V l)) < 0.0 or 9.889523785479379e+236 < (/ 1 (* V l))

    1. Initial program 33.4

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

    3. Applied associate-/r*22.6

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

    if 0.0 < (/ 1 (* V l)) < 9.889523785479379e+236

    1. Initial program 8.4

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

    3. Applied div-inv8.4

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

    4. Applied sqrt-prod0.4

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

Runtime

Time bar (total: 34.0s)Debug log

herbie shell --seed '#(2479486159 2123901208 2662424940 349789437 14252662 202027171)' 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))