Average Error: 18.6 → 12.4
Time: 32.1s
Precision: 64
Internal Precision: 384
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{V \cdot \ell} \le -4.048376700172577 \cdot 10^{-220}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 0.0:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{if}\;\frac{1}{V \cdot \ell} \le 5.56635184074992 \cdot 10^{+264}:\\ \;\;\;\;\left(c0 \cdot \sqrt{A}\right) \cdot \sqrt{\frac{1}{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Derivation

  1. Split input into 3 regimes

  2. if (/ 1 (* V l)) < -4.048376700172577e-220

    1. Initial program 15.6

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

    if -4.048376700172577e-220 < (/ 1 (* V l)) < 0.0 or 5.56635184074992e+264 < (/ 1 (* V l))

    1. Initial program 37.8

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

    3. Applied associate-/r*23.0

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

    if 0.0 < (/ 1 (* V l)) < 5.56635184074992e+264

    1. Initial program 9.3

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

    3. Applied div-inv9.3

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

    4. Applied sqrt-prod0.4

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

    5. Applied associate-*r*2.4

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

Runtime

Time bar (total: 32.1s)Debug logProfile

herbie shell --seed '#(1064269945 2896236262 301053905 1701069080 1701464310 1614783279)' +o rules:numerics
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))