Average Error: 18.9 → 12.2
Time: 32.3s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \le -7.550518528887039 \cdot 10^{-277}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{if}\;V \cdot \ell \le 0.0:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{if}\;V \cdot \ell \le 1.1679805268013716 \cdot 10^{+293}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \end{array}\]

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Derivation

  1. Split input into 4 regimes

  2. if (* V l) < -7.550518528887039e-277

    1. Initial program 14.0

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

    3. Applied div-inv14.0

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

    if -7.550518528887039e-277 < (* V l) < 0.0

    1. Initial program 56.3

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

    3. Applied associate-/r*37.6

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

    5. Applied sqrt-div38.4

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

    6. Applied associate-*r/38.9

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

    if 0.0 < (* V l) < 1.1679805268013716e+293

    1. Initial program 10.3

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

    3. Applied sqrt-div0.7

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

    if 1.1679805268013716e+293 < (* V l)

    1. Initial program 40.4

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

    3. Applied associate-/r*23.4

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

Runtime

Time bar (total: 32.3s)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))