Average Error: 18.9 → 11.6
Time: 34.5s
Precision: 64
Internal Precision: 576
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.2428802990981264 \cdot 10^{+257}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{\ell \cdot V}} \cdot c0\\ \mathbf{if}\;\frac{A}{V} \le -8.461225783080607 \cdot 10^{-107}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{if}\;\frac{A}{V} \le 3.8694727316641 \cdot 10^{-319} \lor \neg \left(\frac{A}{V} \le 1.1045753616166919 \cdot 10^{+303}\right):\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}\]

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) < -2.2428802990981264e+257

    1. Initial program 31.5

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

    3. Applied sqrt-div38.7

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

    if -2.2428802990981264e+257 < (/ A V) < -8.461225783080607e-107

    1. Initial program 15.1

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

    3. Applied associate-/r*7.3

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

    5. Applied div-inv7.3

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

    if -8.461225783080607e-107 < (/ A V) < 3.8694727316641e-319 or 1.1045753616166919e+303 < (/ A V)

    1. Initial program 23.0

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

    3. Applied div-inv23.1

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

    if 3.8694727316641e-319 < (/ A V) < 1.1045753616166919e+303

    1. Initial program 15.9

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

    3. Applied associate-/r*10.3

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

    5. Applied sqrt-div0.6

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

  4. Applied simplify11.6

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{A}{V} \le -2.2428802990981264 \cdot 10^{+257}:\\ \;\;\;\;\frac{\sqrt{A}}{\sqrt{\ell \cdot V}} \cdot c0\\ \mathbf{if}\;\frac{A}{V} \le -8.461225783080607 \cdot 10^{-107}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\ell} \cdot \frac{A}{V}}\\ \mathbf{if}\;\frac{A}{V} \le 3.8694727316641 \cdot 10^{-319} \lor \neg \left(\frac{A}{V} \le 1.1045753616166919 \cdot 10^{+303}\right):\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{\ell \cdot V}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \end{array}}\]

Runtime

Time bar (total: 34.5s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))