Average Error: 18.8 → 11.5
Time: 39.2s
Precision: 64
Internal Precision: 384
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{A}{V} = -\infty:\\ \;\;\;\;c0 \cdot \frac{\sqrt{\frac{A}{\ell}}}{\sqrt{V}}\\ \mathbf{if}\;\frac{A}{V} \le -8.662013682143746 \cdot 10^{-304}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\\ \mathbf{if}\;\frac{A}{V} \le 2.4578593314605 \cdot 10^{-315}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{if}\;\frac{A}{V} \le 3.33359585043328 \cdot 10^{+268}:\\ \;\;\;\;\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \end{array}\]

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 (/ A V)

    1. Initial program 34.0

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

    3. Applied associate-/r*61.0

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

    5. Applied div-inv61.0

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{A}{V} \cdot \frac{1}{\ell}}}\]
    6. Using strategy rm

    7. Applied associate-*l/34.0

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

    8. Applied sqrt-div39.3

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

    9. Applied simplify39.2

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

    if (/ A V) < -8.662013682143746e-304

    1. Initial program 16.3

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

    3. Applied associate-/r*10.2

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

    5. Applied div-inv10.3

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

    if -8.662013682143746e-304 < (/ A V) < 2.4578593314605e-315 or 3.33359585043328e+268 < (/ A V)

    1. Initial program 25.7

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

    3. Applied div-inv25.7

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

    if 2.4578593314605e-315 < (/ A V) < 3.33359585043328e+268

    1. Initial program 16.1

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

    3. Applied associate-/r*9.8

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

    5. Applied sqrt-div0.4

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

    6. Applied associate-*r/2.4

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

Runtime

Time bar (total: 39.2s)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  (* c0 (sqrt (/ A (* V l)))))