Average Error: 59.3 → 34.5
Time: 32.3s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;d \le 1.028014946374977112793459567345674978253 \cdot 10^{-41}:\\ \;\;\;\;0\\ \mathbf{elif}\;d \le 1.879132275263087348510262122271649682884 \cdot 10^{52}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(2 \cdot \frac{{d}^{2} \cdot c0}{w \cdot \left({D}^{2} \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)
↓
\begin{array}{l}
\mathbf{if}\;d \le 1.028014946374977112793459567345674978253 \cdot 10^{-41}:\\
\;\;\;\;0\\

\mathbf{elif}\;d \le 1.879132275263087348510262122271649682884 \cdot 10^{52}:\\
\;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(2 \cdot \frac{{d}^{2} \cdot c0}{w \cdot \left({D}^{2} \cdot h\right)}\right)\\

\mathbf{else}:\\
\;\;\;\;0\\

\end{array}
double f(double c0, double w, double h, double D, double d, double M) {
        double r106430 = c0;
        double r106431 = 2.0;
        double r106432 = w;
        double r106433 = r106431 * r106432;
        double r106434 = r106430 / r106433;
        double r106435 = d;
        double r106436 = r106435 * r106435;
        double r106437 = r106430 * r106436;
        double r106438 = h;
        double r106439 = r106432 * r106438;
        double r106440 = D;
        double r106441 = r106440 * r106440;
        double r106442 = r106439 * r106441;
        double r106443 = r106437 / r106442;
        double r106444 = r106443 * r106443;
        double r106445 = M;
        double r106446 = r106445 * r106445;
        double r106447 = r106444 - r106446;
        double r106448 = sqrt(r106447);
        double r106449 = r106443 + r106448;
        double r106450 = r106434 * r106449;
        return r106450;
}
↓
double f(double c0, double w, double h, double D, double d, double __attribute__((unused)) M) {
        double r106451 = d;
        double r106452 = 1.0280149463749771e-41;
        bool r106453 = r106451 <= r106452;
        double r106454 = 0.0;
        double r106455 = 1.8791322752630873e+52;
        bool r106456 = r106451 <= r106455;
        double r106457 = c0;
        double r106458 = 2.0;
        double r106459 = w;
        double r106460 = r106458 * r106459;
        double r106461 = r106457 / r106460;
        double r106462 = 2.0;
        double r106463 = pow(r106451, r106462);
        double r106464 = r106463 * r106457;
        double r106465 = D;
        double r106466 = pow(r106465, r106462);
        double r106467 = h;
        double r106468 = r106466 * r106467;
        double r106469 = r106459 * r106468;
        double r106470 = r106464 / r106469;
        double r106471 = r106462 * r106470;
        double r106472 = r106461 * r106471;
        double r106473 = r106456 ? r106472 : r106454;
        double r106474 = r106453 ? r106454 : r106473;
        return r106474;
}

Error

Bits error versus c0

Bits error versus w

Bits error versus h

Bits error versus D

Bits error versus d

Bits error versus M

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if d < 1.0280149463749771e-41 or 1.8791322752630873e+52 < d

    1. Initial program 59.9

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

    2. Taylor expanded around inf 34.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{0}\]
    3. Using strategy rm

    4. Applied add-cbrt-cube34.6

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\sqrt[3]{\left(0 \cdot 0\right) \cdot 0}}\]

    5. Applied add-cbrt-cube41.5

      \[\leadsto \frac{c0}{2 \cdot \color{blue}{\sqrt[3]{\left(w \cdot w\right) \cdot w}}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

    6. Applied add-cbrt-cube41.5

      \[\leadsto \frac{c0}{\color{blue}{\sqrt[3]{\left(2 \cdot 2\right) \cdot 2}} \cdot \sqrt[3]{\left(w \cdot w\right) \cdot w}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

    7. Applied cbrt-unprod41.5

      \[\leadsto \frac{c0}{\color{blue}{\sqrt[3]{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)}}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

    8. Applied add-cbrt-cube48.4

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(c0 \cdot c0\right) \cdot c0}}}{\sqrt[3]{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

    9. Applied cbrt-undiv48.8

      \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(c0 \cdot c0\right) \cdot c0}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)}}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

    10. Applied cbrt-unprod48.8

      \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(c0 \cdot c0\right) \cdot c0}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)} \cdot \left(\left(0 \cdot 0\right) \cdot 0\right)}}\]

    11. Simplified32.7

      \[\leadsto \sqrt[3]{\color{blue}{0}}\]

    if 1.0280149463749771e-41 < d < 1.8791322752630873e+52

    1. Initial program 52.7

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
    2. Using strategy rm

    3. Applied associate-/l*53.8

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(\color{blue}{\frac{c0}{\frac{\left(w \cdot h\right) \cdot \left(D \cdot D\right)}{d \cdot d}}} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

    4. Taylor expanded around inf 54.7

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(2 \cdot \frac{{d}^{2} \cdot c0}{w \cdot \left({D}^{2} \cdot h\right)}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification34.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;d \le 1.028014946374977112793459567345674978253 \cdot 10^{-41}:\\ \;\;\;\;0\\ \mathbf{elif}\;d \le 1.879132275263087348510262122271649682884 \cdot 10^{52}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(2 \cdot \frac{{d}^{2} \cdot c0}{w \cdot \left({D}^{2} \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))