Average Error: 59.6 → 32.1
Time: 58.6s
Precision: 64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2} \le 1.884987459885323114731507884787749259003 \cdot 10^{277}:\\ \;\;\;\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2} \cdot \frac{0}{w}\\ \end{array}\]
\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}\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2} \le 1.884987459885323114731507884787749259003 \cdot 10^{277}:\\
\;\;\;\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2}\\

\mathbf{else}:\\
\;\;\;\;\frac{c0}{2} \cdot \frac{0}{w}\\

\end{array}
double f(double c0, double w, double h, double D, double d, double M) {
        double r6032474 = c0;
        double r6032475 = 2.0;
        double r6032476 = w;
        double r6032477 = r6032475 * r6032476;
        double r6032478 = r6032474 / r6032477;
        double r6032479 = d;
        double r6032480 = r6032479 * r6032479;
        double r6032481 = r6032474 * r6032480;
        double r6032482 = h;
        double r6032483 = r6032476 * r6032482;
        double r6032484 = D;
        double r6032485 = r6032484 * r6032484;
        double r6032486 = r6032483 * r6032485;
        double r6032487 = r6032481 / r6032486;
        double r6032488 = r6032487 * r6032487;
        double r6032489 = M;
        double r6032490 = r6032489 * r6032489;
        double r6032491 = r6032488 - r6032490;
        double r6032492 = sqrt(r6032491);
        double r6032493 = r6032487 + r6032492;
        double r6032494 = r6032478 * r6032493;
        return r6032494;
}
↓
double f(double c0, double w, double h, double D, double d, double M) {
        double r6032495 = d;
        double r6032496 = r6032495 * r6032495;
        double r6032497 = c0;
        double r6032498 = r6032496 * r6032497;
        double r6032499 = D;
        double r6032500 = r6032499 * r6032499;
        double r6032501 = w;
        double r6032502 = h;
        double r6032503 = r6032501 * r6032502;
        double r6032504 = r6032500 * r6032503;
        double r6032505 = r6032498 / r6032504;
        double r6032506 = r6032505 * r6032505;
        double r6032507 = M;
        double r6032508 = r6032507 * r6032507;
        double r6032509 = r6032506 - r6032508;
        double r6032510 = sqrt(r6032509);
        double r6032511 = r6032505 + r6032510;
        double r6032512 = 2.0;
        double r6032513 = r6032501 * r6032512;
        double r6032514 = r6032497 / r6032513;
        double r6032515 = r6032511 * r6032514;
        double r6032516 = 1.884987459885323e+277;
        bool r6032517 = r6032515 <= r6032516;
        double r6032518 = r6032497 / r6032512;
        double r6032519 = 0.0;
        double r6032520 = r6032519 / r6032501;
        double r6032521 = r6032518 * r6032520;
        double r6032522 = r6032517 ? r6032515 : r6032521;
        return r6032522;
}

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 (* (/ c0 (* 2.0 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))))) < 1.884987459885323e+277

    1. Initial program 36.0

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

    if 1.884987459885323e+277 < (* (/ c0 (* 2.0 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)))))

    1. Initial program 64.0

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

    2. Simplified57.3

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

    3. Taylor expanded around inf 31.4

      \[\leadsto \frac{c0}{2} \cdot \frac{\color{blue}{0}}{w}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification32.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2} \le 1.884987459885323114731507884787749259003 \cdot 10^{277}:\\ \;\;\;\;\left(\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{\left(d \cdot d\right) \cdot c0}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M}\right) \cdot \frac{c0}{w \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2} \cdot \frac{0}{w}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2.0 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))))))