Average Error: 59.5 → 35.6
Time: 12.9s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;w \leq -4.401938303607714 \cdot 10^{+230}:\\ \;\;\;\;0\\ \mathbf{elif}\;w \leq -1.0977777746385034 \cdot 10^{+145} \lor \neg \left(w \leq 6.267249107531437 \cdot 10^{+46}\right) \land w \leq 1.6586793484181144 \cdot 10^{+66}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(2 \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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}\;w \leq -4.401938303607714 \cdot 10^{+230}:\\
\;\;\;\;0\\

\mathbf{elif}\;w \leq -1.0977777746385034 \cdot 10^{+145} \lor \neg \left(w \leq 6.267249107531437 \cdot 10^{+46}\right) \land w \leq 1.6586793484181144 \cdot 10^{+66}:\\
\;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(2 \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\right)\\

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

\end{array}
double code(double c0, double w, double h, double D, double d, double M) {
	return ((double) ((c0 / ((double) (2.0 * w))) * ((double) ((((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D))))) + ((double) sqrt(((double) (((double) ((((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D))))) * (((double) (c0 * ((double) (d * d)))) / ((double) (((double) (w * h)) * ((double) (D * D))))))) - ((double) (M * M))))))))));
}
↓
double code(double c0, double w, double h, double D, double d, double M) {
	double VAR;
	if ((w <= -4.401938303607714e+230)) {
		VAR = 0.0;
	} else {
		double VAR_1;
		if (((w <= -1.0977777746385034e+145) || (!(w <= 6.267249107531437e+46) && (w <= 1.6586793484181144e+66)))) {
			VAR_1 = ((double) ((c0 / ((double) (w * 2.0))) * ((double) (2.0 * ((double) ((c0 / ((double) (w * h))) * ((double) ((d / D) * (d / D)))))))));
		} else {
			VAR_1 = 0.0;
		}
		VAR = VAR_1;
	}
	return VAR;
}

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 w < -4.40193830360771377e230 or -1.0977777746385034e145 < w < 6.26724910753143732e46 or 1.6586793484181144e66 < w

    1. Initial program Error: 59.7 bits

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

    2. Taylor expanded around inf Error: 36.1 bits

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

    4. Applied mul0-rgtError: 34.3 bits

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

    if -4.40193830360771377e230 < w < -1.0977777746385034e145 or 6.26724910753143732e46 < w < 1.6586793484181144e66

    1. Initial program Error: 56.6 bits

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

    3. Applied flip-+Error: 61.4 bits

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

    4. SimplifiedError: 43.9 bits

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

    5. SimplifiedError: 48.7 bits

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \frac{M \cdot M}{\color{blue}{\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right) - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}}\]

    6. Taylor expanded around 0 Error: 58.0 bits

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

    7. SimplifiedError: 50.2 bits

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

  4. Final simplificationError: 35.6 bits

    \[\leadsto \begin{array}{l} \mathbf{if}\;w \leq -4.401938303607714 \cdot 10^{+230}:\\ \;\;\;\;0\\ \mathbf{elif}\;w \leq -1.0977777746385034 \cdot 10^{+145} \lor \neg \left(w \leq 6.267249107531437 \cdot 10^{+46}\right) \land w \leq 1.6586793484181144 \cdot 10^{+66}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(2 \cdot \left(\frac{c0}{w \cdot h} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ 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))))))