Average Error: 59.4 → 35.4
Time: 11.1s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;D \cdot D \leq 1.98204950743704 \cdot 10^{-26}:\\ \;\;\;\;0\\ \mathbf{elif}\;D \cdot D \leq 1.4558957147657655 \cdot 10^{+106}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0}{\frac{w \cdot h}{\frac{d \cdot d}{D \cdot D}}} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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 \cdot D \leq 1.98204950743704 \cdot 10^{-26}:\\
\;\;\;\;0\\

\mathbf{elif}\;D \cdot D \leq 1.4558957147657655 \cdot 10^{+106}:\\
\;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0}{\frac{w \cdot h}{\frac{d \cdot d}{D \cdot D}}} - M \cdot M}\right)\\

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

\end{array}
(FPCore (c0 w h D d M)
 :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))))))
↓
(FPCore (c0 w h D d M)
 :precision binary64
 (if (<= (* D D) 1.98204950743704e-26)
   0.0
   (if (<= (* D D) 1.4558957147657655e+106)
     (*
      (/ c0 (* 2.0 w))
      (+
       (/ (* c0 (* d d)) (* (* D D) (* w h)))
       (sqrt
        (-
         (*
          (/ (* c0 (* d d)) (* (* D D) (* w h)))
          (/ c0 (/ (* w h) (/ (* d d) (* D D)))))
         (* M M)))))
     0.0)))
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 tmp;
	if ((((double) (D * D)) <= 1.98204950743704e-26)) {
		tmp = 0.0;
	} else {
		double tmp_1;
		if ((((double) (D * D)) <= 1.4558957147657655e+106)) {
			tmp_1 = ((double) ((c0 / ((double) (2.0 * w))) * ((double) ((((double) (c0 * ((double) (d * d)))) / ((double) (((double) (D * D)) * ((double) (w * h))))) + ((double) sqrt(((double) (((double) ((((double) (c0 * ((double) (d * d)))) / ((double) (((double) (D * D)) * ((double) (w * h))))) * (c0 / (((double) (w * h)) / (((double) (d * d)) / ((double) (D * D))))))) - ((double) (M * M))))))))));
		} else {
			tmp_1 = 0.0;
		}
		tmp = tmp_1;
	}
	return tmp;
}

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 (*.f64 D D) < 1.98204950743703987e-26 or 1.4558957147657655e106 < (*.f64 D D)

    1. Initial program 60.1

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

    2. Taylor expanded around inf 35.1

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

    4. Applied mul0-rgt_binary6433.3

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

    if 1.98204950743703987e-26 < (*.f64 D D) < 1.4558957147657655e106

    1. Initial program 53.3

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

    3. Applied associate-/l*_binary6454.8

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

    4. Simplified54.8

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

  4. Final simplification35.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;D \cdot D \leq 1.98204950743704 \cdot 10^{-26}:\\ \;\;\;\;0\\ \mathbf{elif}\;D \cdot D \leq 1.4558957147657655 \cdot 10^{+106}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0}{\frac{w \cdot h}{\frac{d \cdot d}{D \cdot D}}} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(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))))))