Average Error: 60.0 → 33.1
Time: 13.9s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;d \cdot d \leq 1.8523377753969734 \cdot 10^{-162}:\\ \;\;\;\;0\\ \mathbf{elif}\;d \cdot d \leq 9.16870054184859 \cdot 10^{+34}:\\ \;\;\;\;c0 \cdot \frac{\frac{M \cdot M}{\frac{\left(d \cdot d\right) \cdot c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot {d}^{4}}{\left(w \cdot h\right) \cdot {D}^{4}} \cdot \frac{c0}{w \cdot h} - M \cdot M}}}{w \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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 1.8523377753969734 \cdot 10^{-162}:\\
\;\;\;\;0\\

\mathbf{elif}\;d \cdot d \leq 9.16870054184859 \cdot 10^{+34}:\\
\;\;\;\;c0 \cdot \frac{\frac{M \cdot M}{\frac{\left(d \cdot d\right) \cdot c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot {d}^{4}}{\left(w \cdot h\right) \cdot {D}^{4}} \cdot \frac{c0}{w \cdot h} - M \cdot M}}}{w \cdot 2}\\

\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) 1.8523377753969734e-162)
   0.0
   (if (<= (* d d) 9.16870054184859e+34)
     (*
      c0
      (/
       (/
        (* M M)
        (-
         (/ (* (* d d) c0) (* (* w h) (* D D)))
         (sqrt
          (-
           (* (/ (* c0 (pow d 4.0)) (* (* w h) (pow D 4.0))) (/ c0 (* w h)))
           (* M M)))))
       (* w 2.0)))
     0.0)))
double code(double c0, double w, double h, double D, double d, double M) {
	return (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)));
}
↓
double code(double c0, double w, double h, double D, double d, double M) {
	double tmp;
	if ((d * d) <= 1.8523377753969734e-162) {
		tmp = 0.0;
	} else if ((d * d) <= 9.16870054184859e+34) {
		tmp = c0 * (((M * M) / ((((d * d) * c0) / ((w * h) * (D * D))) - sqrt((((c0 * pow(d, 4.0)) / ((w * h) * pow(D, 4.0))) * (c0 / (w * h))) - (M * M)))) / (w * 2.0));
	} else {
		tmp = 0.0;
	}
	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) < 1.85233777539697343e-162 or 9.16870054184858913e34 < (*.f64 d d)

    1. Initial program 60.8

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

    2. Taylor expanded around inf 35.2

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

    4. Applied mul0-rgt_binary64_107131.3

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

    if 1.85233777539697343e-162 < (*.f64 d d) < 9.16870054184858913e34

    1. Initial program 55.1

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

    3. Applied flip-+_binary64_106260.5

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

    4. Simplified43.3

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

    5. Simplified47.2

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

    7. Applied div-inv_binary64_108547.2

      \[\leadsto \color{blue}{\left(c0 \cdot \frac{1}{2 \cdot w}\right)} \cdot \frac{M \cdot M}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}\]

    8. Applied associate-*l*_binary64_103143.6

      \[\leadsto \color{blue}{c0 \cdot \left(\frac{1}{2 \cdot w} \cdot \frac{M \cdot M}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0}{w \cdot h} \cdot \frac{{d}^{4} \cdot c0}{{D}^{4} \cdot \left(w \cdot h\right)} - M \cdot M}}\right)}\]

    9. Simplified43.6

      \[\leadsto c0 \cdot \color{blue}{\frac{\frac{M \cdot M}{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot {d}^{4}}{\left(w \cdot h\right) \cdot {D}^{4}} \cdot \frac{c0}{w \cdot h} - M \cdot M}}}{w \cdot 2}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification33.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;d \cdot d \leq 1.8523377753969734 \cdot 10^{-162}:\\ \;\;\;\;0\\ \mathbf{elif}\;d \cdot d \leq 9.16870054184859 \cdot 10^{+34}:\\ \;\;\;\;c0 \cdot \frac{\frac{M \cdot M}{\frac{\left(d \cdot d\right) \cdot c0}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - \sqrt{\frac{c0 \cdot {d}^{4}}{\left(w \cdot h\right) \cdot {D}^{4}} \cdot \frac{c0}{w \cdot h} - M \cdot M}}}{w \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020277 
(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))))))