Average Error: 59.4 → 27.3
Time: 17.0s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;D \cdot D \leq 1.686723812767609 \cdot 10^{+303}:\\ \;\;\;\;0.25 \cdot \frac{M \cdot \left(M \cdot \frac{\left(D \cdot D\right) \cdot h}{d}\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \sqrt{-{M}^{2}}\\ \end{array}\]
\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 1.686723812767609 \cdot 10^{+303}:\\
\;\;\;\;0.25 \cdot \frac{M \cdot \left(M \cdot \frac{\left(D \cdot D\right) \cdot h}{d}\right)}{d}\\

\mathbf{else}:\\
\;\;\;\;\frac{c0}{2 \cdot w} \cdot \sqrt{-{M}^{2}}\\

\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) 1.686723812767609e+303)
   (* 0.25 (/ (* M (* M (/ (* (* D D) h) d))) d))
   (* (/ c0 (* 2.0 w)) (sqrt (- (pow M 2.0))))))
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) <= 1.686723812767609e+303) {
		tmp = 0.25 * ((M * (M * (((D * D) * h) / d))) / d);
	} else {
		tmp = (c0 / (2.0 * w)) * sqrt(-pow(M, 2.0));
	}
	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) < 1.68672381276760915e303

    1. Initial program 59.1

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

    2. Taylor expanded around -inf 38.9

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(0.5 \cdot \frac{w \cdot \left({M}^{2} \cdot \left({D}^{2} \cdot h\right)\right)}{c0 \cdot {d}^{2}}\right)}\]

    3. Simplified39.5

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\left(0.5 \cdot \frac{\left(M \cdot M\right) \cdot \left(w \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{\left(d \cdot d\right) \cdot c0}\right)}\]

    4. Taylor expanded around 0 32.4

      \[\leadsto \color{blue}{0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{2}}}\]

    5. Simplified32.4

      \[\leadsto \color{blue}{0.25 \cdot \frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d \cdot d}}\]
    6. Using strategy rm

    7. Applied associate-/r*_binary6429.4

      \[\leadsto 0.25 \cdot \color{blue}{\frac{\frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d}}{d}}\]

    8. Simplified28.8

      \[\leadsto 0.25 \cdot \frac{\color{blue}{\left(M \cdot M\right) \cdot \frac{\left(D \cdot D\right) \cdot h}{d}}}{d}\]
    9. Using strategy rm

    10. Applied associate-*l*_binary6424.6

      \[\leadsto 0.25 \cdot \frac{\color{blue}{M \cdot \left(M \cdot \frac{\left(D \cdot D\right) \cdot h}{d}\right)}}{d}\]

    if 1.68672381276760915e303 < (*.f64 D D)

    1. Initial program 62.1

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

    2. Taylor expanded around 0 51.3

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

  4. Final simplification27.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;D \cdot D \leq 1.686723812767609 \cdot 10^{+303}:\\ \;\;\;\;0.25 \cdot \frac{M \cdot \left(M \cdot \frac{\left(D \cdot D\right) \cdot h}{d}\right)}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \sqrt{-{M}^{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021128 
(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))))))