Average Error: 59.8 → 30.1
Time: 15.5s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;M \cdot M \leq 2.859175354539147 \cdot 10^{-206} \lor \neg \left(M \cdot M \leq 1.7772243551819437 \cdot 10^{+277}\right):\\ \;\;\;\;\log \left({1}^{\left(\frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d \cdot d}\\ \end{array}\]
\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}\;M \cdot M \leq 2.859175354539147 \cdot 10^{-206} \lor \neg \left(M \cdot M \leq 1.7772243551819437 \cdot 10^{+277}\right):\\
\;\;\;\;\log \left({1}^{\left(\frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}\right)\\

\mathbf{else}:\\
\;\;\;\;0.25 \cdot \frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d \cdot d}\\

\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 (or (<= (* M M) 2.859175354539147e-206)
         (not (<= (* M M) 1.7772243551819437e+277)))
   (log (pow 1.0 (/ 1.0 (* c0 (* d d)))))
   (* 0.25 (/ (* (* M M) (* (* D D) h)) (* d d)))))
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 (((M * M) <= 2.859175354539147e-206) || !((M * M) <= 1.7772243551819437e+277)) {
		tmp = log(pow(1.0, (1.0 / (c0 * (d * d)))));
	} else {
		tmp = 0.25 * (((M * M) * ((D * D) * h)) / (d * d));
	}
	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 M M) < 2.85917535453914678e-206 or 1.7772243551819437e277 < (*.f64 M M)

    1. Initial program 58.7

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

    2. Taylor expanded around -inf 43.7

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

    3. Simplified44.7

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

    5. Applied add-log-exp_binary6445.0

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

    6. Simplified35.3

      \[\leadsto \log \color{blue}{\left({\left(e^{\frac{c0}{w} \cdot 0.25}\right)}^{\left(\frac{w \cdot \left(\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)}{c0 \cdot \left(d \cdot d\right)}\right)}\right)}\]
    7. Using strategy rm

    8. Applied div-inv_binary6435.4

      \[\leadsto \log \left({\left(e^{\frac{c0}{w} \cdot 0.25}\right)}^{\color{blue}{\left(\left(w \cdot \left(\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)\right) \cdot \frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}}\right)\]

    9. Applied pow-unpow_binary6430.6

      \[\leadsto \log \color{blue}{\left({\left({\left(e^{\frac{c0}{w} \cdot 0.25}\right)}^{\left(w \cdot \left(\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)\right)}\right)}^{\left(\frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}\right)}\]

    10. Simplified30.6

      \[\leadsto \log \left({\color{blue}{\left({\left(e^{0.25 \cdot \frac{c0}{w}}\right)}^{\left(\left(\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)\right) \cdot w\right)}\right)}}^{\left(\frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}\right)\]

    11. Taylor expanded around 0 29.9

      \[\leadsto \log \left({\color{blue}{1}}^{\left(\frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}\right)\]

    if 2.85917535453914678e-206 < (*.f64 M M) < 1.7772243551819437e277

    1. Initial program 61.5

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

    2. Taylor expanded around -inf 37.6

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

    3. Simplified38.0

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

    4. Taylor expanded around 0 30.3

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

    5. Simplified30.3

      \[\leadsto \color{blue}{0.25 \cdot \frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d \cdot d}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification30.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;M \cdot M \leq 2.859175354539147 \cdot 10^{-206} \lor \neg \left(M \cdot M \leq 1.7772243551819437 \cdot 10^{+277}\right):\\ \;\;\;\;\log \left({1}^{\left(\frac{1}{c0 \cdot \left(d \cdot d\right)}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{\left(M \cdot M\right) \cdot \left(\left(D \cdot D\right) \cdot h\right)}{d \cdot d}\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(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))))))