Average Error: 59.7 → 31.3
Time: 20.0s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;d \cdot d \leq 3.412293833312649 \cdot 10^{-117} \lor \neg \left(d \cdot d \leq 1.5860272253884708 \cdot 10^{+144}\right):\\ \;\;\;\;\log 1\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{2}}\\ \end{array}\]
\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 3.412293833312649 \cdot 10^{-117} \lor \neg \left(d \cdot d \leq 1.5860272253884708 \cdot 10^{+144}\right):\\
\;\;\;\;\log 1\\

\mathbf{else}:\\
\;\;\;\;0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{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 (or (<= (* d d) 3.412293833312649e-117)
         (not (<= (* d d) 1.5860272253884708e+144)))
   (log 1.0)
   (* 0.25 (/ (* (pow M 2.0) (* (pow D 2.0) h)) (pow d 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) <= 3.412293833312649e-117) || !((d * d) <= 1.5860272253884708e+144)) {
		tmp = log(1.0);
	} else {
		tmp = 0.25 * ((pow(M, 2.0) * (pow(D, 2.0) * h)) / pow(d, 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) < 3.41229383331264931e-117 or 1.5860272253884708e144 < (*.f64 d d)

    1. Initial program 61.0

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

    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. Simplified44.4

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

    5. Applied add-log-exp_binary64_114045.0

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

    6. Simplified36.6

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

    7. Taylor expanded around inf 31.5

      \[\leadsto \log \color{blue}{1}\]

    if 3.41229383331264931e-117 < (*.f64 d d) < 1.5860272253884708e144

    1. Initial program 54.9

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

    2. Taylor expanded around -inf 37.4

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

    3. Simplified38.2

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

    4. Taylor expanded around 0 30.7

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

  4. Final simplification31.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;d \cdot d \leq 3.412293833312649 \cdot 10^{-117} \lor \neg \left(d \cdot d \leq 1.5860272253884708 \cdot 10^{+144}\right):\\ \;\;\;\;\log 1\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021019 
(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))))))