Average Error: 59.6 → 19.3
Time: 24.0s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
↓
\[\begin{array}{l} \mathbf{if}\;h \leq -2.062391211447 \cdot 10^{-312}:\\ \;\;\;\;0.25 \cdot \left(\left(\left(D \cdot M\right) \cdot \left(\left(D \cdot M\right) \cdot \frac{1}{d}\right)\right) \cdot \frac{h}{d}\right)\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot {\left(\frac{D \cdot \left(M \cdot \sqrt{h}\right)}{d}\right)}^{2}\\ \end{array} \]
\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}\;h \leq -2.062391211447 \cdot 10^{-312}:\\
\;\;\;\;0.25 \cdot \left(\left(\left(D \cdot M\right) \cdot \left(\left(D \cdot M\right) \cdot \frac{1}{d}\right)\right) \cdot \frac{h}{d}\right)\\

\mathbf{else}:\\
\;\;\;\;0.25 \cdot {\left(\frac{D \cdot \left(M \cdot \sqrt{h}\right)}{d}\right)}^{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 (<= h -2.062391211447e-312)
   (* 0.25 (* (* (* D M) (* (* D M) (/ 1.0 d))) (/ h d)))
   (* 0.25 (pow (/ (* D (* M (sqrt h))) 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 (h <= -2.062391211447e-312) {
		tmp = 0.25 * (((D * M) * ((D * M) * (1.0 / d))) * (h / d));
	} else {
		tmp = 0.25 * pow(((D * (M * sqrt(h))) / 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 h < -2.0623912114467e-312

    1. Initial program 59.6

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

    2. Taylor expanded in c0 around -inf 42.2

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

    3. Taylor expanded in c0 around 0 35.5

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

    4. Applied egg-rr23.5

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

    5. Applied egg-rr20.9

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

    if -2.0623912114467e-312 < h

    1. Initial program 59.5

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

    2. Taylor expanded in c0 around -inf 42.1

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

    3. Taylor expanded in c0 around 0 35.6

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

    4. Applied egg-rr17.7

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

  4. Final simplification19.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;h \leq -2.062391211447 \cdot 10^{-312}:\\ \;\;\;\;0.25 \cdot \left(\left(\left(D \cdot M\right) \cdot \left(\left(D \cdot M\right) \cdot \frac{1}{d}\right)\right) \cdot \frac{h}{d}\right)\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot {\left(\frac{D \cdot \left(M \cdot \sqrt{h}\right)}{d}\right)}^{2}\\ \end{array} \]

Reproduce

herbie shell --seed 2022130 
(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))))))