Average Error: 59.4 → 30.7
Time: 20.4s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;M \cdot M \leq 9.229951502073919 \cdot 10^{-113}:\\ \;\;\;\;\log 1\\ \mathbf{elif}\;M \cdot M \leq 5.490890537452743 \cdot 10^{+271}:\\ \;\;\;\;0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(0.5 \cdot \frac{M \cdot \left(M \cdot \left(w \cdot \left(h \cdot \left(D \cdot D\right)\right)\right)\right)}{c0 \cdot \left(d \cdot d\right)}\right)\\ \end{array}\]
\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 9.229951502073919 \cdot 10^{-113}:\\
\;\;\;\;\log 1\\

\mathbf{elif}\;M \cdot M \leq 5.490890537452743 \cdot 10^{+271}:\\
\;\;\;\;0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{2}}\\

\mathbf{else}:\\
\;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(0.5 \cdot \frac{M \cdot \left(M \cdot \left(w \cdot \left(h \cdot \left(D \cdot D\right)\right)\right)\right)}{c0 \cdot \left(d \cdot d\right)}\right)\\

\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 (<= (* M M) 9.229951502073919e-113)
   (log 1.0)
   (if (<= (* M M) 5.490890537452743e+271)
     (* 0.25 (/ (* (pow M 2.0) (* (pow D 2.0) h)) (pow d 2.0)))
     (*
      (/ c0 (* 2.0 w))
      (* 0.5 (/ (* M (* M (* w (* h (* D D))))) (* c0 (* 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) <= 9.229951502073919e-113) {
		tmp = log(1.0);
	} else if ((M * M) <= 5.490890537452743e+271) {
		tmp = 0.25 * ((pow(M, 2.0) * (pow(D, 2.0) * h)) / pow(d, 2.0));
	} else {
		tmp = (c0 / (2.0 * w)) * (0.5 * ((M * (M * (w * (h * (D * D))))) / (c0 * (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 3 regimes

  2. if (*.f64 M M) < 9.2299515020739188e-113

    1. Initial program 56.5

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

    2. Taylor expanded around -inf 36.7

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

    3. Simplified37.6

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

    5. Applied add-log-exp_binary64_114038.0

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

    6. Simplified28.8

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

    7. Taylor expanded around inf 24.5

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

    if 9.2299515020739188e-113 < (*.f64 M M) < 5.4908905374527431e271

    1. Initial program 62.2

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

    2. Taylor expanded around -inf 39.5

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

    3. Simplified39.9

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

    4. Taylor expanded around 0 32.1

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

    if 5.4908905374527431e271 < (*.f64 M M)

    1. Initial program 63.9

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

    2. Taylor expanded around -inf 60.9

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

    3. Simplified61.0

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

    5. Applied associate-*l*_binary64_104248.8

      \[\leadsto \frac{c0}{2 \cdot w} \cdot \left(0.5 \cdot \frac{\color{blue}{M \cdot \left(M \cdot \left(w \cdot \left(\left(D \cdot D\right) \cdot h\right)\right)\right)}}{\left(d \cdot d\right) \cdot c0}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification30.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;M \cdot M \leq 9.229951502073919 \cdot 10^{-113}:\\ \;\;\;\;\log 1\\ \mathbf{elif}\;M \cdot M \leq 5.490890537452743 \cdot 10^{+271}:\\ \;\;\;\;0.25 \cdot \frac{{M}^{2} \cdot \left({D}^{2} \cdot h\right)}{{d}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(0.5 \cdot \frac{M \cdot \left(M \cdot \left(w \cdot \left(h \cdot \left(D \cdot D\right)\right)\right)\right)}{c0 \cdot \left(d \cdot d\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021025 
(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))))))