Average Error: 59.6 → 27.0
Time: 19.8s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
↓
\[\begin{array}{l} \mathbf{if}\;M \leq -1.93057971646278 \cdot 10^{+160}:\\ \;\;\;\;0.25 \cdot \frac{\left(M \cdot \left(M \cdot h\right)\right) \cdot \frac{D \cdot D}{d}}{d}\\ \mathbf{elif}\;M \leq 5.084131809070544 \cdot 10^{+126}:\\ \;\;\;\;0.25 \cdot \frac{\left(\left(h \cdot \left(M \cdot M\right)\right) \cdot \frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}}\right) \cdot \frac{D}{\sqrt[3]{d}}}{d}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot e^{\left(\log \left({D}^{2}\right) + \left(2 \cdot \log M + \log h\right)\right) - \log \left({d}^{2}\right)}\\ \end{array} \]
\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 \leq -1.93057971646278 \cdot 10^{+160}:\\
\;\;\;\;0.25 \cdot \frac{\left(M \cdot \left(M \cdot h\right)\right) \cdot \frac{D \cdot D}{d}}{d}\\

\mathbf{elif}\;M \leq 5.084131809070544 \cdot 10^{+126}:\\
\;\;\;\;0.25 \cdot \frac{\left(\left(h \cdot \left(M \cdot M\right)\right) \cdot \frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}}\right) \cdot \frac{D}{\sqrt[3]{d}}}{d}\\

\mathbf{else}:\\
\;\;\;\;0.25 \cdot e^{\left(\log \left({D}^{2}\right) + \left(2 \cdot \log M + \log h\right)\right) - \log \left({d}^{2}\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 -1.93057971646278e+160)
   (* 0.25 (/ (* (* M (* M h)) (/ (* D D) d)) d))
   (if (<= M 5.084131809070544e+126)
     (*
      0.25
      (/ (* (* (* h (* M M)) (/ D (* (cbrt d) (cbrt d)))) (/ D (cbrt d))) d))
     (*
      0.25
      (exp
       (-
        (+ (log (pow D 2.0)) (+ (* 2.0 (log M)) (log h)))
        (log (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 (M <= -1.93057971646278e+160) {
		tmp = 0.25 * (((M * (M * h)) * ((D * D) / d)) / d);
	} else if (M <= 5.084131809070544e+126) {
		tmp = 0.25 * ((((h * (M * M)) * (D / (cbrt(d) * cbrt(d)))) * (D / cbrt(d))) / d);
	} else {
		tmp = 0.25 * exp((log(pow(D, 2.0)) + ((2.0 * log(M)) + log(h))) - log(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 3 regimes

  2. if M < -1.9305797164627801e160

    1. Initial program 64.0

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

    2. Taylor expanded in c0 around -inf 64.0

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

    3. Taylor expanded in c0 around 0 64.0

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

    4. Applied unpow2_binary6464.0

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

    5. Applied associate-/r*_binary6464.0

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

    6. Simplified64.0

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

    7. Applied associate-*r*_binary6449.6

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

    if -1.9305797164627801e160 < M < 5.084131809070544e126

    1. Initial program 58.8

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

    2. Taylor expanded in c0 around -inf 38.7

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

    3. Taylor expanded in c0 around 0 31.3

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

    4. Applied unpow2_binary6431.3

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

    5. Applied associate-/r*_binary6428.3

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

    6. Simplified27.9

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

    7. Applied add-cube-cbrt_binary6427.9

      \[\leadsto 0.25 \cdot \frac{\left(h \cdot \left(M \cdot M\right)\right) \cdot \frac{D \cdot D}{\color{blue}{\left(\sqrt[3]{d} \cdot \sqrt[3]{d}\right) \cdot \sqrt[3]{d}}}}{d} \]

    8. Applied times-frac_binary6424.5

      \[\leadsto 0.25 \cdot \frac{\left(h \cdot \left(M \cdot M\right)\right) \cdot \color{blue}{\left(\frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}} \cdot \frac{D}{\sqrt[3]{d}}\right)}}{d} \]

    9. Applied associate-*r*_binary6422.9

      \[\leadsto 0.25 \cdot \frac{\color{blue}{\left(\left(h \cdot \left(M \cdot M\right)\right) \cdot \frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}}\right) \cdot \frac{D}{\sqrt[3]{d}}}}{d} \]

    if 5.084131809070544e126 < 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 in c0 around -inf 62.4

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

    3. Taylor expanded in c0 around 0 60.5

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

    4. Applied add-exp-log_binary6460.6

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

    5. Applied add-exp-log_binary6461.9

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

    6. Applied pow-to-exp_binary6461.9

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

    7. Applied prod-exp_binary6457.1

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

    8. Applied add-exp-log_binary6457.1

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

    9. Applied prod-exp_binary6452.3

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

    10. Applied div-exp_binary6450.9

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

  4. Final simplification27.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;M \leq -1.93057971646278 \cdot 10^{+160}:\\ \;\;\;\;0.25 \cdot \frac{\left(M \cdot \left(M \cdot h\right)\right) \cdot \frac{D \cdot D}{d}}{d}\\ \mathbf{elif}\;M \leq 5.084131809070544 \cdot 10^{+126}:\\ \;\;\;\;0.25 \cdot \frac{\left(\left(h \cdot \left(M \cdot M\right)\right) \cdot \frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}}\right) \cdot \frac{D}{\sqrt[3]{d}}}{d}\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot e^{\left(\log \left({D}^{2}\right) + \left(2 \cdot \log M + \log h\right)\right) - \log \left({d}^{2}\right)}\\ \end{array} \]

Reproduce

herbie shell --seed 2022061 
(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))))))