Average Error: 59.6 → 25.5
Time: 18.3s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
↓
\[\begin{array}{l} \mathbf{if}\;M \cdot M \leq 5.901458979163336 \cdot 10^{+291}:\\ \;\;\;\;0.25 \cdot \left(\frac{D}{d} \cdot \left(\frac{D}{d} \cdot \left(\left(M \cdot M\right) \cdot h\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot \left(D \cdot \left(M \cdot \left(M \cdot h\right)\right)\right)}{{d}^{2}}\\ \end{array} \]
\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}\;M \cdot M \leq 5.901458979163336 \cdot 10^{+291}:\\
\;\;\;\;0.25 \cdot \left(\frac{D}{d} \cdot \left(\frac{D}{d} \cdot \left(\left(M \cdot M\right) \cdot h\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;0.25 \cdot \frac{D \cdot \left(D \cdot \left(M \cdot \left(M \cdot h\right)\right)\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 (<= (* M M) 5.901458979163336e+291)
   (* 0.25 (* (/ D d) (* (/ D d) (* (* M M) h))))
   (* 0.25 (/ (* D (* D (* M (* M 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 ((M * M) <= 5.901458979163336e+291) {
		tmp = 0.25 * ((D / d) * ((D / d) * ((M * M) * h)));
	} else {
		tmp = 0.25 * ((D * (D * (M * (M * 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 M M) < 5.9014589791633357e291

    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 38.4

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

    3. Taylor expanded in c0 around 0 31.1

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

    4. Applied unpow2_binary6431.1

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

    5. Applied associate-*l*_binary6427.9

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

    6. Applied add-sqr-sqrt_binary6446.0

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

    7. Applied unpow-prod-down_binary6446.0

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

    8. Applied times-frac_binary6443.4

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

    9. Simplified43.3

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

    10. Simplified21.3

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

    if 5.9014589791633357e291 < (*.f64 M M)

    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 63.1

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

    3. Taylor expanded in c0 around 0 62.8

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

    4. Applied unpow2_binary6462.8

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

    5. Applied associate-*l*_binary6462.7

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

    6. Applied unpow2_binary6462.7

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

    7. Applied associate-*l*_binary6449.6

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

    8. Simplified49.6

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

  4. Final simplification25.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;M \cdot M \leq 5.901458979163336 \cdot 10^{+291}:\\ \;\;\;\;0.25 \cdot \left(\frac{D}{d} \cdot \left(\frac{D}{d} \cdot \left(\left(M \cdot M\right) \cdot h\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.25 \cdot \frac{D \cdot \left(D \cdot \left(M \cdot \left(M \cdot h\right)\right)\right)}{{d}^{2}}\\ \end{array} \]

Reproduce

herbie shell --seed 2021280 
(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))))))