Average Error: 59.5 → 25.4
Time: 22.7s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
↓
\[0.25 \cdot \frac{\left(\left(M \cdot \left(M \cdot h\right)\right) \cdot \frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}}\right) \cdot \frac{D}{\sqrt[3]{d}}}{d} \]
\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)
↓
0.25 \cdot \frac{\left(\left(M \cdot \left(M \cdot h\right)\right) \cdot \frac{D}{\sqrt[3]{d} \cdot \sqrt[3]{d}}\right) \cdot \frac{D}{\sqrt[3]{d}}}{d}

(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
 (*
  0.25
  (/ (* (* (* M (* M h)) (/ D (* (cbrt d) (cbrt d)))) (/ D (cbrt 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) {
	return 0.25 * ((((M * (M * h)) * (D / (cbrt(d) * cbrt(d)))) * (D / cbrt(d))) / d);
}

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. 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 36.3

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

  3. Applied unpow2_binary6436.3

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

  4. Applied associate-/r*_binary6433.6

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

  5. Simplified33.1

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

  6. Applied add-cube-cbrt_binary6433.1

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

  7. Applied times-frac_binary6430.0

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

  8. Applied associate-*r*_binary6428.6

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

  9. Applied associate-*r*_binary6425.4

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

  10. Simplified25.4

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

  11. Final simplification25.4

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

Reproduce

herbie shell --seed 2022055 
(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))))))