Average Error: 59.9 → 26.9
Time: 16.6s
Precision: binary64
\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \]
↓
\[0.25 \cdot \left(\frac{D}{d} \cdot \left(\frac{D}{d} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right)\right) \]
\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 \left(\frac{D}{d} \cdot \left(\frac{D}{d} \cdot \left(h \cdot \left(M \cdot M\right)\right)\right)\right)

(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 (* (/ D d) (* (/ D d) (* h (* M M))))))
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 * ((D / d) * ((D / d) * (h * (M * M))));
}

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 59.9

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

  2. Taylor expanded in c0 around -inf 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 35.3

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

  4. Applied unpow2_binary6435.3

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

  5. Applied associate-*l*_binary6432.6

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

  6. Applied add-sqr-sqrt_binary6448.3

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

  7. Applied unpow-prod-down_binary6448.3

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

  8. Applied times-frac_binary6446.1

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

  9. Simplified46.1

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

  10. Simplified26.9

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

  11. Final simplification26.9

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

Reproduce

herbie shell --seed 2021215 
(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))))))