Average Error: 26.6 → 15.2
Time: 41.1s
Precision: binary64
Cost: 118016
\[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
↓
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{1}}}\right)\right)\right)\]
\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)↓
\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{1}}}\right)\right)\right)(FPCore (d h l M D)
:precision binary64
(*
(* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0)))
(- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))
↓
(FPCore (d h l M D)
:precision binary64
(*
(-
1.0
(*
(* (* 0.5 (pow (/ (* M D) (* d 2.0)) 2.0)) (* (cbrt h) (cbrt h)))
(/ (cbrt h) l)))
(*
(* (fabs (/ 1.0 (cbrt h))) (sqrt (/ d (cbrt h))))
(*
(sqrt (/ 1.0 (* (cbrt l) (cbrt l))))
(*
(sqrt (/ (cbrt d) (cbrt l)))
(sqrt (/ (* (cbrt d) (cbrt d)) (cbrt 1.0))))))))double code(double d, double h, double l, double M, double D) {
return (pow((d / h), (1.0 / 2.0)) * pow((d / l), (1.0 / 2.0))) * (1.0 - (((1.0 / 2.0) * pow(((M * D) / (2.0 * d)), 2.0)) * (h / l)));
}
↓
double code(double d, double h, double l, double M, double D) {
return (1.0 - (((0.5 * pow(((M * D) / (d * 2.0)), 2.0)) * (cbrt(h) * cbrt(h))) * (cbrt(h) / l))) * ((fabs(1.0 / cbrt(h)) * sqrt(d / cbrt(h))) * (sqrt(1.0 / (cbrt(l) * cbrt(l))) * (sqrt(cbrt(d) / cbrt(l)) * sqrt((cbrt(d) * cbrt(d)) / cbrt(1.0)))));
}
Try it out
Enter valid numbers for all inputs
Alternatives
| Alternative 1 |
|---|
| Error | 25.1 |
|---|
| Cost | 145216 |
|---|
\[\sqrt{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right)} \cdot \sqrt{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right)}\]
| Alternative 2 |
|---|
| Error | 22.2 |
|---|
| Cost | 139904 |
|---|
\[\sqrt[3]{\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)} \cdot \left(\sqrt[3]{\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)} \cdot \sqrt[3]{\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)}\right)\]
| Alternative 3 |
|---|
| Error | 15.2 |
|---|
| Cost | 137344 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}} \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\sqrt[3]{\ell}}}}\right)\right)\right)\]
| Alternative 4 |
|---|
| Error | 16.2 |
|---|
| Cost | 130944 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt[3]{\sqrt{\frac{d}{\sqrt[3]{\ell}}}} \cdot \left(\sqrt[3]{\sqrt{\frac{d}{\sqrt[3]{\ell}}}} \cdot \sqrt[3]{\sqrt{\frac{d}{\sqrt[3]{\ell}}}}\right)\right)\right)\right)\]
| Alternative 5 |
|---|
| Error | 39.6 |
|---|
| Cost | 130816 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{\sqrt{\ell}}}} \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\sqrt{\ell}}}}\right)\right)\right)\]
| Alternative 6 |
|---|
| Error | 15.3 |
|---|
| Cost | 124288 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\sqrt[3]{\ell}}}} \cdot \left|\frac{\sqrt[3]{d}}{\sqrt[3]{\sqrt[3]{\ell}}}\right|\right)\right)\right)\]
| Alternative 7 |
|---|
| Error | 15.3 |
|---|
| Cost | 118016 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\sqrt[3]{\ell}}}}\right)\right)\right)\]
| Alternative 8 |
|---|
| Error | 15.9 |
|---|
| Cost | 111488 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\sqrt{\frac{d}{\sqrt[3]{\ell}}}} \cdot \sqrt{\sqrt{\frac{d}{\sqrt[3]{\ell}}}}\right)\right)\right)\]
| Alternative 9 |
|---|
| Error | 15.3 |
|---|
| Cost | 105088 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt[3]{h} \cdot \sqrt[3]{h}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}\right) \cdot \frac{\sqrt[3]{h}}{\sqrt[3]{\ell}}\right)\]
| Alternative 10 |
|---|
| Error | 15.2 |
|---|
| Cost | 104960 |
|---|
\[\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\left|\sqrt[3]{d}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}}\right)\right)\right)\]
| Alternative 11 |
|---|
| Error | 17.7 |
|---|
| Cost | 104832 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\sqrt[3]{\ell}}}} \cdot \left|\frac{\sqrt[3]{d}}{\sqrt[3]{\sqrt[3]{\ell}}}\right|\right)\right)\right)\]
| Alternative 12 |
|---|
| Error | 28.8 |
|---|
| Cost | 93248 |
|---|
\[\sqrt{\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)} \cdot \sqrt{\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)}\]
| Alternative 13 |
|---|
| Error | 18.1 |
|---|
| Cost | 92032 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\sqrt{\frac{d}{\sqrt[3]{\ell}}}} \cdot \sqrt{\sqrt{\frac{d}{\sqrt[3]{\ell}}}}\right)\right)\right)\]
| Alternative 14 |
|---|
| Error | 31.9 |
|---|
| Cost | 91968 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \frac{\sqrt[3]{h}}{\ell} \cdot e^{\log 0.5 + 2 \cdot \log \left(\sqrt[3]{h} \cdot \frac{M \cdot D}{d \cdot 2}\right)}\right)\]
| Alternative 15 |
|---|
| Error | 25.4 |
|---|
| Cost | 91584 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \log \left({\left(\sqrt{e^{{\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}}}\right)}^{\left(\frac{h}{\ell}\right)}\right)\right)\]
| Alternative 16 |
|---|
| Error | 15.9 |
|---|
| Cost | 85632 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
| Alternative 17 |
|---|
| Error | 59.7 |
|---|
| Cost | 85312 |
|---|
\[\log \left({\left(e^{\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)}\right)}^{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)}\right)\]
| Alternative 18 |
|---|
| Error | 27.1 |
|---|
| Cost | 81536 |
|---|
\[\sqrt[3]{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)} \cdot \left(\sqrt[3]{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)} \cdot \sqrt[3]{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)}\right)\]
| Alternative 19 |
|---|
| Error | 22.4 |
|---|
| Cost | 80960 |
|---|
\[\frac{\left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)}{\left|\sqrt[3]{\ell}\right| \cdot \left(1 + \left(\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\right)}\]
| Alternative 20 |
|---|
| Error | 43.1 |
|---|
| Cost | 80832 |
|---|
\[\frac{\left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right) \cdot \left(d \cdot \left|\frac{1}{\sqrt[3]{h}}\right|\right)}{\left(1 + \left(\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\right) \cdot \left(\sqrt{\sqrt[3]{h}} \cdot \left(\sqrt{\sqrt[3]{\ell}} \cdot \left|\sqrt[3]{\ell}\right|\right)\right)}\]
| Alternative 21 |
|---|
| Error | 20.0 |
|---|
| Cost | 79104 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt[3]{h} \cdot \sqrt[3]{h}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}\right) \cdot \frac{\sqrt[3]{h}}{\sqrt[3]{\ell}}\right)\]
| Alternative 22 |
|---|
| Error | 25.0 |
|---|
| Cost | 79040 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt[3]{{\left(\sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)}^{3}}\right)\right)\]
| Alternative 23 |
|---|
| Error | 21.9 |
|---|
| Cost | 74112 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \sqrt[3]{\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)} \cdot \left(\sqrt[3]{\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)} \cdot \sqrt[3]{\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}\right)\right)\]
| Alternative 24 |
|---|
| Error | 22.2 |
|---|
| Cost | 72704 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt[3]{\sqrt{\frac{d}{\ell}}} \cdot \left(\sqrt[3]{\sqrt{\frac{d}{\ell}}} \cdot \sqrt[3]{\sqrt{\frac{d}{\ell}}}\right)\right)\right)\]
| Alternative 25 |
|---|
| Error | 17.7 |
|---|
| Cost | 72448 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\left|\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}}\right)\right)\]
| Alternative 26 |
|---|
| Error | 45.8 |
|---|
| Cost | 67904 |
|---|
\[\frac{\left(\sqrt{\frac{d}{\ell}} \cdot \left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{d}\right)\right) \cdot \left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right)}{\sqrt{\sqrt[3]{h}} \cdot \left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} + \frac{h}{\ell} \cdot \left(0.25 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4}\right)\right)\right)}\]
| Alternative 27 |
|---|
| Error | 29.4 |
|---|
| Cost | 67264 |
|---|
\[\frac{\left(1 - 0.25 \cdot \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4} \cdot \left(\frac{h}{\ell} \cdot \frac{h}{\ell}\right)\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left|\sqrt[3]{\ell}\right|}\]
| Alternative 28 |
|---|
| Error | 46.8 |
|---|
| Cost | 67136 |
|---|
\[\frac{\left(1 - 0.25 \cdot \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4} \cdot \left(\frac{h}{\ell} \cdot \frac{h}{\ell}\right)\right)\right) \cdot \left(d \cdot \left|\frac{1}{\sqrt[3]{h}}\right|\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\sqrt[3]{h}} \cdot \left(\sqrt{\sqrt[3]{\ell}} \cdot \left|\sqrt[3]{\ell}\right|\right)\right)}\]
| Alternative 29 |
|---|
| Error | 18.0 |
|---|
| Cost | 66176 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right)\]
| Alternative 30 |
|---|
| Error | 17.7 |
|---|
| Cost | 66176 |
|---|
\[\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right)\]
| Alternative 31 |
|---|
| Error | 15.8 |
|---|
| Cost | 66176 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \frac{h \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}{\ell}\right)\]
| Alternative 32 |
|---|
| Error | 18.0 |
|---|
| Cost | 66048 |
|---|
\[\frac{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)}{\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\]
| Alternative 33 |
|---|
| Error | 40.6 |
|---|
| Cost | 65920 |
|---|
\[\frac{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(d \cdot \left|\frac{1}{\sqrt[3]{h}}\right|\right)}{\sqrt{\sqrt[3]{h}} \cdot \left(\sqrt{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \sqrt{\sqrt[3]{\ell}}\right)}\]
| Alternative 34 |
|---|
| Error | 29.9 |
|---|
| Cost | 65600 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \log \left({\left(\sqrt{e^{{\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}}}\right)}^{\left(\frac{h}{\ell}\right)}\right)\right)\]
| Alternative 35 |
|---|
| Error | 27.0 |
|---|
| Cost | 59968 |
|---|
\[\left(1 - 0.125 \cdot \frac{h \cdot \left(\left(M \cdot D\right) \cdot \left(M \cdot D\right)\right)}{\ell \cdot \left(d \cdot d\right)}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right)\]
| Alternative 36 |
|---|
| Error | 22.0 |
|---|
| Cost | 59648 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\left|\sqrt[3]{\frac{d}{\ell}}\right| \cdot \sqrt{\sqrt[3]{\frac{d}{\ell}}}\right)\right)\]
| Alternative 37 |
|---|
| Error | 21.9 |
|---|
| Cost | 59648 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\sqrt{\frac{d}{\ell}}} \cdot \sqrt{\sqrt{\frac{d}{\ell}}}\right)\right)\]
| Alternative 38 |
|---|
| Error | 20.7 |
|---|
| Cost | 59648 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{h}{\sqrt[3]{\ell}}\right)\]
| Alternative 39 |
|---|
| Error | 25.1 |
|---|
| Cost | 59648 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt[3]{h} \cdot \sqrt[3]{h}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}\right) \cdot \frac{\sqrt[3]{h}}{\sqrt[3]{\ell}}\right)\]
| Alternative 40 |
|---|
| Error | 18.2 |
|---|
| Cost | 59520 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\left|\sqrt[3]{d}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{\ell}}\right)\right)\]
| Alternative 41 |
|---|
| Error | 42.6 |
|---|
| Cost | 59520 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt{h}}} \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt{h}}}\right)\right)\]
| Alternative 42 |
|---|
| Error | 43.2 |
|---|
| Cost | 59520 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{\sqrt{d}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt{d}}{\sqrt[3]{\ell}}}\right)\right)\]
| Alternative 43 |
|---|
| Error | 43.2 |
|---|
| Cost | 59520 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt{\ell}}}\right)\right)\]
| Alternative 44 |
|---|
| Error | 62.7 |
|---|
| Cost | 59392 |
|---|
\[0.125 \cdot \left(\frac{\left(\left(M \cdot D\right) \cdot \left(M \cdot D\right)\right) \cdot \left|\frac{\sqrt[3]{\frac{-1}{h}}}{\sqrt[3]{-1}}\right|}{d} \cdot \left(\sqrt{\frac{{\left(\sqrt[3]{-1}\right)}^{5}}{{\ell}^{3}}} \cdot {\left(-{h}^{5}\right)}^{0.16666666666666666}\right)\right)\]
| Alternative 45 |
|---|
| Error | 26.7 |
|---|
| Cost | 54656 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \sqrt[3]{\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)} \cdot \left(\sqrt[3]{\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)} \cdot \sqrt[3]{\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}\right)\right)\]
| Alternative 46 |
|---|
| Error | 47.6 |
|---|
| Cost | 54336 |
|---|
\[\frac{\left(\sqrt{\frac{d}{\ell}} \cdot \left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{d}\right)\right) \cdot \left(1 - 0.25 \cdot \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4} \cdot \left(\frac{h}{\ell} \cdot \frac{h}{\ell}\right)\right)\right)}{\sqrt{\sqrt[3]{h}} \cdot \left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)}\]
| Alternative 47 |
|---|
| Error | 33.2 |
|---|
| Cost | 54336 |
|---|
\[\sqrt{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)} \cdot \sqrt{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)}\]
| Alternative 48 |
|---|
| Error | 27.1 |
|---|
| Cost | 53248 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\sqrt[3]{\sqrt{\frac{d}{\ell}}} \cdot \left(\sqrt[3]{\sqrt{\frac{d}{\ell}}} \cdot \sqrt[3]{\sqrt{\frac{d}{\ell}}}\right)\right) \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 49 |
|---|
| Error | 44.5 |
|---|
| Cost | 53120 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt{h}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}\right) \cdot \frac{\sqrt{h}}{\sqrt[3]{\ell}}\right)\]
| Alternative 50 |
|---|
| Error | 44.5 |
|---|
| Cost | 53120 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt[3]{h} \cdot \sqrt[3]{h}}{\sqrt{\ell}}\right) \cdot \frac{\sqrt[3]{h}}{\sqrt{\ell}}\right)\]
| Alternative 51 |
|---|
| Error | 30.4 |
|---|
| Cost | 53056 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{d}{\ell}}\right)}^{3}}\right)\]
| Alternative 52 |
|---|
| Error | 20.8 |
|---|
| Cost | 52992 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\left|\frac{\sqrt[3]{d}}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{h}}}\right)\right)\]
| Alternative 53 |
|---|
| Error | 22.5 |
|---|
| Cost | 52992 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}}\right) \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 54 |
|---|
| Error | 30.8 |
|---|
| Cost | 49408 |
|---|
\[\frac{\left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)}{1 + \left(\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) + \left(\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\right)}\]
| Alternative 55 |
|---|
| Error | 46.4 |
|---|
| Cost | 48448 |
|---|
\[\frac{\left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right) \cdot \left(\sqrt{d} \cdot \sqrt{\frac{d}{h}}\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} + \frac{h}{\ell} \cdot \left(0.25 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4}\right)\right)\right) \cdot \sqrt{\ell}}\]
| Alternative 56 |
|---|
| Error | 45.7 |
|---|
| Cost | 48448 |
|---|
\[\frac{\left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{d}\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} + \frac{h}{\ell} \cdot \left(0.25 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4}\right)\right)\right) \cdot \sqrt{h}}\]
| Alternative 57 |
|---|
| Error | 22.9 |
|---|
| Cost | 46720 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right) \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 58 |
|---|
| Error | 42.5 |
|---|
| Cost | 46592 |
|---|
\[\frac{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{d}\right)\right)}{\sqrt{\sqrt[3]{h}}}\]
| Alternative 59 |
|---|
| Error | 40.7 |
|---|
| Cost | 46592 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \frac{\sqrt{d}}{\sqrt{\ell}}\right)\]
| Alternative 60 |
|---|
| Error | 44.5 |
|---|
| Cost | 46592 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \frac{\sqrt{h}}{\sqrt{\ell}} \cdot \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt{h}}{\sqrt{\ell}}\right)\right)\]
| Alternative 61 |
|---|
| Error | 34.9 |
|---|
| Cost | 46144 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \log \left(\sqrt{{\left(e^{\frac{h}{\ell}}\right)}^{\left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}}\right)\right)\]
| Alternative 62 |
|---|
| Error | 43.7 |
|---|
| Cost | 41920 |
|---|
\[\frac{d \cdot \left(1 - 0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2} + \frac{h}{\ell} \cdot \left(0.25 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4}\right)\right)\right) \cdot \left(\sqrt{\ell} \cdot \sqrt{h}\right)}\]
| Alternative 63 |
|---|
| Error | 26.7 |
|---|
| Cost | 40448 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \sqrt[3]{\frac{h}{\ell}} \cdot \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{\frac{h}{\ell}} \cdot \sqrt[3]{\frac{h}{\ell}}\right)\right)\right)\]
| Alternative 64 |
|---|
| Error | 22.1 |
|---|
| Cost | 40192 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M}{d} \cdot \frac{D}{2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
| Alternative 65 |
|---|
| Error | 21.8 |
|---|
| Cost | 40192 |
|---|
\[\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\right)\]
| Alternative 66 |
|---|
| Error | 20.7 |
|---|
| Cost | 40192 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}{\ell}\right)\]
| Alternative 67 |
|---|
| Error | 21.9 |
|---|
| Cost | 40192 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\]
| Alternative 68 |
|---|
| Error | 26.7 |
|---|
| Cost | 40192 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\sqrt{\sqrt{\frac{d}{h}}} \cdot \sqrt{\sqrt{\frac{d}{h}}}\right)\right)\]
| Alternative 69 |
|---|
| Error | 43.6 |
|---|
| Cost | 40192 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{1}{\sqrt{\ell}}} \cdot \sqrt{\frac{d}{\sqrt{\ell}}}\right)\right)\]
| Alternative 70 |
|---|
| Error | 26.9 |
|---|
| Cost | 40192 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\sqrt[3]{\frac{d}{\ell}}\right| \cdot \sqrt{\sqrt[3]{\frac{d}{\ell}}}\right) \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 71 |
|---|
| Error | 26.7 |
|---|
| Cost | 40192 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\sqrt{\sqrt{\frac{d}{\ell}}} \cdot \sqrt{\sqrt{\frac{d}{\ell}}}\right) \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 72 |
|---|
| Error | 25.7 |
|---|
| Cost | 40192 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \frac{0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{h}{\sqrt[3]{\ell}}\right)\]
| Alternative 73 |
|---|
| Error | 25.6 |
|---|
| Cost | 40192 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
| Alternative 74 |
|---|
| Error | 43.6 |
|---|
| Cost | 40064 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\sqrt{\sqrt{d}} \cdot \sqrt{\frac{\sqrt{d}}{h}}\right)\right)\]
| Alternative 75 |
|---|
| Error | 22.2 |
|---|
| Cost | 40064 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\left|\sqrt[3]{d}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{h}}\right)\right)\]
| Alternative 76 |
|---|
| Error | 23.1 |
|---|
| Cost | 40064 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\left(\left|\sqrt[3]{d}\right| \cdot \sqrt{\frac{\sqrt[3]{d}}{\ell}}\right) \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 77 |
|---|
| Error | 48.8 |
|---|
| Cost | 34880 |
|---|
\[\frac{\left(1 - 0.25 \cdot \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4} \cdot \left(\frac{h}{\ell} \cdot \frac{h}{\ell}\right)\right)\right) \cdot \left(\sqrt{d} \cdot \sqrt{\frac{d}{h}}\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \sqrt{\ell}}\]
| Alternative 78 |
|---|
| Error | 47.4 |
|---|
| Cost | 34880 |
|---|
\[\frac{\left(1 - 0.25 \cdot \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4} \cdot \left(\frac{h}{\ell} \cdot \frac{h}{\ell}\right)\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{d}\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \sqrt{h}}\]
| Alternative 79 |
|---|
| Error | 31.2 |
|---|
| Cost | 33984 |
|---|
\[\left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - 0.125 \cdot \frac{h \cdot \left(\left(M \cdot D\right) \cdot \left(M \cdot D\right)\right)}{\ell \cdot \left(d \cdot d\right)}\right)\]
| Alternative 80 |
|---|
| Error | 26.6 |
|---|
| Cost | 33792 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \sqrt{\frac{h}{\ell}} \cdot \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \sqrt{\frac{h}{\ell}}\right)\right)\]
| Alternative 81 |
|---|
| Error | 44.9 |
|---|
| Cost | 33664 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \frac{0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}}{\sqrt{\ell}} \cdot \frac{h}{\sqrt{\ell}}\right)\]
| Alternative 82 |
|---|
| Error | 44.8 |
|---|
| Cost | 33664 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \sqrt{h}\right) \cdot \frac{\sqrt{h}}{\ell}\right)\]
| Alternative 83 |
|---|
| Error | 35.0 |
|---|
| Cost | 33600 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt[3]{{\left(\sqrt{\frac{d}{h}}\right)}^{3}}\right)\]
| Alternative 84 |
|---|
| Error | 34.5 |
|---|
| Cost | 33600 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt[3]{{\left(\sqrt{\frac{d}{\ell}}\right)}^{3}} \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 85 |
|---|
| Error | 30.3 |
|---|
| Cost | 33600 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \sqrt[3]{0.125 \cdot {\left(\frac{h}{\ell} \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}^{3}}\right)\]
| Alternative 86 |
|---|
| Error | 28.8 |
|---|
| Cost | 33536 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot e^{\log \left(\sqrt{\frac{d}{\ell}}\right)}\right)\]
| Alternative 87 |
|---|
| Error | 27.1 |
|---|
| Cost | 33536 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - e^{\log \left(\frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)}\right)\]
| Alternative 88 |
|---|
| Error | 46.1 |
|---|
| Cost | 28352 |
|---|
\[\frac{d \cdot \left(1 - 0.25 \cdot \left({\left(\frac{M \cdot D}{d \cdot 2}\right)}^{4} \cdot \left(\frac{h}{\ell} \cdot \frac{h}{\ell}\right)\right)\right)}{\left(1 + \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\ell} \cdot \sqrt{h}\right)}\]
| Alternative 89 |
|---|
| Error | 42.4 |
|---|
| Cost | 27264 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \left(\sqrt{d} \cdot \sqrt{\frac{1}{h}}\right)\right)\]
| Alternative 90 |
|---|
| Error | 43.1 |
|---|
| Cost | 27264 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \left(\sqrt{\frac{1}{\ell}} \cdot \sqrt{d}\right)\right)\]
| Alternative 91 |
|---|
| Error | 43.1 |
|---|
| Cost | 27136 |
|---|
\[\frac{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{d} \cdot \sqrt{\frac{d}{h}}\right)}{\sqrt{\ell}}\]
| Alternative 92 |
|---|
| Error | 42.6 |
|---|
| Cost | 27136 |
|---|
\[\frac{\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{d}\right)}{\sqrt{h}}\]
| Alternative 93 |
|---|
| Error | 42.4 |
|---|
| Cost | 27136 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \frac{\sqrt{d}}{\sqrt{h}}\right)\]
| Alternative 94 |
|---|
| Error | 43.1 |
|---|
| Cost | 27136 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\frac{\sqrt{d}}{\sqrt{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 95 |
|---|
| Error | 43.7 |
|---|
| Cost | 26496 |
|---|
\[\left(d \cdot \left|\sqrt[3]{\frac{1}{h}}\right|\right) \cdot \left(\sqrt{\frac{1}{\ell}} \cdot {\left(\frac{1}{h}\right)}^{0.16666666666666666}\right)\]
| Alternative 96 |
|---|
| Error | 25.8 |
|---|
| Cost | 20864 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \frac{1}{\ell} \cdot \left(h \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\right)\]
| Alternative 97 |
|---|
| Error | 26.6 |
|---|
| Cost | 20864 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left({\left(\frac{d}{h}\right)}^{0.5} \cdot {\left(\frac{d}{\ell}\right)}^{0.5}\right)\]
| Alternative 98 |
|---|
| Error | 26.6 |
|---|
| Cost | 20736 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right)\]
| Alternative 99 |
|---|
| Error | 47.3 |
|---|
| Cost | 20736 |
|---|
\[d \cdot \sqrt{\frac{1}{h \cdot \ell}} + -0.125 \cdot \left(\frac{\left(M \cdot D\right) \cdot \left(M \cdot D\right)}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right)\]
| Alternative 100 |
|---|
| Error | 26.7 |
|---|
| Cost | 20736 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)\right) \cdot \sqrt{\frac{d}{h}}\]
| Alternative 101 |
|---|
| Error | 25.8 |
|---|
| Cost | 20736 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - \frac{h \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)}{\ell}\right)\]
| Alternative 102 |
|---|
| Error | 40.0 |
|---|
| Cost | 20608 |
|---|
\[\frac{d \cdot \left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right)}{\sqrt{\ell} \cdot \sqrt{h}}\]
| Alternative 103 |
|---|
| Error | 42.7 |
|---|
| Cost | 14528 |
|---|
\[\left(\sqrt{\frac{d}{\ell}} \cdot \sqrt{\frac{d}{h}}\right) \cdot \left(1 - 0.125 \cdot \frac{\left(M \cdot M\right) \cdot \left(h \cdot \left(D \cdot D\right)\right)}{\ell \cdot \left(d \cdot d\right)}\right)\]
| Alternative 104 |
|---|
| Error | 64.0 |
|---|
| Cost | 14464 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \left(\frac{d}{\ell} \cdot \mathsf{NaN}\right)\right)\]
| Alternative 105 |
|---|
| Error | 64.0 |
|---|
| Cost | 14336 |
|---|
\[\left(1 - \frac{h}{\ell} \cdot \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right)\right) \cdot \left(\sqrt{\frac{d}{h}} \cdot \frac{\mathsf{NaN}}{\ell}\right)\]
| Alternative 106 |
|---|
| Error | 58.8 |
|---|
| Cost | 13824 |
|---|
\[-0.125 \cdot \left(\frac{\left(M \cdot D\right) \cdot \left(M \cdot D\right)}{d} \cdot \sqrt{\frac{h}{{\ell}^{3}}}\right)\]
| Alternative 107 |
|---|
| Error | 44.4 |
|---|
| Cost | 6848 |
|---|
\[d \cdot \sqrt{\frac{1}{h \cdot \ell}}\]
| Alternative 108 |
|---|
| Error | 64.0 |
|---|
| Cost | 6784 |
|---|
\[\frac{{\mathsf{NaN}}^{2}}{h \cdot \ell}\]
| Alternative 109 |
|---|
| Error | 64.0 |
|---|
| Cost | 320 |
|---|
\[\frac{d}{\ell} \cdot \mathsf{NaN}\]
| Alternative 110 |
|---|
| Error | 61.3 |
|---|
| Cost | 64 |
|---|
\[1\]
| Alternative 111 |
|---|
| Error | 60.0 |
|---|
| Cost | 64 |
|---|
\[0\]
| Alternative 112 |
|---|
| Error | 62.3 |
|---|
| Cost | 64 |
|---|
\[-1\]
Error
Derivation
Initial program 26.6
\[\left({\left(\frac{d}{h}\right)}^{\left(\frac{1}{2}\right)} \cdot {\left(\frac{d}{\ell}\right)}^{\left(\frac{1}{2}\right)}\right) \cdot \left(1 - \left(\frac{1}{2} \cdot {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Simplified26.6
\[\leadsto \color{blue}{\left(\sqrt{\frac{d}{h}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)}\]
- Using strategy
rm Applied add-cube-cbrt_binary64_113626.8
\[\leadsto \left(\sqrt{\frac{d}{\color{blue}{\left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right) \cdot \sqrt[3]{h}}}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Applied *-un-lft-identity_binary64_110126.8
\[\leadsto \left(\sqrt{\frac{\color{blue}{1 \cdot d}}{\left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right) \cdot \sqrt[3]{h}}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Applied times-frac_binary64_110726.9
\[\leadsto \left(\sqrt{\color{blue}{\frac{1}{\sqrt[3]{h} \cdot \sqrt[3]{h}} \cdot \frac{d}{\sqrt[3]{h}}}} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Applied sqrt-prod_binary64_111721.9
\[\leadsto \left(\color{blue}{\left(\sqrt{\frac{1}{\sqrt[3]{h} \cdot \sqrt[3]{h}}} \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right)} \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Simplified21.9
\[\leadsto \left(\left(\color{blue}{\left|\frac{1}{\sqrt[3]{h}}\right|} \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\ell}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
- Using strategy
rm Applied add-cube-cbrt_binary64_113622.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{d}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Applied *-un-lft-identity_binary64_110122.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\frac{\color{blue}{1 \cdot d}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Applied times-frac_binary64_110722.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \sqrt{\color{blue}{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{d}{\sqrt[3]{\ell}}}}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
Applied sqrt-prod_binary64_111718.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \color{blue}{\left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)}\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\ell}\right)\]
- Using strategy
rm Applied *-un-lft-identity_binary64_110118.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{h}{\color{blue}{1 \cdot \ell}}\right)\]
Applied add-cube-cbrt_binary64_113618.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right) \cdot \sqrt[3]{h}}}{1 \cdot \ell}\right)\]
Applied times-frac_binary64_110718.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{h} \cdot \sqrt[3]{h}}{1} \cdot \frac{\sqrt[3]{h}}{\ell}\right)}\right)\]
Applied associate-*r*_binary64_104115.9
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \color{blue}{\left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \frac{\sqrt[3]{h} \cdot \sqrt[3]{h}}{1}\right) \cdot \frac{\sqrt[3]{h}}{\ell}}\right)\]
Simplified15.9
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \color{blue}{\left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right)} \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
- Using strategy
rm Applied *-un-lft-identity_binary64_110115.9
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\sqrt[3]{\color{blue}{1 \cdot \ell}}}}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
Applied cbrt-prod_binary64_113215.9
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{d}{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{\ell}}}}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
Applied add-cube-cbrt_binary64_113616.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\color{blue}{\left(\sqrt[3]{d} \cdot \sqrt[3]{d}\right) \cdot \sqrt[3]{d}}}{\sqrt[3]{1} \cdot \sqrt[3]{\ell}}}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
Applied times-frac_binary64_110716.0
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\color{blue}{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{1}} \cdot \frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}}}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
Applied sqrt-prod_binary64_111715.2
\[\leadsto \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \color{blue}{\left(\sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{1}}} \cdot \sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}}\right)}\right)\right) \cdot \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right)\]
Simplified15.2
\[\leadsto \color{blue}{\left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{1}}}\right)\right)\right)}\]
Final simplification15.2
\[\leadsto \left(1 - \left(\left(0.5 \cdot {\left(\frac{M \cdot D}{d \cdot 2}\right)}^{2}\right) \cdot \left(\sqrt[3]{h} \cdot \sqrt[3]{h}\right)\right) \cdot \frac{\sqrt[3]{h}}{\ell}\right) \cdot \left(\left(\left|\frac{1}{\sqrt[3]{h}}\right| \cdot \sqrt{\frac{d}{\sqrt[3]{h}}}\right) \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \left(\sqrt{\frac{\sqrt[3]{d}}{\sqrt[3]{\ell}}} \cdot \sqrt{\frac{\sqrt[3]{d} \cdot \sqrt[3]{d}}{\sqrt[3]{1}}}\right)\right)\right)\]
Reproduce
herbie shell --seed 2021022
(FPCore (d h l M D)
:name "Henrywood and Agarwal, Equation (12)"
:precision binary64
(* (* (pow (/ d h) (/ 1.0 2.0)) (pow (/ d l) (/ 1.0 2.0))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))))
