Average Error: 19.1 → 1.2
Time: 9.1s
Precision: binary64
Cost: 52032
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
↓
\[\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}
(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (*
  (* c0 (fabs (/ (/ (cbrt A) (cbrt V)) (cbrt l))))
  (sqrt (/ (/ (cbrt A) (cbrt V)) (cbrt l)))))
double code(double c0, double A, double V, double l) {
	return c0 * sqrt(A / (V * l));
}
↓
double code(double c0, double A, double V, double l) {
	return (c0 * fabs((cbrt(A) / cbrt(V)) / cbrt(l))) * sqrt((cbrt(A) / cbrt(V)) / cbrt(l));
}

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error1.5
Cost84288
\[\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot \left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\sqrt[3]{\ell}} \cdot \left(\sqrt[3]{\sqrt[3]{\ell}} \cdot \sqrt[3]{\sqrt[3]{\ell}}\right)}\right|\right)\]
Alternative 2
Error1.3
Cost84288
\[\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\sqrt[3]{\ell}} \cdot \left(\sqrt[3]{\sqrt[3]{\ell}} \cdot \sqrt[3]{\sqrt[3]{\ell}}\right)}}\]
Alternative 3
Error32.6
Cost71360
\[\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot \left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt{V}} \cdot \sqrt[3]{\sqrt{V}}}}{\sqrt[3]{\ell}}\right|\right)\]
Alternative 4
Error32.6
Cost71360
\[\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{\sqrt{V}} \cdot \sqrt[3]{\sqrt{V}}}}{\sqrt[3]{\ell}}}\]
Alternative 5
Error33.8
Cost65088
\[c0 \cdot \left(\sqrt{\frac{\frac{\sqrt{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{\sqrt{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\right)\]
Alternative 6
Error9.4
Cost52288
\[\left(c0 \cdot \sqrt{\frac{\frac{1}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right) \cdot \sqrt{\frac{\frac{A}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]
Alternative 7
Error34.2
Cost52096
\[\sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}} \cdot \left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{{V}^{0.3333333333333333}}}{\sqrt[3]{\ell}}\right|\right)\]
Alternative 8
Error2.1
Cost52032
\[c0 \cdot \left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\right)\]
Alternative 9
Error35.4
Cost45632
\[c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{\sqrt{A}}{V}}{\sqrt[3]{\ell}}}\right)\]
Alternative 10
Error34.3
Cost45632
\[c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}} \cdot \sqrt{\frac{\frac{\sqrt{A}}{\sqrt[3]{V}}}{\ell}}\right)\]
Alternative 11
Error36.0
Cost45632
\[\sqrt{\frac{\frac{\sqrt{A}}{V}}{\sqrt[3]{\ell}}} \cdot \left(c0 \cdot \sqrt{\frac{\sqrt{A}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right)\]
Alternative 12
Error19.7
Cost39872
\[\sqrt[3]{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt[3]{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt[3]{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}}\right)\]
Alternative 13
Error19.7
Cost39616
\[\sqrt[3]{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \left(\sqrt[3]{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt[3]{\sqrt{\frac{A}{V \cdot \ell}}}\right)\right)\]
Alternative 14
Error19.7
Cost39616
\[c0 \cdot \left(\sqrt[3]{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(\sqrt[3]{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt[3]{\sqrt{\frac{A}{V \cdot \ell}}}\right)\right)\]
Alternative 15
Error41.7
Cost39360
\[\left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0}\right) \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0}\right)\]
Alternative 16
Error11.6
Cost39232
\[c0 \cdot \left(\left|\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{V}}}{\sqrt[3]{\ell}}}\right)\]
Alternative 17
Error6.0
Cost39104
\[\left(c0 \cdot \left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\ell}}\]
Alternative 18
Error6.2
Cost39104
\[c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{\ell}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{V}}{\sqrt[3]{\ell}}}\right)\]
Alternative 19
Error4.8
Cost39104
\[c0 \cdot \left(\left|\frac{\sqrt[3]{A}}{\sqrt[3]{V}}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\ell}}\right)\]
Alternative 20
Error36.3
Cost32832
\[c0 \cdot \left(\sqrt{\frac{A}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{1}{V}}{\sqrt[3]{\ell}}}\right)\]
Alternative 21
Error13.5
Cost32832
\[c0 \cdot \left(\sqrt{\frac{1}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{A}{V}}{\sqrt[3]{\ell}}}\right)\]
Alternative 22
Error37.7
Cost32704
\[\left(c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\]
Alternative 23
Error36.9
Cost32704
\[c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V}} \cdot \sqrt{\frac{\sqrt[3]{A}}{\ell}}\right)\]
Alternative 24
Error19.4
Cost26816
\[c0 \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \left(\sqrt[3]{\frac{A}{V \cdot \ell}} \cdot \sqrt[3]{\frac{A}{V \cdot \ell}}\right)}\]
Alternative 25
Error38.2
Cost26560
\[\sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}}\]
Alternative 26
Error19.4
Cost26432
\[\left(c0 \cdot \left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right|\right) \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\]
Alternative 27
Error19.2
Cost26432
\[\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \left(c0 \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\]
Alternative 28
Error19.4
Cost26432
\[c0 \cdot \left(\left|\sqrt[3]{\frac{A}{V \cdot \ell}}\right| \cdot \sqrt{\sqrt[3]{\frac{A}{V \cdot \ell}}}\right)\]
Alternative 29
Error19.2
Cost26432
\[c0 \cdot \left(\sqrt{\sqrt{\frac{A}{V \cdot \ell}}} \cdot \sqrt{\sqrt{\frac{A}{V \cdot \ell}}}\right)\]
Alternative 30
Error18.8
Cost26432
\[c0 \cdot \left(\sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}} \cdot \sqrt{\sqrt{\frac{\frac{A}{V}}{\ell}}}\right)\]
Alternative 31
Error18.0
Cost26304
\[c0 \cdot \sqrt{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{V} \cdot \frac{\sqrt[3]{A}}{\ell}}\]
Alternative 32
Error39.2
Cost26304
\[\left(c0 \cdot \sqrt{\frac{1}{\sqrt{\ell}}}\right) \cdot \sqrt{\frac{\frac{A}{V}}{\sqrt{\ell}}}\]
Alternative 33
Error39.3
Cost26304
\[\left(c0 \cdot \sqrt{\frac{1}{\sqrt{V}}}\right) \cdot \sqrt{\frac{\frac{A}{\sqrt{V}}}{\ell}}\]
Alternative 34
Error37.9
Cost26304
\[\left(c0 \cdot \sqrt{\sqrt{\frac{A}{V}}}\right) \cdot \sqrt{\frac{\sqrt{\frac{A}{V}}}{\ell}}\]
Alternative 35
Error14.6
Cost26304
\[\left(c0 \cdot \left|\sqrt[3]{\frac{A}{V}}\right|\right) \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{V}}}{\ell}}\]
Alternative 36
Error50.1
Cost26304
\[c0 \cdot \left(\sqrt{\frac{A}{\sqrt{\ell}}} \cdot \sqrt{\frac{\frac{1}{\sqrt{\ell}}}{V}}\right)\]
Alternative 37
Error38.9
Cost26304
\[c0 \cdot \left(\sqrt{\frac{1}{\sqrt{V}}} \cdot \sqrt{\frac{\frac{A}{\sqrt{V}}}{\ell}}\right)\]
Alternative 38
Error13.6
Cost26304
\[c0 \cdot \left(\left|\sqrt[3]{\frac{A}{V}}\right| \cdot \sqrt{\frac{\sqrt[3]{\frac{A}{V}}}{\ell}}\right)\]
Alternative 39
Error50.7
Cost26240
\[c0 \cdot \left(\sqrt{\frac{\sqrt[3]{A}}{\ell}} \cdot \sqrt{\frac{{A}^{0.6666666666666666}}{V}}\right)\]
Alternative 40
Error50.5
Cost26176
\[\left(c0 \cdot \sqrt{\frac{\sqrt{A}}{V}}\right) \cdot \sqrt{\frac{\sqrt{A}}{\ell}}\]
Alternative 41
Error50.0
Cost26176
\[c0 \cdot \left(\sqrt{\frac{\sqrt{A}}{V}} \cdot \sqrt{\frac{\sqrt{A}}{\ell}}\right)\]
Alternative 42
Error14.8
Cost26176
\[\left(c0 \cdot \left|\sqrt[3]{A}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{V}}{\ell}}\]
Alternative 43
Error13.5
Cost26176
\[c0 \cdot \left(\left|\sqrt[3]{A}\right| \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{V}}{\ell}}\right)\]
Alternative 44
Error47.9
Cost26048
\[c0 \cdot \left|\frac{\frac{\sqrt{A}}{\sqrt{V}}}{\sqrt{\ell}}\right|\]
Alternative 45
Error40.6
Cost19904
\[c0 \cdot \sqrt{\frac{\frac{1}{\sqrt{V}}}{\frac{\ell}{\frac{A}{\sqrt{V}}}}}\]
Alternative 46
Error41.6
Cost19776
\[\sqrt{c0} \cdot \left(\sqrt{\frac{A}{V \cdot \ell}} \cdot \sqrt{c0}\right)\]
Alternative 47
Error40.0
Cost19776
\[c0 \cdot \sqrt{\frac{\sqrt{A}}{V} \cdot \frac{\sqrt{A}}{\ell}}\]
Alternative 48
Error41.5
Cost19712
\[\sqrt[3]{{\left(c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\right)}^{3}}\]
Alternative 49
Error40.1
Cost19712
\[c0 \cdot \sqrt{\sqrt[3]{{\left(\frac{A}{V \cdot \ell}\right)}^{3}}}\]
Alternative 50
Error27.6
Cost19712
\[c0 \cdot \sqrt[3]{{\left(\sqrt{\frac{A}{V \cdot \ell}}\right)}^{3}}\]
Alternative 51
Error41.5
Cost19712
\[\sqrt[3]{{\left(c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\right)}^{3}}\]
Alternative 52
Error21.5
Cost19648
\[c0 \cdot e^{\log \left(\sqrt{\frac{A}{V \cdot \ell}}\right)}\]
Alternative 53
Error38.5
Cost13376
\[\left(c0 \cdot \sqrt{\frac{1}{V}}\right) \cdot \sqrt{\frac{A}{\ell}}\]
Alternative 54
Error37.4
Cost13376
\[c0 \cdot \left(\sqrt{A} \cdot \sqrt{\frac{1}{V \cdot \ell}}\right)\]
Alternative 55
Error37.6
Cost13376
\[c0 \cdot \left(\sqrt{\frac{1}{V}} \cdot \sqrt{\frac{A}{\ell}}\right)\]
Alternative 56
Error38.1
Cost13376
\[\left(c0 \cdot \sqrt{A}\right) \cdot \sqrt{\frac{\frac{1}{V}}{\ell}}\]
Alternative 57
Error38.1
Cost13248
\[\frac{c0 \cdot \sqrt{A}}{\sqrt{V \cdot \ell}}\]
Alternative 58
Error37.1
Cost13248
\[c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\]
Alternative 59
Error38.3
Cost13248
\[\frac{c0 \cdot \sqrt{\frac{A}{V}}}{\sqrt{\ell}}\]
Alternative 60
Error38.6
Cost13248
\[\frac{c0 \cdot \sqrt{\frac{A}{\ell}}}{\sqrt{V}}\]
Alternative 61
Error37.2
Cost13248
\[c0 \cdot \frac{\sqrt{\frac{A}{V}}}{\sqrt{\ell}}\]
Alternative 62
Error37.5
Cost13248
\[c0 \cdot \frac{\sqrt{\frac{A}{\ell}}}{\sqrt{V}}\]
Alternative 63
Error19.4
Cost6976
\[c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\]
Alternative 64
Error19.3
Cost6976
\[c0 \cdot \sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}}\]
Alternative 65
Error19.1
Cost6976
\[c0 \cdot \sqrt{\frac{1}{V} \cdot \frac{A}{\ell}}\]
Alternative 66
Error18.7
Cost6976
\[c0 \cdot \sqrt{\frac{A}{V} \cdot \frac{1}{\ell}}\]
Alternative 67
Error19.2
Cost6976
\[c0 \cdot \sqrt{A \cdot \frac{\frac{1}{V}}{\ell}}\]
Alternative 68
Error18.6
Cost6848
\[c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\]
Alternative 69
Error19.1
Cost6848
\[c0 \cdot \sqrt{\frac{\frac{A}{\ell}}{V}}\]
Alternative 70
Error19.1
Cost6848
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
Alternative 71
Error64.0
Cost576
\[c0 \cdot \left(\mathsf{NaN} \cdot \frac{A}{V \cdot \ell}\right)\]
Alternative 72
Error64.0
Cost448
\[c0 \cdot \frac{\mathsf{NaN}}{V \cdot \ell}\]
Alternative 73
Error61.7
Cost64
\[1\]
Alternative 74
Error55.2
Cost64
\[0\]
Alternative 75
Error61.7
Cost64
\[-1\]

Error

Derivation

  1. Initial program 19.1

    \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}\]
  2. Using strategy rm

  3. Applied associate-/r*_binary64_68118.6

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt_binary64_77219.0

    \[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{V}}{\color{blue}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}}\]

  6. Applied add-cube-cbrt_binary64_77219.1

    \[\leadsto c0 \cdot \sqrt{\frac{\frac{A}{\color{blue}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  7. Applied add-cube-cbrt_binary64_77219.2

    \[\leadsto c0 \cdot \sqrt{\frac{\frac{\color{blue}{\left(\sqrt[3]{A} \cdot \sqrt[3]{A}\right) \cdot \sqrt[3]{A}}}{\left(\sqrt[3]{V} \cdot \sqrt[3]{V}\right) \cdot \sqrt[3]{V}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  8. Applied times-frac_binary64_74319.2

    \[\leadsto c0 \cdot \sqrt{\frac{\color{blue}{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}} \cdot \frac{\sqrt[3]{A}}{\sqrt[3]{V}}}}{\left(\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}\right) \cdot \sqrt[3]{\ell}}}\]

  9. Applied times-frac_binary64_74315.3

    \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}} \cdot \frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}\]

  10. Applied sqrt-prod_binary64_7537.4

    \[\leadsto c0 \cdot \color{blue}{\left(\sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\right)}\]

  11. Applied associate-*r*_binary64_6777.4

    \[\leadsto \color{blue}{\left(c0 \cdot \sqrt{\frac{\frac{\sqrt[3]{A} \cdot \sqrt[3]{A}}{\sqrt[3]{V} \cdot \sqrt[3]{V}}}{\sqrt[3]{\ell} \cdot \sqrt[3]{\ell}}}\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}\]

  12. Simplified1.2

    \[\leadsto \color{blue}{\left(\left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right| \cdot c0\right)} \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]

  13. Simplified1.2

    \[\leadsto \color{blue}{\left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}}\]

  14. Final simplification1.2

    \[\leadsto \left(c0 \cdot \left|\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}\right|\right) \cdot \sqrt{\frac{\frac{\sqrt[3]{A}}{\sqrt[3]{V}}}{\sqrt[3]{\ell}}}\]

Reproduce

herbie shell --seed 2021042 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))