Details

sample35.0ms

Algorithm

intervals

Results

10.0ms	286×	body	80	valid
7.0ms	287×	body	80	nan

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	12	8
2	14	8
done	14	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b	(* c0 (sqrt (/ A (* V l))))
6.8b	(/ A (* V l))
15.2b	(sqrt (/ A (* V l)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
6×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `*-commutative`

Counts

3 → 72

Calls

3 calls:

11.0ms	(* c0 (sqrt (/ A (* V l))))
3.0ms	(/ A (* V l))
3.0ms	(sqrt (/ A (* V l)))

series102.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* c0 (sqrt (/ A (* V l))))
24.0ms	(/ A (* V l))
31.0ms	(sqrt (/ A (* V l)))

simplify727.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	109	705
1	219	657
2	662	605
3	2034	605
done	5000	605

prune221.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt A)
0.7b	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
4.7b	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
15.2b	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
28×	`times-frac`
27×	`add-exp-log`
26×	`associate-r`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
14×	`cbrt-prod`
11×	`pow1`
10×	`associate-l`
9×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`sqrt-div` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `pow-prod-down` `associate-*l/`
2×	`sqrt-pow1` `sqrt-prod` `*-commutative` `div-inv`
1×	`pow1/2` `pow1/3`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt A)
43.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
26.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
14.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

series537.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(cbrt A)
73.0ms	(* c0 (sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))))
42.0ms	(* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l))
55.0ms	(sqrt (* (/ (* (cbrt A) (cbrt A)) V) (/ (cbrt A) l)))

simplify731.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (172.0ms)

Iter	Nodes	Cost
0	193	1812
1	528	1718
2	2172	1223
done	5000	1223

prune428.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.7b

localize7.0ms

Local error

Found 3 expressions with local error:

0.7b	(* c0 (sqrt (/ (/ A V) l)))
6.3b	(/ (/ A V) l)
15.2b	(sqrt (/ (/ A V) l))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

213×	`times-frac`
134×	`add-sqr-sqrt`
117×	`add-cube-cbrt` `*-un-lft-identity`
89×	`sqrt-prod`
46×	`associate-r`
13×	`div-inv` `associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`unswap-sqr`
3×	`cbrt-undiv` `expm1-log1p-u` `rem-sqrt-square` `div-exp` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div`
1×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `cbrt-unprod` `associate-/l/`

Counts

3 → 197

Calls

3 calls:

26.0ms	(* c0 (sqrt (/ (/ A V) l)))
6.0ms	(/ (/ A V) l)
8.0ms	(sqrt (/ (/ A V) l))

series102.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* c0 (sqrt (/ (/ A V) l)))
20.0ms	(/ (/ A V) l)
34.0ms	(sqrt (/ (/ A V) l))

simplify144.0ms

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	316	2554
1	592	2368