Details

sample1.2s

Algorithm

intervals

Results

905.0ms	1062×	body	80	nan
169.0ms	386×	body	80	valid

simplify4.9s

Counts

1 → 1

Iterations

Iter	Nodes
4	9030
3	1081
2	188
1	55
0	22

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.8b

localize54.0ms

Local error

Found 4 expressions with local error:

10.9b	(sqrt (/ d l))
10.9b	(sqrt (/ d l))
12.0b	(sqrt (/ d h))
12.8b	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))

rewrite549.0ms

Algorithm

rewrite-expression-head

Rules

16265×	`times-frac`
5466×	`add-sqr-sqrt`
5457×	`*-un-lft-identity` `add-cube-cbrt`
4043×	`sqrt-prod`
3808×	`frac-times`
3375×	`associate-/r/`
2464×	`associate-l/` `associate-r/`
908×	`div-inv`
460×	`add-cbrt-cube` `add-exp-log`
357×	`associate-/l*`
270×	`cbrt-undiv` `div-exp`
130×	`prod-exp` `cbrt-unprod`
13×	`associate-/r*`
7×	`pow1`
6×	`rem-sqrt-square`
4×	`add-log-exp`
3×	`sqrt-pow1` `pow1/2` `sqrt-div`
1×	`clear-num` `frac-2neg` `associate-/l/`

Counts

4 → 5210

Calls

4 calls:

2.0ms	(sqrt (/ d l))
2.0ms	(sqrt (/ d l))
2.0ms	(sqrt (/ d h))
78.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))

series563.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (/ d l))
84.0ms	(sqrt (/ d l))
75.0ms	(sqrt (/ d h))
323.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))

simplify1.2m

Counts

5222 → 5222

Iterations

Iter	Nodes
1	28332
0	8552

prune1.6m

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.5b

localize62.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))
10.9b	(sqrt (/ d l))
10.9b	(sqrt (/ d l))
12.8b	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

16865×	`times-frac`
5674×	`add-sqr-sqrt`
5668×	`*-un-lft-identity` `add-cube-cbrt`
4329×	`sqrt-prod`
4097×	`frac-times`
3631×	`associate-/r/`
2651×	`associate-l/` `associate-r/`
948×	`div-inv`
645×	`add-cbrt-cube` `add-exp-log`
373×	`associate-/l*`
363×	`cbrt-undiv` `div-exp`
195×	`prod-exp` `cbrt-unprod`
35×	`associate-/r*`
6×	`pow1`
4×	`rem-sqrt-square` `add-log-exp`
3×	`sqrt-div`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 5641

Calls

4 calls:

54.0ms	(/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))
2.0ms	(sqrt (/ d l))
2.0ms	(sqrt (/ d l))
61.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))

series501.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d)))))
48.0ms	(sqrt (/ d l))
47.0ms	(sqrt (/ d l))
254.0ms	(/ (/ (sqrt (/ d l)) (/ 2 (* (* (/ M 2) (/ D d)) (* (/ M 2) (/ D d))))) (/ l h))

simplify42.2s

Counts

5653 → 5653

Iterations

Iter	Nodes
1	28395
0	8548

prune1.6m

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 8.5b

localize103.0ms

Local error

Found 4 expressions with local error:

4.1b	(/ (/ (sqrt 2) (/ M 2)) (/ D d))
4.4b	(/ (sqrt (/ (cbrt d) l)) (/ (/ (sqrt 2) (/ M 2)) (/ D d)))
6.9b	(/ (/ (sqrt (* (cbrt d) (cbrt d))) (/ (/ (sqrt 2) (/ M 2)) (/ D d))) (* (/ (cbrt l) (cbrt h)) (/ (cbrt l) (cbrt h))))
10.9b	(sqrt (/ d l))

rewrite4.2s

Algorithm

rewrite-expression-head

Rules

183764×	`times-frac`
69214×	`add-sqr-sqrt`
69211×	`*-un-lft-identity` `add-cube-cbrt`
43835×	`sqrt-prod`
9765×	`cbrt-prod`
7223×	`div-inv`
4449×	`associate-/l*`
1098×	`associate-/r*`
497×	`associate-/r/`
308×	`add-exp-log`
244×	`add-cbrt-cube`
219×	`cbrt-undiv` `div-exp`
32×	`prod-exp` `cbrt-unprod`
5×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
2×	`rem-sqrt-square` `sqrt-div`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/`

Counts

4 → 38236

Calls

4 calls:

11.0ms	(/ (/ (sqrt 2) (/ M 2)) (/ D d))
95.0ms	(/ (sqrt (/ (cbrt d) l)) (/ (/ (sqrt 2) (/ M 2)) (/ D d)))
93.0ms	(/ (/ (sqrt (* (cbrt d) (cbrt d))) (/ (/ (sqrt 2) (/ M 2)) (/ D d))) (* (/ (cbrt l) (cbrt h)) (/ (cbrt l) (cbrt h))))
2.0ms	(sqrt (/ d l))

series870.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (sqrt 2) (/ M 2)) (/ D d))
401.0ms	(/ (sqrt (/ (cbrt d) l)) (/ (/ (sqrt 2) (/ M 2)) (/ D d)))
300.0ms	(/ (/ (sqrt (* (cbrt d) (cbrt d))) (/ (/ (sqrt 2) (/ M 2)) (/ D d))) (* (/ (cbrt l) (cbrt h)) (/ (cbrt l) (cbrt h))))
59.0ms	(sqrt (/ d l))

simplify4.7m

Iterations

Iter	Nodes
0	48145