Details

sample733.0ms

Algorithm

intervals

Results

417.0ms	3810×	body	80	nan
74.0ms	175×	body	640	valid
14.0ms	45×	body	320	valid
4.0ms	17×	body	160	valid
2.0ms	16×	body	80	valid
2.0ms	3×	body	1280	valid

simplify275.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	31
1	51	31
2	154	31
3	879	31
done	5000	31

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 4.8b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series51.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
19.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify613.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (194.0ms)

Iter	Nodes	Cost
0	282	1592
1	697	1508
2	2730	1452
done	5000	1452

prune300.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 3.5b

Counts

89 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.4b	(- (+ z 1.0) z)
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`sqrt-prod`
15×	`add-log-exp`
13×	`difference-of-squares`
11×	`distribute-lft-out--`
5×	`diff-log`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
1×	`associate--l+` `sum-log`

Counts

4 → 74

Calls

4 calls:

9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
7.0ms	(- (+ z 1.0) z)
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series34.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
1.0ms	(- (+ z 1.0) z)
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
12.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify529.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (161.0ms)

Iter	Nodes	Cost
0	248	1345
1	601	1278
2	2270	1225
done	5000	1225

prune273.0ms

Filtered

58 candidates to 86 candidates (-48.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 2.7b

Counts

94 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
3.1b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
40×	`sqrt-prod`
39×	`add-sqr-sqrt`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

11.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series49.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
10.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
17.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify679.0ms

Counts

110 → 110

Iterations

Useful iterations: done (675.0ms)

Iter	Nodes	Cost
0	333	1965
1	818	1866
2	3098	1751
done	5000	1749

prune380.0ms

Filtered

73 candidates to 110 candidates (-50.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	7	110
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 2.7b

Counts

118 → 12

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.0b	(- (sqrt (+ y 1.0)) (sqrt y))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (+ t 1.0) t)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`sqrt-prod`
19×	`distribute-lft-out`
18×	`times-frac`
15×	`add-cube-cbrt`
13×	`add-log-exp`
9×	`difference-of-squares`
8×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `diff-log`
3×	`sub-neg` `flip3--` `flip--` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `associate--l+` `clear-num` `sum-log` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

11.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
9.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
14.0ms	(- (+ t 1.0) t)

series33.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
1.0ms	(- (+ t 1.0) t)

simplify607.0ms

Counts

108 → 108

Iterations

Useful iterations: done (603.0ms)

Iter	Nodes	Cost
0	298	1718
1	725	1636
2	2639	1524
done	5001	1522

prune276.0ms

Filtered

71 candidates to 108 candidates (-52.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	109	11	120

Merged error: 1.3b

Counts

120 → 11

regimes1.2s

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	35
1	35	35
done	35	35

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.7s	15471×	body	80	nan
348.0ms	694×	body	640	valid
69.0ms	195×	body	320	valid
17.0ms	19×	body	1280	valid
15.0ms	69×	body	160	valid
8.0ms	76×	body	80	valid

Details

sample733.0ms

simplify275.0ms

prune6.0ms

localize34.0ms

rewrite39.0ms

series51.0ms

simplify613.0ms

prune300.0ms

localize35.0ms

rewrite36.0ms

series34.0ms

simplify529.0ms

prune273.0ms

localize26.0ms

rewrite42.0ms

series49.0ms

simplify679.0ms

prune380.0ms

localize27.0ms

rewrite46.0ms

series33.0ms

simplify607.0ms

prune276.0ms

regimes1.2s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample2.9s

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