Details

sample431.0ms

Algorithm

intervals

Results

252.0ms	4141×	body	80	nan
44.0ms	177×	body	640	valid
9.0ms	50×	body	320	valid
2.0ms	13×	body	160	valid
1.0ms	14×	body	80	valid
1.0ms	2×	body	1280	valid

simplify259.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize28.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))
4.3b	(- (sqrt (+ t 1.0)) (sqrt t))
4.9b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite91.0ms

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:

24.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
22.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
21.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
22.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series279.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
66.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify435.0ms

Counts

88 → 88

Iterations

Useful iterations: done (432.0ms)

Iter	Nodes	Cost
0	208	1242
1	473	1140
2	1479	1050
done	5001	1036

prune410.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.8b

localize25.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.7b	(- (+ y 1.0) y)
4.3b	(- (sqrt (+ t 1.0)) (sqrt t))

rewrite86.0ms

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:

21.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
21.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
20.0ms	(- (+ y 1.0) y)
21.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series220.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
73.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(- (+ y 1.0) y)
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify410.0ms

Counts

86 → 86

Iterations

Useful iterations: done (407.0ms)

Iter	Nodes	Cost
0	191	1083
1	429	1001
2	1318	923
done	5000	879

prune424.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))
3.7b	(- (+ y 1.0) y)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
36×	`sqrt-prod`
34×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`times-frac`
16×	`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` `associate-/l*`
3×	`sub-neg` `flip3--` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate--l+` `clear-num` `sum-log` `div-inv`

Counts

4 → 105

Calls

4 calls:

31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
21.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
22.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
20.0ms	(- (+ y 1.0) y)

series292.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
74.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
1.0ms	(- (+ y 1.0) y)

simplify830.0ms

Counts

117 → 117

Iterations

Useful iterations: done (827.0ms)

Iter	Nodes	Cost
0	254	1766
1	596	1514
2	2083	1381
done	5001	1375

prune557.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
2.8b	(- (sqrt (+ x 1.0)) (sqrt x))
2.9b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

30.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
23.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
24.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
21.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series446.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
150.0ms	(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
74.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
74.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify944.0ms

Counts

141 → 141

Iterations

Useful iterations: done (940.0ms)

Iter	Nodes	Cost
0	310	2330
1	735	2042
2	2595	1848
done	5000	1840

prune596.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

regimes696.0ms

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	30	39
1	40	37
2	50	37
done	50	37

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	21971×	body	80	nan
240.0ms	954×	body	640	valid
56.0ms	300×	body	320	valid
12.0ms	92×	body	160	valid
8.0ms	123×	body	80	valid
8.0ms	23×	body	1280	valid