Details

sample1.2s

Algorithm

intervals

Results

518.0ms	3503×	body	80	nan
379.0ms	167×	body	640	valid
54.0ms	50×	body	320	valid
3.0ms	16×	body	160	valid
3.0ms	21×	body	80	valid
1.0ms	2×	body	1280	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	31
1	51	31
2	155	31
3	895	31
done	5000	31

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize48.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ z 1.0)) (sqrt z))
3.2b	(- (sqrt (+ y 1.0)) (sqrt y))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite175.0ms

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:

41.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
42.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
45.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
42.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series282.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify802.0ms

Counts

88 → 88

Iterations

Useful iterations: done (800.0ms)

Iter	Nodes	Cost
0	208	1242
1	476	1140
2	1698	1050
done	5000	1036

prune704.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
3.0b	(- (sqrt (+ z 1.0)) (sqrt z))
3.2b	(- (sqrt (+ y 1.0)) (sqrt y))
3.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

89.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
63.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
57.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
52.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series433.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
91.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
92.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.3s

Counts

119 → 119

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	271	1925
1	646	1631
2	2664	1510
done	5002	1494

prune836.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
3.0b	(- (sqrt (+ z 1.0)) (sqrt z))
3.2b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite230.0ms

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:

44.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
55.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series492.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
141.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
78.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
83.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify1.4s

Counts

141 → 141

Iterations

Useful iterations: 2 (550.0ms)

Iter	Nodes	Cost
0	310	2330
1	747	2006
2	3155	1852
done	5000	1852

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.9b	(- (+ y 1.0) y)
3.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

68.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
64.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
42.0ms	(- (+ y 1.0) y)
42.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series429.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
193.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.0ms	(- (+ y 1.0) y)
76.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.4s

Counts

139 → 139

Iterations

Useful iterations: 2 (511.0ms)

Iter	Nodes	Cost
0	293	2171
1	707	1867
2	2995	1725
done	5000	1725

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

regimes1.8s

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	51
1	40	51
done	40	51

end0.0ms

sample846.0ms

Algorithm

intervals

Results

551.0ms	2906×	body	80	nan
66.0ms	123×	body	640	valid
21.0ms	45×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	10×	body	80	valid
1.0ms	1×	body	1280	valid