Details

sample1.1s

Algorithm

intervals

Results

723.0ms	3786×	body	80	nan
95.0ms	179×	body	640	valid
14.0ms	38×	body	320	valid
5.0ms	19×	body	160	valid
3.0ms	4×	body	1280	valid
2.0ms	16×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize64.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite275.0ms

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:

50.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
87.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
58.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
77.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series371.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
86.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
99.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
85.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.3s

Counts

88 → 88

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	208	1242
1	476	1140
2	1698	1050
done	5001	1036

prune516.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite322.0ms

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:

105.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
46.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
83.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
79.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series495.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
123.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
79.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
97.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify1.6s

Counts

119 → 119

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	271	1925
1	646	1631
2	2662	1510
done	5004	1494

prune960.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))
2.3b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite282.0ms

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:

88.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
85.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
46.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
51.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series545.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
155.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
97.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
104.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify1.5s

Counts

141 → 141

Iterations

Useful iterations: 2 (605.0ms)

Iter	Nodes	Cost
0	308	2328
1	741	2006
2	3110	1854
done	5000	1854

prune910.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.4b	(- (+ y 1.0) y)
2.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite223.0ms

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:

69.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
60.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
35.0ms	(- (+ y 1.0) y)
49.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series395.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
149.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
1.0ms	(- (+ y 1.0) y)
91.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts

139 → 139

Iterations

Useful iterations: 2 (669.0ms)

Iter	Nodes	Cost
0	291	2169
1	701	1867
2	2958	1727
done	5001	1727

prune864.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

regimes726.0ms

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	29	39
1	40	37
2	44	37
done	44	37

end0.0ms

sample6.3s

Algorithm

intervals

Results

4.4s	21956×	body	80	nan
438.0ms	979×	body	640	valid
110.0ms	239×	body	320	valid
21.0ms	37×	body	1280	valid
18.0ms	85×	body	160	valid
9.0ms	90×	body	80	valid