Details

analyze267.0ms (3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

sample136.0ms (1.5%)

Algorithm

1×

intervals

Results

66.0ms	170×	body	640	valid
30.0ms	283×	body	80	nan
13.0ms	46×	body	320	valid
3.0ms	29×	body	80	valid
2.0ms	9×	body	160	valid
1.0ms	2×	body	1280	valid

simplify41.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5040	31

prune19.0ms (0.2%)

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: 6.2b

Counts

2 → 2

localize23.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
3.6b	(- (sqrt (+ y 1.0)) (sqrt y))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite34.0ms (0.4%)

Algorithm

1×	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 → 72

Calls

4 calls:

8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series41.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

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

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4985	1360
1	4985	1360

prune308.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 0.6b

Counts

86 → 7

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
2.4b	(- (sqrt (+ x 1.0)) (sqrt x))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite41.0ms (0.5%)

Algorithm

1×	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 → 104

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series39.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))

simplify42.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4959	1837
1	4959	1837

prune425.0ms (4.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	109	7	116
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	114	9	123

Merged error: 0.3b

Counts

123 → 9

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
2.5b	(- (sqrt (+ t 1.0)) (sqrt t))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite42.0ms (0.5%)

Algorithm

1×	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 → 127

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
7.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series41.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5049	2132

prune737.0ms (8.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 0.2b

Counts

148 → 9

localize28.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ 1.0 t)) (sqrt t)))
0.2b	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
4.0b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 150

Calls

4 calls:

13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
10.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 t)) (sqrt t)))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series38.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
10.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 y)) (sqrt y)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
9.0ms	(/ 1.0 (+ (sqrt (+ 1.0 t)) (sqrt t)))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5812	2423

prune610.0ms (6.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	161	10	171

Merged error: 0.0b

Counts

171 → 10

regimes1.5s (17%)

Accuracy

Total 0.0b remaining (50.5%)

Threshold costs 0.0b (50.5%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	39
1	42	39

end0.0ms (0%)

sample4.2s (47.3%)

Algorithm

1×

intervals

Results

2.1s	5316×	body	640	valid
951.0ms	9523×	body	80	nan
473.0ms	1573×	body	320	valid
79.0ms	406×	body	160	valid
73.0ms	136×	body	1280	valid
57.0ms	569×	body	80	valid

Details

analyze267.0ms (3%)

sample136.0ms (1.5%)

simplify41.0ms (0.5%)

prune19.0ms (0.2%)

localize23.0ms (0.3%)

rewrite34.0ms (0.4%)

series41.0ms (0.5%)

simplify44.0ms (0.5%)

prune308.0ms (3.5%)

localize26.0ms (0.3%)

rewrite41.0ms (0.5%)

series39.0ms (0.4%)

simplify42.0ms (0.5%)

prune425.0ms (4.8%)

localize31.0ms (0.3%)

rewrite42.0ms (0.5%)

series41.0ms (0.5%)

simplify47.0ms (0.5%)

prune737.0ms (8.3%)

localize28.0ms (0.3%)

rewrite48.0ms (0.5%)

series38.0ms (0.4%)

simplify69.0ms (0.8%)

prune610.0ms (6.9%)

regimes1.5s (17%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample4.2s (47.3%)

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