Details

sample574.0ms

Algorithm

intervals

Results

369.0ms	4117×	body	80	nan
63.0ms	168×	body	640	valid
16.0ms	48×	body	320	valid
3.0ms	16×	body	160	valid
2.0ms	5×	body	1280	valid
2.0ms	19×	body	80	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 5.9b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))
4.8b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite37.0ms

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:

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

series283.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
72.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune383.0ms

Filtered

88 candidates to 56 candidates (63.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 0.6b

Counts

89 → 5

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ x 1.0)) (sqrt x))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite39.0ms

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:

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

series378.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
77.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify67.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	627	1071
1	2344	979
2	5002	943

prune481.0ms

Filtered

119 candidates to 71 candidates (59.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	118	6	124

Merged error: 0.0b

Counts

124 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite45.0ms

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:

9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series423.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
137.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	721	1296
1	2733	1177
2	5001	1135

prune561.0ms

Filtered

141 candidates to 83 candidates (58.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	140	7	147

Merged error: 0.0b

Counts

147 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.5b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

755×	`*-un-lft-identity`
676×	`sqrt-prod`
591×	`times-frac`
285×	`distribute-lft-out`
260×	`add-sqr-sqrt`
244×	`add-cube-cbrt`
37×	`associate-/l*`
24×	`associate-/r/`
22×	`sqrt-div`
15×	`associate-/r*`
13×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp` `difference-of-squares`
6×	`distribute-lft-out--`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `flip--`

Counts

4 → 444

Calls

4 calls:

12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
28.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series434.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
145.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
75.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify108.0ms

Algorithm

egg-herbie

Counts

456 → 456

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1312	8626
1	5002	7486

prune1.0s

Filtered

456 candidates to 146 candidates (32.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	456	0	456
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	456	7	463

Merged error: 0.0b

Counts

463 → 7

regimes520.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	22
1	48	22
2	48	22

end0.0ms

sample635.0ms

Algorithm

intervals

Results

417.0ms	4594×	body	80	nan
69.0ms	191×	body	640	valid
14.0ms	53×	body	320	valid
3.0ms	17×	body	160	valid
3.0ms	6×	body	1280	valid
2.0ms	20×	body	80	valid

Details

sample574.0ms

simplify28.0ms

prune5.0ms

localize22.0ms

rewrite37.0ms

series283.0ms

simplify46.0ms

prune383.0ms

localize29.0ms

rewrite39.0ms

series378.0ms

simplify67.0ms

prune481.0ms

localize25.0ms

rewrite45.0ms

series423.0ms

simplify68.0ms

prune561.0ms

localize28.0ms

rewrite98.0ms

series434.0ms

simplify108.0ms

prune1.0s

regimes520.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample635.0ms

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