Details

sample56.0ms

Algorithm

intervals

Results

19.0ms	276×	body	80	valid
11.0ms	28×	body	1280	valid
8.0ms	29×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	11×	body	160	valid

simplify39.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	68	8
2	243	8
3	1266	8
4	5001	8

prune3.0ms

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: 30.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.4b	(* (* x (pow sin 2.0)) x)
7.4b	(* x (pow sin 2.0))
20.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`associate-r`
11×	`associate-l`
9×	`*-commutative`
8×	`associate-/r*`
6×	`sqr-pow`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 24

Calls

4 calls:

8.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
7.0ms	(* (* x (pow sin 2.0)) x)
3.0ms	(* x (pow sin 2.0))
7.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series826.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
146.0ms	(* (* x (pow sin 2.0)) x)
137.0ms	(* x (pow sin 2.0))
250.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify58.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	122	171
1	397	165
2	1998	165
3	5001	165

prune116.0ms

Filtered

36 candidates to 29 candidates (80.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	28	8	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	29	8	37

Merged error: 11.5b

Counts

37 → 8

localize15.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
8.3b	(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
14.1b	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-/r*`
12×	`associate-r`
9×	`associate-/l/`
8×	`*-commutative` `sqr-pow`
6×	`div-inv`
5×	`associate-l`
3×	`frac-2neg` `times-frac` `clear-num`
1×	`associate-/l*`

Counts

3 → 33

Calls

3 calls:

6.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
9.0ms	(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
5.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

series724.0ms

Counts

3 → 9

Calls

3 calls:

217.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
295.0ms	(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
211.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify169.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	211	319
1	766	280
2	4786	260
3	5002	260

prune165.0ms

Filtered

42 candidates to 37 candidates (88.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	34	8	42
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	40	10	50

Merged error: 5.8b

Counts

50 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
1.7b	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
6.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
8.3b	(/ (/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
39×	`div-inv`
32×	`associate-r`
27×	`sqr-pow`
24×	`*-commutative`
22×	`associate-/l/`
18×	`associate-/r*`
16×	`associate-l`
9×	`associate-/l*`
6×	`frac-2neg` `clear-num`

Counts

4 → 77

Calls

4 calls:

4.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
8.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
6.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
17.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))

series911.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
224.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
210.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
296.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))

simplify54.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	442	1043
1	1610	870
2	5001	838

prune326.0ms

Filtered

89 candidates to 71 candidates (79.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	76	13	89
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	84	15	99

Merged error: 1.4b

Counts

99 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
0.2b	(/ (/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2))))
6.0b	(* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2)))
6.0b	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
36×	`div-inv`
25×	`sqr-pow`
24×	`associate-l`
22×	`*-commutative`
19×	`associate-/l/`
16×	`associate-r`
15×	`associate-/r*`
6×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 71

Calls

4 calls:

4.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
13.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2))))
6.0ms	(* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2)))
7.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

series949.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
301.0ms	(/ (/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2))))
211.0ms	(* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2)))
256.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

simplify56.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	449	985
1	1693	831
2	5001	805

prune282.0ms

Filtered

83 candidates to 69 candidates (83.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	87	11	98

Merged error: 0.9b

Counts

98 → 11

regimes275.0ms

Accuracy

0% (1.8b remaining)

Error of 2.6b against oracle of 0.8b and baseline of 2.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

sample1.7s

Algorithm

intervals

Results

623.0ms	9056×	body	80	valid
371.0ms	889×	body	1280	valid
263.0ms	912×	body	640	valid
130.0ms	548×	body	320	valid
43.0ms	298×	body	160	valid