Details

analyze1.2s

Algorithm: search

sample66.0ms

Algorithm

intervals

Results

15.0ms	182×	body	80	valid
12.0ms	25×	body	1280	valid
10.0ms	31×	body	640	valid
5.0ms	64×	body	80	invalid
3.0ms	14×	body	320	valid
2.0ms	4×	body	1280	invalid
2.0ms	6×	body	640	invalid
1.0ms	4×	body	320	invalid
1.0ms	4×	body	160	valid
0.0ms	3×	body	160	invalid

simplify41.0ms

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

prune4.0ms

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: 29.8b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
2.9b	(* (* x (pow s 2.0)) x)
8.9b	(* x (pow s 2.0))
20.2b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
82×	`prod-exp`
34×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
17×	`add-sqr-sqrt`
16×	`div-exp` `cbrt-unprod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`associate-r` `associate-l`
7×	`unpow-prod-down`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 115

Calls

4 calls:

10.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms	(* (* x (pow s 2.0)) x)
5.0ms	(* x (pow s 2.0))
9.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series240.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
33.0ms	(* (* x (pow s 2.0)) x)
32.0ms	(* x (pow s 2.0))
90.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	571	1041
1	2506	875
2	5001	871

prune247.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 14.9b

Counts

128 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.5b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
2.9b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
20.2b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

416×	`add-exp-log`
343×	`prod-exp`
84×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
43×	`div-exp`
29×	`cbrt-unprod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
9×	`associate-l`
6×	`pow1` `unpow-prod-down`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
2×	`sqr-pow`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 186

Calls

4 calls:

8.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
14.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
9.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
12.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

series235.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
80.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
36.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
85.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify96.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	721	2340
1	3234	1837
2	5001	1781

prune238.0ms

Filtered

69 candidates to 198 candidates (-187.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Merged error: 3.3b

Counts

209 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.5b	(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
44×	`prod-exp`
21×	`add-cbrt-cube`
17×	`associate-l`
16×	`add-sqr-sqrt`
14×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity` `pow-exp`
11×	`pow1`
8×	`cbrt-unprod`
6×	`unpow-prod-down`
5×	`associate-r`
4×	`add-log-exp`
3×	`times-frac` `swap-sqr` `-commutative` `associate-/l`
2×	`cbrt-undiv` `div-exp` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `pow-prod-down` `clear-num` `associate-/r*` `pow-sqr` `pow-prod-up` `div-inv` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

3.0ms	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series208.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
47.0ms	(/ (cos (* 2.0 x)) (* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))))
73.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
71.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify54.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	402	1518
1	1482	1245
2	5002	1172

prune375.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	107	11	118
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	113	14	127

Merged error: 0.1b

Counts

127 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
0.4b	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.4b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
63×	`add-exp-log`
58×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`prod-exp`
21×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`pow-to-exp` `associate-l` `pow-exp`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative` `sqr-pow`
1×	`associate-/l/`

Counts

4 → 157

Calls

4 calls:

6.0ms	(/ (/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
4.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
7.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series226.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2)))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
30.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
72.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
75.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify72.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	595	3343
1	2082	3048
2	5001	2963

prune595.0ms

Filtered

111 candidates to 169 candidates (-52.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	169	14	183

Merged error: 0.0b

Counts

183 → 14

regimes650.0ms

Accuracy

19.2% (2.3b remaining)

Error of 2.4b against oracle of 0.1b and baseline of 2.9b

bsearch691.0ms

Steps

Iters	Range		Point
7	2.230462229123498e+211	5.704467340174107e+213	3.441638225356468e+213
7	-1.954975831013636e+164	-8.227617384747178e+161	-5.409162069956886e+162

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	24
1	45	24

end0.0ms

analyze998.0ms

Algorithm: search

sample1.9s

Algorithm

intervals

Results

511.0ms	5976×	body	80	valid
332.0ms	667×	body	1280	valid
256.0ms	719×	body	640	valid
155.0ms	1804×	body	80	invalid
111.0ms	428×	body	320	valid
90.0ms	279×	body	640	invalid
63.0ms	137×	body	1280	invalid
47.0ms	185×	body	320	invalid
36.0ms	210×	body	160	valid
20.0ms	101×	body	160	invalid

Details

analyze1.2s

sample66.0ms

simplify41.0ms

prune4.0ms

localize19.0ms

rewrite35.0ms

series240.0ms

simplify65.0ms

prune247.0ms

localize16.0ms

rewrite58.0ms

series235.0ms

simplify96.0ms

prune238.0ms

localize16.0ms

rewrite27.0ms

series208.0ms

simplify54.0ms

prune375.0ms

localize19.0ms

rewrite30.0ms

series226.0ms

simplify72.0ms

prune595.0ms

regimes650.0ms

bsearch691.0ms

simplify2.0ms

end0.0ms

analyze998.0ms

sample1.9s

Profiling