Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	305×	body	80	valid
14.0ms	25×	body	1280	valid
7.0ms	25×	body	640	valid
3.0ms	13×	body	320	valid
2.0ms	15×	body	160	valid

simplify42.0ms

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: 29.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
3.7b	(* (* x (pow sin 2.0)) x)
9.2b	(* x (pow sin 2.0))
18.6b	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite22.0ms

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:

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

series835.0ms

Counts

4 → 12

Calls

4 calls:

304.0ms	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
143.0ms	(* (* x (pow sin 2.0)) x)
131.0ms	(* x (pow sin 2.0))
257.0ms	(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify59.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	171
1	393	165
2	1987	165
3	5002	165

prune123.0ms

Filtered

36 candidates to 29 candidates (80.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	27	9	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	9	37

Merged error: 9.9b

Counts

37 → 9

localize15.0ms

Local error

Found 3 expressions with local error:

0.8b	(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2)))))
5.8b	(/ (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))) (* (pow sin (/ 2.0 2)) x))
11.6b	(* (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))))

series727.0ms

Counts

3 → 9

Calls

3 calls:

229.0ms	(/ (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))
203.0ms	(* (pow cos 2.0) (* x (pow sin (/ 2.0 2))))

simplify170.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	209	319
1	760	280
2	4765	260
3	5001	260

prune158.0ms

Filtered

42 candidates to 36 candidates (85.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	34	8	42
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	41	10	51

Merged error: 4.4b

Counts

51 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
1.0b	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2)))))
4.0b	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
5.8b	(/ (/ (/ (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))

rewrite34.0ms

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))))
13.0ms	(/ (/ (/ (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))

series920.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ (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)))))
213.0ms	(* (pow cos (/ 2.0 2)) (* x (pow sin (/ 2.0 2))))
297.0ms	(/ (/ (/ (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))

simplify52.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	440	1043
1	1603	870
2	5001	838

prune304.0ms

Filtered

89 candidates to 69 candidates (77.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	8	1	9
Picked	0	1	1
Done	0	0	0
Total	87	12	99

Merged error: 0.7b

Counts

99 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (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))))
4.0b	(* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2)))
4.2b	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

rewrite32.0ms

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

series943.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (cos (* 2.0 x)) (pow cos (/ 2.0 2)))
302.0ms	(/ (/ (/ (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))))
207.0ms	(* (* (pow sin (/ 2.0 2)) x) (pow cos (/ 2.0 2)))
252.0ms	(/ (/ (cos (* 2.0 x)) (pow cos (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))

simplify54.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	447	985
1	1686	831
2	5001	805

prune280.0ms

Filtered

83 candidates to 69 candidates (83.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	84	11	95

Merged error: 0.6b

Counts

95 → 11

regimes254.0ms

Accuracy

0% (1.8b remaining)

Error of 2.7b against oracle of 0.8b and baseline of 2.7b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	17
1	23	17

end0.0ms

sample1.7s

Algorithm

intervals

Results

654.0ms	9168×	body	80	valid
334.0ms	793×	body	1280	valid
266.0ms	923×	body	640	valid
120.0ms	522×	body	320	valid
43.0ms	308×	body	160	valid