Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample70.0ms

Algorithm

intervals

Results

17.0ms	186×	body	80	valid
13.0ms	25×	body	1280	valid
8.0ms	23×	body	640	valid
6.0ms	9×	body	640	invalid
5.0ms	56×	body	80	invalid
4.0ms	15×	body	320	valid
2.0ms	7×	body	320	invalid
1.0ms	7×	body	160	valid
1.0ms	1×	body	1280	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4845	16
1	4845	16

prune13.0ms

Filtered

1 candidates to 1 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: 24.9b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
6.0b	(* (* x (pow s 2.0)) x)
7.3b	(* x (pow s 2.0))
16.6b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite37.0ms

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:

14.0ms	(/ (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))

series222.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
31.0ms	(* (* x (pow s 2.0)) x)
33.0ms	(* x (pow s 2.0))
79.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify66.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4965	1594
1	4965	1594

prune257.0ms

Filtered

72 candidates to 127 candidates (-76.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	116	11	127
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 12.0b

Counts

129 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

4.3b	(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
5.6b	(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
7.3b	(* x (pow s 2.0))
8.3b	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

226×	`add-exp-log`
202×	`prod-exp`
50×	`pow-to-exp` `pow-exp`
34×	`add-cbrt-cube`
20×	`cbrt-unprod`
17×	`add-sqr-sqrt`
16×	`associate-r`
14×	`associate-l`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`unpow-prod-down`
6×	`pow1`
4×	`*-commutative` `add-log-exp` `sqr-pow`
3×	`unswap-sqr`
1×	`pow-prod-down`

Counts

4 → 146

Calls

4 calls:

12.0ms	(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
8.0ms	(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
5.0ms	(* x (pow s 2.0))
7.0ms	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
60.0ms	(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
30.0ms	(* x (pow s 2.0))
56.0ms	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

simplify61.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4992	1911
1	4992	1911

prune283.0ms

Filtered

71 candidates to 158 candidates (-122.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	151	7	158
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	156	14	170

Merged error: 10.6b

Counts

170 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos (* 2.0 x)) (* (* x (pow c (/ 2.0 2))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
6.9b	(* (* x (pow c (/ 2.0 2))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
7.3b	(* x (pow s 2.0))
8.3b	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

461×	`add-exp-log`
374×	`prod-exp`
90×	`pow-to-exp` `pow-exp`
61×	`add-cbrt-cube`
53×	`div-exp`
34×	`cbrt-unprod`
16×	`add-sqr-sqrt`
15×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-undiv` `unpow-prod-down`
6×	`pow1`
5×	`associate-l`
4×	`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 → 201

Calls

4 calls:

14.0ms	(/ (cos (* 2.0 x)) (* (* x (pow c (/ 2.0 2))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
10.0ms	(* (* x (pow c (/ 2.0 2))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
5.0ms	(* x (pow s 2.0))
7.0ms	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ (cos (* 2.0 x)) (* (* x (pow c (/ 2.0 2))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
60.0ms	(* (* x (pow c (/ 2.0 2))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
29.0ms	(* x (pow s 2.0))
56.0ms	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

simplify51.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5798	3236

prune274.0ms

Filtered

71 candidates to 213 candidates (-200.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	207	6	213
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	212	15	227

Merged error: 9.1b

Counts

227 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* x 2.0)) (* x (pow c (/ 2.0 2))))
7.2b	(/ (/ (cos (* x 2.0)) (* x (pow c (/ 2.0 2)))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
7.3b	(* x (pow s 2.0))
8.3b	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

323×	`add-exp-log`
171×	`prod-exp`
121×	`div-exp`
57×	`pow-to-exp` `pow-exp`
52×	`add-cbrt-cube`
20×	`add-sqr-sqrt`
17×	`cbrt-undiv` `cbrt-unprod`
16×	`times-frac`
15×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
10×	`associate-/l*`
7×	`unpow-prod-down`
4×	`pow1` `associate-l` `div-inv` `add-log-exp`
3×	`unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `associate-/r` `-commutative`
1×	`associate-/l/`

Counts

4 → 178

Calls

4 calls:

5.0ms	(/ (cos (* x 2.0)) (* x (pow c (/ 2.0 2))))
12.0ms	(/ (/ (cos (* x 2.0)) (* x (pow c (/ 2.0 2)))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
5.0ms	(* x (pow s 2.0))
6.0ms	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (cos (* x 2.0)) (* x (pow c (/ 2.0 2))))
76.0ms	(/ (/ (cos (* x 2.0)) (* x (pow c (/ 2.0 2)))) (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
30.0ms	(* x (pow s 2.0))
55.0ms	(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

simplify74.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5001	3223

prune255.0ms

Filtered

84 candidates to 190 candidates (-126.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	3	10	13
Picked	1	0	1
Done	0	1	1
Total	191	14	205

Merged error: 9.1b

Counts

205 → 14

regimes729.0ms

Accuracy

-10% (6.9b remaining)

Error of 15.0b against oracle of 8.1b and baseline of 14.4b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	95
1	52	95

end0.0ms

sample2.0s

Algorithm

intervals

Results

550.0ms	5979×	body	80	valid
340.0ms	661×	body	1280	valid
262.0ms	730×	body	640	valid
165.0ms	1844×	body	80	invalid
113.0ms	429×	body	320	valid
79.0ms	228×	body	640	invalid
62.0ms	131×	body	1280	invalid
47.0ms	176×	body	320	invalid
36.0ms	201×	body	160	valid
18.0ms	105×	body	160	invalid

Details

analyze1.0s

sample70.0ms

simplify66.0ms

prune13.0ms

localize14.0ms

rewrite37.0ms

series222.0ms

simplify66.0ms

prune257.0ms

localize18.0ms

rewrite40.0ms

series225.0ms

simplify61.0ms

prune283.0ms

localize17.0ms

rewrite49.0ms

series221.0ms

simplify51.0ms

prune274.0ms

localize17.0ms

rewrite38.0ms

series204.0ms

simplify74.0ms

prune255.0ms

regimes729.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample2.0s

Profiling