Details

sample7.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.260864%

Guaranteed chance to sample good point: 71.201281%

Results

17.0ms	195×	body	80	valid
9.0ms	20×	body	1280	valid
8.0ms	23×	body	640	valid
5.0ms	59×	body	80	invalid
3.0ms	8×	body	640	invalid
2.0ms	9×	body	320	valid
2.0ms	4×	body	1280	invalid
2.0ms	7×	body	320	invalid
2.0ms	9×	body	160	valid
0.0ms	2×	body	160	invalid

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

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: 28.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.4b	(* (* x (pow s 2.0)) x)
8.3b	(* x (pow s 2.0))
18.8b	(* (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:

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))
13.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series217.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
30.0ms	(* (* x (pow s 2.0)) x)
29.0ms	(* x (pow s 2.0))
81.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify64.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (53.0ms)

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

prune266.0ms

Filtered

70 candidates to 127 candidates (-81.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	13	128

Merged error: 15.8b

Counts

128 → 13

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)))
3.4b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
18.8b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite55.0ms

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:

7.0ms	(* (* 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))

series214.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
74.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
34.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
76.0ms	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

simplify95.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (73.0ms)

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

prune276.0ms

Filtered

69 candidates to 198 candidates (-187.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	190	8	198
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	197	14	211

Merged error: 2.9b

Counts

211 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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)))))))
5.3b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.3b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

rewrite25.0ms

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))))

series190.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
42.0ms	(/ (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)))))))
66.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
66.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (37.0ms)

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

prune396.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	104	14	118
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	114	18	132

Merged error: 0.1b

Counts

132 → 18

localize16.0ms

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))))))
0.6b	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
5.3b	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
5.3b	(* (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))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (/ (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))))))
27.0ms	(/ (cos (* 2.0 x)) (fabs (* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))))
66.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
64.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify73.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (44.0ms)

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

prune610.0ms

Filtered

110 candidates to 169 candidates (-53.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	9	8	17
Picked	1	0	1
Done	0	0	0
Total	172	15	187

Merged error: 0.0b

Counts

187 → 15

regimes558.0ms

Accuracy

14.3% (2.3b remaining)

Error of 2.4b against oracle of 0.2b and baseline of 2.8b

bsearch145.0ms

Steps

Iters	Range		Point
8	-9.069329554030634e-237	-2.0119557874523273e-241	-3.9412058536221336e-237
7	-1.1274221818133427e+248	-1.591717915014377e+246	-4.694771603218296e+247

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	62
1	51	62

end0.0ms

sample9.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.260864%

Guaranteed chance to sample good point: 71.201281%

Results

550.0ms	5971×	body	80	valid
344.0ms	672×	body	1280	valid
257.0ms	728×	body	640	valid
122.0ms	1406×	body	80	invalid
113.0ms	427×	body	320	valid
91.0ms	268×	body	640	invalid
66.0ms	130×	body	1280	invalid
50.0ms	212×	body	320	invalid
37.0ms	202×	body	160	valid
17.0ms	101×	body	160	invalid

Details

sample7.5s

simplify42.0ms

prune4.0ms

localize14.0ms

rewrite37.0ms

series217.0ms

simplify64.0ms

prune266.0ms

localize16.0ms

rewrite55.0ms

series214.0ms

simplify95.0ms

prune276.0ms

localize16.0ms

rewrite25.0ms

series190.0ms

simplify51.0ms

prune396.0ms

localize16.0ms

rewrite30.0ms

series201.0ms

simplify73.0ms

prune610.0ms

regimes558.0ms

bsearch145.0ms

simplify2.0ms

end0.0ms

sample9.7s

Profiling