Details

analyze1.0s

Algorithm: search

sample61.0ms

Algorithm

intervals

Results

17.0ms	190×	body	80	valid
10.0ms	19×	body	1280	valid
8.0ms	23×	body	640	valid
5.0ms	56×	body	80	invalid
4.0ms	15×	body	320	valid
3.0ms	8×	body	640	invalid
2.0ms	9×	body	160	valid
1.0ms	4×	body	160	invalid
1.0ms	2×	body	320	invalid
0.0ms	1×	body	1280	invalid

simplify40.0ms

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: 25.9b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
3.7b	(* (* x (pow s 2.0)) x)
8.6b	(* x (pow s 2.0))
16.4b	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite34.0ms

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))

series220.0ms

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)
29.0ms	(* x (pow s 2.0))
82.0ms	(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (54.0ms)

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

prune244.0ms

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: 13.5b

Counts

128 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
0.8b	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
3.7b	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
16.4b	(* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x))

rewrite57.0ms

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:

9.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
15.0ms	(/ (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))

series217.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2)))
75.0ms	(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)))
31.0ms	(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) x)
81.0ms	(* (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 (74.0ms)

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

prune227.0ms

Filtered

68 candidates to 198 candidates (-191.2%)

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: 2.8b

Counts

209 → 9

localize15.0ms

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))))))
0.8b	(/ (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))))

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))))
9.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

series193.0ms

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))))))
43.0ms	(/ (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)))))))
67.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
65.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (38.0ms)

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

prune355.0ms

Filtered

69 candidates to 118 candidates (-71.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	114	13	127

Merged error: 0.0b

Counts

127 → 13

localize15.0ms

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))))

rewrite31.0ms

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

series203.0ms

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))))))
67.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))
65.0ms	(* (pow c (/ 2.0 2)) (* x (pow s (/ 2.0 2))))

simplify71.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (43.0ms)

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

prune724.0ms

Filtered

111 candidates to 169 candidates (-52.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	171	11	182

Merged error: 0.0b

Counts

182 → 11

regimes522.0ms

Accuracy

6.2% (2.5b remaining)

Error of 2.7b against oracle of 0.2b and baseline of 2.9b

bsearch519.0ms

Steps

Iters	Range		Point
7	7.728760299098014e-213	5.842911068853307e-211	1.1635982518154759e-212

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	32
1	40	32

end0.0ms

analyze1.0s

Algorithm: search

sample1.9s

Algorithm

intervals

Results

543.0ms	6016×	body	80	valid
326.0ms	666×	body	1280	valid
259.0ms	722×	body	640	valid
162.0ms	1837×	body	80	invalid
98.0ms	388×	body	320	valid
70.0ms	212×	body	640	invalid
52.0ms	114×	body	1280	invalid
46.0ms	180×	body	320	invalid
36.0ms	208×	body	160	valid
20.0ms	115×	body	160	invalid

Details

analyze1.0s

sample61.0ms

simplify40.0ms

prune4.0ms

localize17.0ms

rewrite34.0ms

series220.0ms

simplify65.0ms

prune244.0ms

localize15.0ms

rewrite57.0ms

series217.0ms

simplify95.0ms

prune227.0ms

localize15.0ms

rewrite27.0ms

series193.0ms

simplify52.0ms

prune355.0ms

localize15.0ms

rewrite31.0ms

series203.0ms

simplify71.0ms

prune724.0ms

regimes522.0ms

bsearch519.0ms

simplify2.0ms

end0.0ms

analyze1.0s

sample1.9s

Profiling