Details

sample8.7s

Algorithm

intervals

Results

35.0ms	60×	body	1280	nan
28.0ms	330×	body	80	valid
27.0ms	56×	body	640	nan
20.0ms	146×	body	80	overflowed
19.0ms	342×	body	80	nan
8.0ms	26×	body	320	nan
3.0ms	15×	body	160	nan

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.6b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series90.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))
59.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify109.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	953	1493
1	4233	1364
2	5002	1352

prune302.0ms

Filtered

161 candidates to 107 candidates (33.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	150	11	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	11	162

Merged error: 0.0b

Counts

162 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series171.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
140.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify101.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	939	1410
1	4082	1188
2	5002	1188

prune197.0ms

Filtered

130 candidates to 60 candidates (53.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	130	11	141

Merged error: 0.0b

Counts

141 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.4b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`add-exp-log`
40×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
23×	`sqrt-prod`
22×	`prod-exp`
21×	`add-cbrt-cube`
14×	`pow1`
11×	`associate-r`
8×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 129

Calls

4 calls:

4.0ms	(* (* 2.0 PI) n)
4.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
10.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
83.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	621	1038
1	2688	925
2	5001	915

prune249.0ms

Filtered

141 candidates to 93 candidates (34.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	141	11	152

Merged error: 0.0b

Counts

152 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.5b	(* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
49×	`prod-exp`
37×	`add-cbrt-cube`
34×	`sqrt-prod`
30×	`add-sqr-sqrt`
21×	`pow1`
18×	`div-exp`
16×	`cbrt-unprod`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`swap-sqr` `associate-l` `sqr-pow`
9×	`pow-prod-down` `pow-exp` `unswap-sqr`
6×	`cbrt-undiv` `sqrt-pow1` `pow1/2`
4×	`unpow-prod-down` `add-log-exp`
3×	`pow-to-exp` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-2neg` `times-frac` `pow-plus` `sqrt-unprod` `clear-num` `associate-/r` `rem-square-sqrt` `div-inv` `associate-/l`

Counts

4 → 131

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
16.0ms	(/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
10.0ms	(* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))

series269.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
144.0ms	(/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
119.0ms	(* (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))

simplify131.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	914	1861
1	4641	1418
2	5001	1398

prune242.0ms

Filtered

143 candidates to 73 candidates (49.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	143	11	154

Merged error: 0.0b

Counts

154 → 11

regimes284.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms

sample13.5s

Algorithm

intervals

Results

1.2s	1946×	body	1280	nan
937.0ms	10659×	body	80	valid
724.0ms	1645×	body	640	nan
716.0ms	5087×	body	80	overflowed
668.0ms	11580×	body	80	nan
242.0ms	805×	body	320	nan
75.0ms	432×	body	160	nan

Details

sample8.7s

simplify38.0ms

prune3.0ms

localize14.0ms

rewrite35.0ms

series90.0ms

simplify109.0ms

prune302.0ms

localize20.0ms

rewrite31.0ms

series171.0ms

simplify101.0ms

prune197.0ms

localize18.0ms

rewrite27.0ms

series97.0ms

simplify69.0ms

prune249.0ms

localize22.0ms

rewrite40.0ms

series269.0ms

simplify131.0ms

prune242.0ms

regimes284.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample13.5s

Profiling