Details

sample189.0ms

Algorithm

intervals

Results

76.0ms	925×	body	80	nan
28.0ms	339×	body	80	valid
18.0ms	30×	body	1280	nan
12.0ms	27×	body	640	nan
11.0ms	83×	body	80	overflowed
3.0ms	9×	body	320	nan
1.0ms	7×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 0.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (/ 1.0 (sqrt k)) (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)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
8.0ms	(/ 1.0 (sqrt k))
63.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

simplify106.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	953	1493
1	4233	1364
2	5002	1351

prune308.0ms

Filtered

161 candidates to 107 candidates (33.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	152	9	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	9	162

Merged error: 0.0b

Counts

162 → 9

localize18.0ms

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))))

rewrite32.0ms

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))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
150.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify105.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (21.0ms)

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

prune197.0ms

Filtered

130 candidates to 59 candidates (54.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	128	11	139

Merged error: 0.0b

Counts

139 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

260×	`add-exp-log`
122×	`prod-exp`
91×	`div-exp`
66×	`pow-exp`
52×	`times-frac`
28×	`add-cbrt-cube`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`pow-to-exp`
14×	`pow1` `associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`unpow-prod-down` `associate-r` `pow-prod-down` `div-inv` `sqr-pow`
4×	`associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`associate-/r/`

Counts

4 → 173

Calls

4 calls:

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ 1.0 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
119.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify54.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2862
1	5001	2541

prune363.0ms

Filtered

185 candidates to 99 candidates (46.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	186	10	196

Merged error: 0.0b

Counts

196 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

2182×	`times-frac`
823×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
438×	`sqrt-prod`
310×	`unpow-prod-down` `sqr-pow`
236×	`add-exp-log`
208×	`associate-/r*`
129×	`div-exp`
66×	`prod-exp`
60×	`pow-exp`
37×	`div-inv`
28×	`add-cbrt-cube`
20×	`pow-to-exp`
14×	`pow1`
9×	`cbrt-undiv` `associate-/l*`
6×	`associate-r` `pow-prod-down` `associate-/r/` `cbrt-unprod`
4×	`add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`

Counts

4 → 1044

Calls

4 calls:

41.0ms	(/ 1.0 (/ (sqrt k) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
5.0ms	(* (* 2.0 PI) n)
7.0ms	(* (* 2.0 PI) n)
15.0ms	(/ (sqrt k) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1.0 (/ (sqrt k) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
253.0ms	(/ (sqrt k) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify286.0ms

Algorithm

egg-herbie

Counts

1056 → 1056

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	3987	24513
1	5001	24080

prune4.5s

Filtered

1056 candidates to 668 candidates (36.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1054	2	1056
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	1056	10	1066

Merged error: 0b

Counts

1066 → 10

regimes211.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12
1	17	12

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.1s	27073×	body	80	nan
882.0ms	10589×	body	80	valid
625.0ms	1036×	body	1280	nan
364.0ms	815×	body	640	nan
331.0ms	2409×	body	80	overflowed
126.0ms	425×	body	320	nan
39.0ms	195×	body	160	nan

Details

sample189.0ms

simplify35.0ms

prune6.0ms

localize14.0ms

rewrite35.0ms

series90.0ms

simplify106.0ms

prune308.0ms

localize18.0ms

rewrite32.0ms

series181.0ms

simplify105.0ms

prune197.0ms

localize18.0ms

rewrite41.0ms

series260.0ms

simplify54.0ms

prune363.0ms

localize18.0ms

rewrite161.0ms

series394.0ms

simplify286.0ms

prune4.5s

regimes211.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

Profiling