Details

sample208.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 80.57251%

Guaranteed chance to sample good point: 96.481307%

Results

22.0ms	256×	body	80	valid
0.0ms	2×	body	80	nan
0.0ms	1×	body	80	invalid

simplify37.0ms

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

prune3.0ms

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: 0.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
7.0ms	(/ 1.0 (sqrt k))
3.0ms	(* (* 2.0 PI) n)
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (89.0ms)

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

prune312.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	148	13	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	13	162

Merged error: 0.0b

Counts

162 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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

series169.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify103.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	939	1410
1	4082	1188
2	5001	1188

prune200.0ms

Filtered

59 candidates to 130 candidates (-120.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	130	13	143

Merged error: 0.0b

Counts

143 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

222×	`add-exp-log`
140×	`prod-exp`
45×	`pow-exp`
42×	`div-exp`
35×	`add-cbrt-cube`
23×	`pow1`
16×	`cbrt-unprod`
15×	`associate-r`
13×	`pow-to-exp`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ (* 1.0 (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
4.0ms	(* (* 2.0 PI) n)
11.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
6.0ms	(* (* 2.0 PI) (sqrt n))

series139.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ (* 1.0 (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
4.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))
5.0ms	(* (* 2.0 PI) (sqrt n))

simplify42.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1104	1701
1	5002	1452

prune189.0ms

Filtered

58 candidates to 134 candidates (-131.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	134	13	147

Merged error: 0.0b

Counts

147 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

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

series94.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
78.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (57.0ms)

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

prune216.0ms

Filtered

93 candidates to 141 candidates (-51.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	141	13	154

Merged error: 0b

Counts

154 → 13

regimes293.0ms

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	24	15
1	24	15

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 80.57251%

Guaranteed chance to sample good point: 96.481307%

Results

680.0ms	8000×	body	80	valid
11.0ms	125×	body	80	invalid
10.0ms	169×	body	80	nan

Details

sample208.0ms

simplify37.0ms

prune3.0ms

localize13.0ms

rewrite36.0ms

series85.0ms

simplify105.0ms

prune312.0ms

localize18.0ms

rewrite30.0ms

series169.0ms

simplify103.0ms

prune200.0ms

localize21.0ms

rewrite38.0ms

series139.0ms

simplify42.0ms

prune189.0ms

localize18.0ms

rewrite30.0ms

series94.0ms

simplify68.0ms

prune216.0ms

regimes293.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling