Details

sample196.0ms

Algorithm

intervals

Results

74.0ms	924×	body	80	nan
29.0ms	345×	body	80	valid
20.0ms	33×	body	1280	nan
16.0ms	87×	body	80	overflowed
11.0ms	26×	body	640	nan
4.0ms	13×	body	320	nan
1.0ms	5×	body	160	nan

simplify39.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.4b

Counts

2 → 1

localize14.0ms

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

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

series555.0ms

Counts

4 → 12

Calls

4 calls:

329.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
33.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))
148.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5003	1344

prune404.0ms

Filtered

161 candidates to 107 candidates (66.5%)

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: 0b

Counts

162 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.4b	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
0.5b	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt` `*-un-lft-identity`
60×	`times-frac`
50×	`pow-unpow`
43×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`add-exp-log`
15×	`pow1`
12×	`difference-of-squares`
11×	`pow-exp` `add-cbrt-cube`
9×	`prod-exp`
7×	`unpow-prod-down`
6×	`pow-prod-down` `associate-/r*` `distribute-lft-out` `distribute-lft-out--`
4×	`pow-pow` `add-log-exp`
3×	`pow-to-exp` `associate-r` `cbrt-unprod` `div-inv` `associate-/l*` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `pow-sub`

Counts

4 → 144

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
16.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
11.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) n)
39.0ms	(/ 1.0 (sqrt k))
855.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
302.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

simplify72.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1827	3752
1	5001	3640

prune513.0ms

Filtered

156 candidates to 97 candidates (62.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	155	1	156
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	156	11	167

Merged error: 0b

Counts

167 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`times-frac`
32×	`add-cube-cbrt`
30×	`add-exp-log`
28×	`pow1`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`sqrt-prod`
15×	`pow-prod-down` `prod-exp`
12×	`associate-r`
9×	`cbrt-unprod`
6×	`associate-/r*`
4×	`pow-pow` `pow-exp` `add-log-exp`
3×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`associate-l` `*-commutative` `div-inv`
1×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `div-exp` `clear-num` `pow-sub` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
12.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
6.0ms	(* (* 2.0 PI) (sqrt n))
9.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series367.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt k))
200.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
78.0ms	(* (* 2.0 PI) (sqrt n))
51.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify81.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	732	985
1	3017	833
2	5002	812

prune311.0ms

Filtered

134 candidates to 84 candidates (62.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	134	11	145

Merged error: 0b

Counts

145 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

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)
0.3b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

rewrite33.0ms

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:

10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

919.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
31.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
267.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	916	1358
1	3951	1199
2	5002	1199

prune227.0ms

Filtered

130 candidates to 60 candidates (46.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	130	11	141

Merged error: 0b

Counts

141 → 11

regimes215.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	15
1	24	15

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.2s	27351×	body	80	nan
913.0ms	10696×	body	80	valid
640.0ms	1025×	body	1280	nan
373.0ms	831×	body	640	nan
351.0ms	2492×	body	80	overflowed
125.0ms	406×	body	320	nan
38.0ms	209×	body	160	nan

Details

sample196.0ms

simplify39.0ms

prune3.0ms

localize14.0ms

rewrite35.0ms

series555.0ms

simplify100.0ms

prune404.0ms

localize20.0ms

rewrite42.0ms

series1.2s

simplify72.0ms

prune513.0ms

localize16.0ms

rewrite36.0ms

series367.0ms

simplify81.0ms

prune311.0ms

localize19.0ms

rewrite33.0ms

series1.2s

simplify100.0ms

prune227.0ms

regimes215.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.5s

Profiling