Details

sample232.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 50%

Guaranteed chance to sample good point: 50%

Results

33.0ms	374×	body	80	valid
22.0ms	29×	body	1280	nan
13.0ms	30×	body	640	nan
11.0ms	202×	body	80	nan
9.0ms	72×	body	80	overflowed
3.0ms	9×	body	320	nan
1.0ms	4×	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

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: 0.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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:

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

series86.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
56.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(* (* 2.0 PI) n)
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (87.0ms)

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

prune299.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

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

localize20.0ms

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)

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:

7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
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)

series171.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
141.0ms	(/ (* 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)

simplify99.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (19.0ms)

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

prune187.0ms

Filtered

60 candidates to 130 candidates (-116.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	130	9	139

Merged error: 0.0b

Counts

139 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.5b	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
0.6b	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

93×	`add-sqr-sqrt`
68×	`times-frac`
67×	`*-un-lft-identity`
59×	`add-exp-log`
50×	`pow-unpow`
43×	`add-cube-cbrt`
37×	`sqrt-prod`
29×	`prod-exp`
27×	`pow-exp`
23×	`associate-l`
19×	`unpow-prod-down`
15×	`pow1`
14×	`add-cbrt-cube`
12×	`associate-r` `difference-of-squares` `unswap-sqr`
11×	`sqr-pow`
7×	`pow-to-exp` `div-exp`
6×	`pow-prod-down` `distribute-lft-out` `distribute-lft-out--`
5×	`cbrt-unprod`
4×	`pow-pow` `add-log-exp`
3×	`div-sub` `div-inv` `pow-sub`
2×	`*-commutative`
1×	`cbrt-undiv` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 175

Calls

4 calls:

14.0ms	(* (/ 1.0 (sqrt k)) (pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0)))
5.0ms	(* (* 2.0 PI) n)
12.0ms	(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))

series333.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (/ 1.0 (sqrt k)) (pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0)))
3.0ms	(* (* 2.0 PI) n)
70.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
33.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

simplify72.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1824	4418
1	5002	4252

prune738.0ms

Filtered

116 candidates to 187 candidates (-61.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	187	9	196

Merged error: 0b

Counts

196 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* 1.0 (pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.5b	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
0.6b	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt` `*-un-lft-identity`
50×	`pow-unpow`
48×	`times-frac`
46×	`add-exp-log`
32×	`add-cube-cbrt`
30×	`sqrt-prod`
19×	`pow-exp` `prod-exp`
15×	`pow1`
14×	`add-cbrt-cube`
12×	`difference-of-squares`
8×	`div-exp`
7×	`unpow-prod-down`
6×	`pow-prod-down` `associate-/r*` `distribute-lft-out` `distribute-lft-out--`
5×	`pow-to-exp`
4×	`pow-pow` `cbrt-unprod` `add-log-exp`
3×	`associate-r` `div-inv` `sqr-pow`
2×	`cbrt-undiv` `div-sub` `pow-sub`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*`

Counts

4 → 139

Calls

4 calls:

10.0ms	(/ (* 1.0 (pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))
5.0ms	(* (* 2.0 PI) n)
12.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
12.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

series246.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (* 1.0 (pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))
3.0ms	(* (* 2.0 PI) n)
72.0ms	(pow (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (/ (- (sqrt 1.0) (sqrt k)) 2.0))
30.0ms	(pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))

simplify67.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1740	3626
1	5002	3445

prune567.0ms

Filtered

91 candidates to 151 candidates (-65.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	151	9	160

Merged error: 0b

Counts

160 → 9

regimes266.0ms

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	19	12
1	19	12

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 50%

Guaranteed chance to sample good point: 50%

Results

933.0ms	10739×	body	80	valid
558.0ms	953×	body	1280	nan
365.0ms	836×	body	640	nan
327.0ms	2440×	body	80	overflowed
320.0ms	5760×	body	80	nan
128.0ms	438×	body	320	nan
36.0ms	211×	body	160	nan

Details

sample232.0ms

simplify35.0ms

prune3.0ms

localize14.0ms

rewrite34.0ms

series86.0ms

simplify105.0ms

prune299.0ms

localize20.0ms

rewrite31.0ms

series171.0ms

simplify99.0ms

prune187.0ms

localize21.0ms

rewrite50.0ms

series333.0ms

simplify72.0ms

prune738.0ms

localize19.0ms

rewrite46.0ms

series246.0ms

simplify67.0ms

prune567.0ms

regimes266.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling