Details

analyze395.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

sample81.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
17.0ms	29×	body	1280	nan
13.0ms	31×	body	640	nan
9.0ms	66×	body	80	overflowed
5.0ms	15×	body	320	nan
1.0ms	26×	body	80	nan
1.0ms	13×	body	80	invalid
1.0ms	5×	body	160	nan

simplify44.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4987	16
1	4987	16

prune10.0ms

Filtered

1 candidates to 1 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: 0.3b

Counts

2 → 2

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
33×	`add-cube-cbrt`
23×	`add-exp-log`
19×	`pow-unpow`
18×	`sqrt-prod`
11×	`pow1`
8×	`unpow-prod-down` `sqr-pow`
7×	`prod-exp` `add-cbrt-cube`
6×	`pow-exp` `associate-/r*`
5×	`div-exp` `associate-/l*`
4×	`pow-prod-down`
3×	`pow-pow` `associate-r` `associate-l` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `frac-2neg` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

3 → 112

Calls

3 calls:

9.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms	(* PI n)
6.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))

series257.0ms

Counts

3 → 9

Calls

3 calls:

222.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms	(* PI n)
33.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))

simplify56.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5008	2183

prune217.0ms

Filtered

80 candidates to 121 candidates (-51.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Merged error: 0.0b

Counts

123 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-exp-log`
63×	`prod-exp`
36×	`pow-exp`
30×	`div-exp`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1` `times-frac`
13×	`pow-unpow` `add-cbrt-cube`
12×	`pow-to-exp`
6×	`associate-r` `associate-l`
5×	`pow-prod-down` `associate-/l*`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-pow` `cbrt-unprod` `sqr-pow`
2×	`cbrt-undiv` `*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*`

Counts

4 → 118

Calls

4 calls:

6.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
3.0ms	(* PI n)
3.0ms	(* PI n)
9.0ms	(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* 2.0 (* PI n)) (/ k 2.0))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
2.0ms	(* PI n)
2.0ms	(* PI n)
133.0ms	(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (sqrt k) (pow (* 2.0 (* PI n)) (/ k 2.0))))

simplify56.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4972	2036
1	4972	2036

prune199.0ms

Filtered

71 candidates to 130 candidates (-83.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	130	8	138

Merged error: 0b

Counts

138 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (* (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (pow (* 2.0 (* PI n)) (/ k 2.0))))
0.2b	(* PI n)
0.2b	(* PI n)
0.4b	(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ 1.0 2.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

375×	`add-exp-log`
194×	`prod-exp`
142×	`div-exp`
102×	`pow-exp`
34×	`pow-to-exp`
33×	`add-sqr-sqrt` `times-frac`
31×	`rec-exp` `1-exp`
29×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-cbrt-cube`
18×	`sqrt-prod`
9×	`pow1` `associate-/l*`
7×	`unpow-prod-down` `sqr-pow`
6×	`associate-r` `associate-l` `associate-/r*`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow-flip` `associate-*l/` `associate-/r/` `inv-pow`

Counts

4 → 209

Calls

4 calls:

13.0ms	(/ 1 (* (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (pow (* 2.0 (* PI n)) (/ k 2.0))))
3.0ms	(* PI n)
3.0ms	(* PI n)
6.0ms	(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ 1.0 2.0)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ 1 (* (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (pow (* 2.0 (* PI n)) (/ k 2.0))))
2.0ms	(* PI n)
2.0ms	(* PI n)
82.0ms	(/ (sqrt k) (pow (* 2.0 (* PI n)) (/ 1.0 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5309	4094

prune244.0ms

Filtered

85 candidates to 221 candidates (-160.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	221	8	229

Merged error: 0b

Counts

229 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

335×	`add-exp-log`
170×	`add-sqr-sqrt`
167×	`times-frac`
154×	`prod-exp`
146×	`div-exp`
110×	`pow-exp`
76×	`add-cube-cbrt` `*-un-lft-identity`
61×	`sqr-pow`
60×	`sqrt-prod`
59×	`unpow-prod-down`
58×	`pow-to-exp`
52×	`associate-l`
37×	`unswap-sqr`
35×	`associate-r`
22×	`add-cbrt-cube`
10×	`pow1`
7×	`associate-/l*`
6×	`associate-/r*` `cbrt-unprod`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`pow-prod-down` `*-commutative` `div-inv`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 315

Calls

4 calls:

34.0ms	(* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (/ (pow (* PI n) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))))
4.0ms	(* PI n)
3.0ms	(* PI n)
6.0ms	(/ (pow 2.0 (/ 1.0 2.0)) (sqrt k))

series175.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (/ (pow 2.0 (/ 1.0 2.0)) (sqrt k)) (/ (pow (* PI n) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))))
2.0ms	(* PI n)
2.0ms	(* PI n)
42.0ms	(/ (pow 2.0 (/ 1.0 2.0)) (sqrt k))

simplify93.0ms

Algorithm

egg-herbie

Counts

327 → 327

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5219	8512

prune757.0ms

Filtered

170 candidates to 327 candidates (-92.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	327	0	327
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	327	8	335

Merged error: 0b

Counts

335 → 8

regimes119.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	24
1	19	24

end0.0ms

sample2.5s

Algorithm

intervals

Results

713.0ms	8000×	body	80	valid
591.0ms	973×	body	1280	nan
370.0ms	849×	body	640	nan
324.0ms	2407×	body	80	overflowed
129.0ms	421×	body	320	nan
43.0ms	745×	body	80	nan
33.0ms	193×	body	160	nan
22.0ms	241×	body	80	invalid

Details

analyze395.0ms

sample81.0ms

simplify44.0ms

prune10.0ms

localize17.0ms

rewrite23.0ms

series257.0ms

simplify56.0ms

prune217.0ms

localize19.0ms

rewrite27.0ms

series163.0ms

simplify56.0ms

prune199.0ms

localize21.0ms

rewrite39.0ms

series211.0ms

simplify60.0ms

prune244.0ms

localize23.0ms

rewrite67.0ms

series175.0ms

simplify93.0ms

prune757.0ms

regimes119.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

Profiling