Details

analyze417.0ms

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

sample78.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
16.0ms	26×	body	1280	nan
11.0ms	24×	body	640	nan
8.0ms	56×	body	80	overflowed
4.0ms	12×	body	320	nan
2.0ms	33×	body	80	nan
1.0ms	8×	body	160	nan
1.0ms	11×	body	80	invalid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4987	16
1	4987	16

prune14.0ms

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: 0.4b

Counts

2 → 2

localize14.0ms

Local error

Found 3 expressions with local error:

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

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:

6.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
3.0ms	(* PI n)
10.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

series52.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
2.0ms	(* PI n)
16.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5008	2183

prune235.0ms

Filtered

80 candidates to 121 candidates (-51.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 0.0b

Counts

123 → 10

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)))
0.2b	(* (* 2.0 PI) n)
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:

4.0ms	(/ 1.0 (sqrt k))
10.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
11.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series85.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
59.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(* (* 2.0 PI) n)
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4953	2442
1	4953	2442

prune291.0ms

Filtered

109 candidates to 161 candidates (-47.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	162	9	171

Merged error: 0b

Counts

171 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
87×	`times-frac`
59×	`*-un-lft-identity`
54×	`add-exp-log`
53×	`add-cube-cbrt`
39×	`sqrt-prod`
37×	`associate-r`
26×	`sqr-pow`
22×	`unpow-prod-down`
21×	`prod-exp`
19×	`pow-unpow`
16×	`div-exp` `unswap-sqr`
15×	`pow-exp`
13×	`add-cbrt-cube`
10×	`pow-to-exp` `associate-l`
9×	`pow1`
6×	`associate-/r*`
5×	`associate-/l*`
4×	`div-sub` `pow-sub` `add-log-exp`
3×	`cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `pow-pow` `pow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/l/`

Counts

4 → 193

Calls

4 calls:

6.0ms	(/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k))
3.0ms	(* PI n)
14.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k)))
7.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))

series140.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k))
2.0ms	(* PI n)
94.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k)))
14.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5652	4475

prune417.0ms

Filtered

132 candidates to 205 candidates (-55.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	206	8	214

Merged error: 0b

Counts

214 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

358×	`times-frac`
156×	`add-sqr-sqrt`
152×	`add-cube-cbrt` `*-un-lft-identity`
111×	`add-exp-log`
90×	`sqrt-prod`
71×	`unpow-prod-down` `sqr-pow`
51×	`div-exp`
35×	`prod-exp`
33×	`pow-exp`
29×	`associate-/l*`
14×	`pow1`
13×	`pow-unpow` `add-cbrt-cube`
11×	`pow-to-exp`
9×	`div-inv`
6×	`associate-r` `associate-l` `associate-/r*`
5×	`pow-prod-down`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-pow`
2×	`*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 313

Calls

4 calls:

6.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
14.0ms	(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
3.0ms	(* PI n)
3.0ms	(* PI n)

series158.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
129.0ms	(/ (/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0))) (sqrt k))
2.0ms	(* PI n)
2.0ms	(* PI n)

simplify110.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4988	10397
1	4988	10397

prune815.0ms

Filtered

206 candidates to 325 candidates (-57.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	325	8	333

Merged error: 0b

Counts

333 → 8

regimes131.0ms

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	18	24
1	18	24

end0.0ms

sample2.6s

Algorithm

intervals

Results

728.0ms	8000×	body	80	valid
612.0ms	977×	body	1280	nan
366.0ms	781×	body	640	nan
339.0ms	2297×	body	80	overflowed
119.0ms	374×	body	320	nan
51.0ms	781×	body	80	nan
41.0ms	217×	body	160	nan
30.0ms	237×	body	80	invalid

Details

analyze417.0ms

sample78.0ms

simplify43.0ms

prune14.0ms

localize14.0ms

rewrite23.0ms

series52.0ms

simplify47.0ms

prune235.0ms

localize14.0ms

rewrite35.0ms

series85.0ms

simplify66.0ms

prune291.0ms

localize16.0ms

rewrite40.0ms

series140.0ms

simplify61.0ms

prune417.0ms

localize21.0ms

rewrite45.0ms

series158.0ms

simplify110.0ms

prune815.0ms

regimes131.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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