Details

sample8.8s

Algorithm

intervals

Results

31.0ms	348×	body	80	valid
22.0ms	35×	body	1280	nan
12.0ms	26×	body	640	nan
11.0ms	79×	body	80	overflowed
11.0ms	191×	body	80	nan
5.0ms	15×	body	320	nan
1.0ms	5×	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: 0.4b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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:

10.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series87.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))

simplify105.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	953	1493
1	4234	1364
2	5002	1350

prune305.0ms

Filtered

107 candidates to 161 candidates (-50.5%)

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: 0.0b

Counts

162 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(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)

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:

8.0ms	(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)

series172.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(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)

simplify100.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (20.0ms)

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

prune196.0ms

Filtered

59 candidates to 130 candidates (-120.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	128	13	141

Merged error: 0.0b

Counts

141 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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:

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

series96.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
82.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify69.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (57.0ms)

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

prune252.0ms

Filtered

93 candidates to 141 candidates (-51.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

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

Merged error: 0.0b

Counts

154 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

22.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series142.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
3.0ms	(* (* 2.0 PI) n)
3.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt k))

simplify53.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1280	2683
1	5001	2479

prune353.0ms

Filtered

126 candidates to 221 candidates (-75.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	1	9	10
Picked	0	1	1
Done	1	1	2
Total	222	12	234

Merged error: 0b

Counts

234 → 12

regimes305.0ms

Accuracy

0% (0.3b 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 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample11.9s

Algorithm

intervals

Results

994.0ms	10640×	body	80	valid
614.0ms	898×	body	1280	nan
426.0ms	854×	body	640	nan
370.0ms	2419×	body	80	overflowed
352.0ms	5649×	body	80	nan
132.0ms	389×	body	320	nan
43.0ms	194×	body	160	nan

Details

sample8.8s

simplify35.0ms

prune3.0ms

localize17.0ms

rewrite33.0ms

series87.0ms

simplify105.0ms

prune305.0ms

localize18.0ms

rewrite33.0ms

series172.0ms

simplify100.0ms

prune196.0ms

localize20.0ms

rewrite28.0ms

series96.0ms

simplify69.0ms

prune252.0ms

localize18.0ms

rewrite49.0ms

series142.0ms

simplify53.0ms

prune353.0ms

regimes305.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample11.9s

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