Details

sample380.0ms

Algorithm

intervals

Results

199.0ms	15×	body	320	nan
65.0ms	833×	body	80	nan
29.0ms	341×	body	80	valid
16.0ms	27×	body	1280	nan
15.0ms	36×	body	640	nan
12.0ms	89×	body	80	overflowed
0.0ms	2×	body	160	nan

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4992	16
1	4992	16

prune11.0ms

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

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

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))
12.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
3.0ms	(* PI n)

series48.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
16.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms	(* PI n)

simplify47.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4975	2183
1	4975	2183

prune249.0ms

Filtered

82 candidates to 121 candidates (-47.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Merged error: 0b

Counts

123 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

7.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
6.0ms	(/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k))
16.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k)))
3.0ms	(* PI n)

series139.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
28.0ms	(/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k))
93.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k)))
2.0ms	(* PI n)

simplify56.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5625	4475

prune435.0ms

Filtered

132 candidates to 205 candidates (-55.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	205	11	216

Merged error: 0b

Counts

216 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

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

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
7.0ms	(/ 1.0 (sqrt k))
3.0ms	(* (* 2.0 PI) n)
61.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4983	2442
1	4983	2442

prune274.0ms

Filtered

109 candidates to 161 candidates (-47.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	163	9	172

Merged error: 0b

Counts

172 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

530×	`times-frac`
250×	`add-sqr-sqrt`
248×	`*-un-lft-identity`
242×	`add-cube-cbrt`
164×	`unpow-prod-down`
138×	`sqrt-prod`
92×	`sqr-pow`
54×	`add-exp-log`
40×	`associate-/r*`
31×	`div-exp`
19×	`pow-unpow`
15×	`pow-exp`
13×	`add-cbrt-cube` `associate-/l*`
11×	`div-sub` `div-inv` `pow-sub`
10×	`pow-to-exp` `associate-/r/`
9×	`pow1`
6×	`prod-exp`
4×	`cbrt-undiv` `add-log-exp`
3×	`associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `frac-2neg` `pow-prod-down` `clear-num`
1×	`*-commutative` `cbrt-unprod` `associate-/l/` `unswap-sqr`

Counts

4 → 425

Calls

4 calls:

5.0ms	(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
3.0ms	(* PI n)
15.0ms	(/ (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))

series161.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0)))
14.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
2.0ms	(* PI n)
95.0ms	(/ (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (sqrt k) (pow (* PI n) (/ (- 1.0 k) 2.0))))

simplify102.0ms

Algorithm

egg-herbie

Counts

437 → 437

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5091	14428

prune1.1s

Filtered

268 candidates to 437 candidates (-63.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	437	0	437
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	437	9	446

Merged error: 0b

Counts

446 → 9

regimes140.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.2s	27095×	body	80	nan
925.0ms	10650×	body	80	valid
601.0ms	982×	body	1280	nan
371.0ms	808×	body	640	nan
343.0ms	2472×	body	80	overflowed
124.0ms	410×	body	320	nan
40.0ms	226×	body	160	nan

Details

sample380.0ms

simplify43.0ms

prune11.0ms

localize13.0ms

rewrite26.0ms

series48.0ms

simplify47.0ms

prune249.0ms

localize15.0ms

rewrite39.0ms

series139.0ms

simplify56.0ms

prune435.0ms

localize14.0ms

rewrite35.0ms

series88.0ms

simplify60.0ms

prune274.0ms

localize15.0ms

rewrite57.0ms

series161.0ms

simplify102.0ms

prune1.1s

regimes140.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

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