Details

sample189.0ms

Algorithm

intervals

Results

71.0ms	848×	body	80	nan
29.0ms	342×	body	80	valid
22.0ms	39×	body	1280	nan
11.0ms	25×	body	640	nan
11.0ms	81×	body	80	overflowed
3.0ms	9×	body	320	nan
1.0ms	5×	body	160	nan

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4987	16
1	4987	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: 0.4b

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

rewrite24.0ms

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:

7.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
10.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
4.0ms	(* PI n)

series51.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
17.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))
2.0ms	(* PI n)

simplify54.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5008	2183

prune251.0ms

Filtered

82 candidates to 121 candidates (-47.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Merged error: 0.0b

Counts

123 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

7.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
9.0ms	(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
3.0ms	(* PI n)
5.0ms	(* PI (* 2.0 n))

series164.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))
133.0ms	(/ (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
2.0ms	(* PI n)
3.0ms	(* PI (* 2.0 n))

simplify40.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5040	2023

prune213.0ms

Filtered

70 candidates to 130 candidates (-85.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	3	130
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	131	9	140

Merged error: 0.0b

Counts

140 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-exp-log`
91×	`prod-exp`
42×	`pow-exp`
36×	`div-exp`
21×	`add-cbrt-cube`
16×	`pow1` `add-sqr-sqrt`
13×	`associate-r`
12×	`pow-to-exp` `add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-unprod`
7×	`associate-l` `pow-prod-down` `sqrt-prod`
5×	`times-frac` `associate-/l*`
4×	`add-log-exp`
3×	`*-commutative`
2×	`cbrt-undiv` `unpow-prod-down` `unswap-sqr` `sqr-pow`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 120

Calls

4 calls:

11.0ms	(/ (pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
7.0ms	(* (* PI (sqrt n)) (sqrt n))
5.0ms	(* PI (* 2.0 n))
5.0ms	(* PI (sqrt n))

series130.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (pow (* 2.0 (* (* PI (sqrt n)) (sqrt n))) (/ 1.0 2.0)) (* (pow (* PI (* 2.0 n)) (/ k 2.0)) (sqrt k)))
3.0ms	(* (* PI (sqrt n)) (sqrt n))
3.0ms	(* PI (* 2.0 n))
4.0ms	(* PI (sqrt n))

simplify38.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5138	2058

prune197.0ms

Filtered

67 candidates to 132 candidates (-97.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	131	10	141

Merged error: 0b

Counts

141 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (pow (* PI (* 2.0 n)) (/ k 2.0)) (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k))
0.2b	(/ 1 (* (/ (pow (* PI (* 2.0 n)) (/ k 2.0)) (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k)))
0.3b	(* PI (* 2.0 n))
0.3b	(* PI (* 2.0 n))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

432×	`add-exp-log`
230×	`prod-exp`
154×	`div-exp`
120×	`pow-exp`
41×	`add-sqr-sqrt`
40×	`pow-to-exp`
36×	`times-frac`
35×	`associate-l`
28×	`add-cbrt-cube`
27×	`rec-exp` `1-exp`
21×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
18×	`sqr-pow`
10×	`unpow-prod-down` `cbrt-unprod` `unswap-sqr`
8×	`associate-r` `pow-prod-down` `sqrt-prod`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`-commutative` `associate-/l`
2×	`pow-flip` `associate-*l/` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `inv-pow`

Counts

4 → 224

Calls

4 calls:

16.0ms	(* (/ (pow (* PI (* 2.0 n)) (/ k 2.0)) (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k))
14.0ms	(/ 1 (* (/ (pow (* PI (* 2.0 n)) (/ k 2.0)) (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k)))
5.0ms	(* PI (* 2.0 n))
5.0ms	(* PI (* 2.0 n))

series279.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (/ (pow (* PI (* 2.0 n)) (/ k 2.0)) (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k))
132.0ms	(/ 1 (* (/ (pow (* PI (* 2.0 n)) (/ k 2.0)) (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k)))
3.0ms	(* PI (* 2.0 n))
3.0ms	(* PI (* 2.0 n))

simplify60.0ms

Algorithm

egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5044	5110

prune299.0ms

Filtered

91 candidates to 236 candidates (-159.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	2	5	7
Picked	1	0	1
Done	0	2	2
Total	238	8	246

Merged error: 0b

Counts

246 → 8

regimes124.0ms

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	23	24
1	23	24

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.1s	26993×	body	80	nan
907.0ms	10641×	body	80	valid
604.0ms	1016×	body	1280	nan
383.0ms	863×	body	640	nan
330.0ms	2432×	body	80	overflowed
141.0ms	449×	body	320	nan
43.0ms	246×	body	160	nan

Details

sample189.0ms

simplify47.0ms

prune11.0ms

localize17.0ms

rewrite24.0ms

series51.0ms

simplify54.0ms

prune251.0ms

localize21.0ms

rewrite30.0ms

series164.0ms

simplify40.0ms

prune213.0ms

localize23.0ms

rewrite36.0ms

series130.0ms

simplify38.0ms

prune197.0ms

localize20.0ms

rewrite57.0ms

series279.0ms

simplify60.0ms

prune299.0ms

regimes124.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

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