Details

sample193.0ms

Algorithm

intervals

Results

69.0ms	880×	body	80	nan
28.0ms	351×	body	80	valid
19.0ms	31×	body	1280	nan
12.0ms	24×	body	640	nan
11.0ms	83×	body	80	overflowed
4.0ms	12×	body	320	nan
2.0ms	9×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

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: 0.6b

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))
0.3b	(* PI n)
0.5b	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

rewrite30.0ms

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))
4.0ms	(* PI n)
14.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

series55.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(/ (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt k))
2.0ms	(* PI n)
18.0ms	(pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5013	2181

prune242.0ms

Filtered

80 candidates to 121 candidates (-51.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	7	123

Merged error: 0.3b

Counts

123 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `pow-unpow`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`pow1` `add-exp-log`
18×	`times-frac`
8×	`pow-prod-down` `prod-exp` `add-cbrt-cube`
6×	`pow-pow` `associate-r` `associate-l` `pow-exp`
4×	`add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

8.0ms	(pow (* 2.0 (* PI n)) (/ k 2.0))
4.0ms	(* PI n)
4.0ms	(* PI n)
7.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

series49.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (* 2.0 (* PI n)) (/ k 2.0))
2.0ms	(* PI n)
3.0ms	(* PI n)
27.0ms	(pow (* 2.0 (* PI n)) (/ 1.0 2.0))

simplify56.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	875
1	4951	875

prune193.0ms

Filtered

71 candidates to 106 candidates (-49.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	106	7	113

Merged error: 0.3b

Counts

113 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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)) (sqrt k))
16.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k)))
4.0ms	(* PI n)
8.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))

series156.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k))
103.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (sqrt k)))
3.0ms	(* PI n)
19.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5660	4438

prune434.0ms

Filtered

132 candidates to 205 candidates (-55.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	204	8	212

Merged error: 0.0b

Counts

212 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow n (/ (- 1.0 k) 2.0))
0.2b	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (sqrt k)))
0.7b	(pow PI (/ (- 1.0 k) 2.0))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-exp-log`
69×	`prod-exp`
62×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
38×	`pow-unpow`
37×	`pow-to-exp` `pow-exp`
36×	`times-frac`
33×	`add-cube-cbrt`
30×	`div-exp`
22×	`unpow-prod-down`
17×	`associate-r`
15×	`add-cbrt-cube`
14×	`associate-l`
12×	`unswap-sqr` `sqr-pow`
8×	`div-sub` `pow-sub`
6×	`pow1` `distribute-lft-out--` `difference-of-squares`
5×	`cbrt-unprod`
4×	`add-log-exp`
3×	`sqrt-prod` `div-inv`
2×	`cbrt-undiv` `frac-times` `pow-pow` `associate-r/` `associate-l/` `*-commutative`
1×	`pow-prod-down`

Counts

4 → 180

Calls

4 calls:

7.0ms	(pow n (/ (- 1.0 k) 2.0))
9.0ms	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
14.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (sqrt k)))
7.0ms	(pow PI (/ (- 1.0 k) 2.0))

series241.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow n (/ (- 1.0 k) 2.0))
44.0ms	(* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
178.0ms	(* (pow 2.0 (/ (- 1.0 k) 2.0)) (/ (* (pow PI (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (sqrt k)))
5.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	4998	4035
1	4998	4035

prune493.0ms

Filtered

120 candidates to 192 candidates (-60.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	190	2	192
Fresh	1	4	5
Picked	1	0	1
Done	1	1	2
Total	193	7	200

Merged error: 0.0b

Counts

200 → 7

regimes119.0ms

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	22	32
1	22	32

end0.0ms

sample5.9s

Algorithm

intervals

Results

2.1s	26913×	body	80	nan
850.0ms	10648×	body	80	valid
664.0ms	1054×	body	1280	nan
414.0ms	879×	body	640	nan
352.0ms	2518×	body	80	overflowed
149.0ms	457×	body	320	nan
43.0ms	210×	body	160	nan

Details

sample193.0ms

simplify35.0ms

prune11.0ms

localize13.0ms

rewrite30.0ms

series55.0ms

simplify45.0ms

prune242.0ms

localize16.0ms

rewrite26.0ms

series49.0ms

simplify56.0ms

prune193.0ms

localize14.0ms

rewrite44.0ms

series156.0ms

simplify51.0ms

prune434.0ms

localize17.0ms

rewrite44.0ms

series241.0ms

simplify37.0ms

prune493.0ms

regimes119.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

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