Details

sample139.0ms

Algorithm

intervals

Results

44.0ms	809×	body	80	nan
25.0ms	64×	body	1280	nan
19.0ms	325×	body	80	valid
15.0ms	59×	body	640	nan
5.0ms	24×	body	320	nan
2.0ms	17×	body	160	nan

simplify38.0ms

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

prune2.0ms

Filtered

1 candidates to 0 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 → 1

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`unpow-prod-down`
7×	`associate-l` `*-commutative`
5×	`div-sub` `associate-r` `pow-sub`
3×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `div-inv`
2×	`sqr-pow`
1×	`pow-to-exp` `pow-unpow` `associate-*r/`

Counts

4 → 28

Calls

4 calls:

2.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(* (* 2.0 PI) n)

series518.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (sqrt k))
313.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
31.0ms	(* (* 2.0 PI) n)

simplify59.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	582	496
1	2170	463
2	5003	455

prune157.0ms

Filtered

40 candidates to 38 candidates (95.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	7	41

Merged error: 0.0b

Counts

41 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`div-sub` `pow-sub`
16×	`frac-times` `associate-*l/`
6×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
5×	`associate-r`
4×	`unpow-prod-down` `associate-*r/` `sqr-pow`
3×	`div-inv`
1×	`pow-to-exp` `pow-unpow`

Counts

4 → 40

Calls

4 calls:

3.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
9.0ms	(* (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0)))
2.0ms	(* PI n)
4.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))

series856.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
556.0ms	(* (* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0)))
19.0ms	(* PI n)
177.0ms	(* (/ 1.0 (sqrt k)) (pow 2.0 (/ (- 1.0 k) 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	818	809
1	3352	761
2	5001	757

prune227.0ms

Filtered

52 candidates to 49 candidates (94.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	47	5	52
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	52	7	59

Merged error: 0.0b

Counts

59 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`associate-l`
13×	`neg-mul-1`
12×	`associate-r`
11×	`*-commutative`
9×	`times-frac` `div-sub` `associate-/l*` `pow-sub`
8×	`unpow-prod-down`
7×	`sqr-pow`
6×	`associate-*r/`
4×	`distribute-lft-neg-out`
3×	`associate-/l/`
2×	`frac-times` `associate-*l/` `div-inv`
1×	`pow-to-exp` `pow-unpow` `frac-2neg` `distribute-frac-neg` `clear-num` `associate-/r*`

Counts

4 → 45

Calls

4 calls:

3.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
10.0ms	(/ (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0))) (- (sqrt k)))
2.0ms	(* PI n)
7.0ms	(* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0)))

series983.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(pow (* PI n) (/ (- 1.0 k) 2.0))
562.0ms	(/ (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0))) (- (sqrt k)))
19.0ms	(* PI n)
302.0ms	(* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* PI n) (/ (- 1.0 k) 2.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	823	946
1	3301	880
2	5002	876

prune257.0ms

Filtered

57 candidates to 54 candidates (94.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Merged error: 0b

Counts

64 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0))) (- (sqrt k)))
0.2b	(* (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0)))
0.3b	(* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.6b	(pow PI (/ (- 1.0 k) 2.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

41×	`associate-l`
29×	`div-sub` `pow-sub`
17×	`associate-*r/`
15×	`neg-mul-1`
12×	`sqr-pow`
11×	`frac-times` `associate-r` `associate-l/` `-commutative`
10×	`times-frac` `associate-/l*`
8×	`distribute-lft-neg-out`
7×	`associate-/l/`
2×	`div-inv`
1×	`pow-to-exp` `pow-unpow` `frac-2neg` `distribute-frac-neg` `clear-num` `associate-/r*`

Counts

4 → 63

Calls

4 calls:

13.0ms	(/ (* (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0))) (- (sqrt k)))
12.0ms	(* (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0)))
7.0ms	(* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
3.0ms	(pow PI (/ (- 1.0 k) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

820.0ms	(/ (* (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0))) (- (sqrt k)))
435.0ms	(* (* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))) (pow PI (/ (- 1.0 k) 2.0)))
196.0ms	(* (* (- 1.0) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
45.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	960	1273
1	4103	1197
2	5001	1191

prune348.0ms

Filtered

75 candidates to 74 candidates (98.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Merged error: 0b

Counts

81 → 6

regimes86.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	16
1	30	16
2	42	16
3	49	16
4	49	16

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	27202×	body	80	nan
707.0ms	2044×	body	1280	nan
661.0ms	10624×	body	80	valid
452.0ms	1711×	body	640	nan
161.0ms	839×	body	320	nan
48.0ms	427×	body	160	nan