Details

sample416.0ms

Algorithm

intervals

Results

125.0ms	66×	body	2560	valid
120.0ms	39×	body	5120	valid
91.0ms	131×	body	1280	valid
43.0ms	97×	body	640	valid
7.0ms	67×	body	80	valid
6.0ms	21×	body	320	valid
3.0ms	14×	body	160	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	11

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 40.5b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.6b	(* (pow t 3.0) (tan k))
20.7b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
27.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

54×	`associate-l`
38×	`associate-r` `*-commutative`
36×	`times-frac`
14×	`sqr-pow`
9×	`associate-/r*`
8×	`div-inv`
7×	`unpow-prod-down`
5×	`associate-*r/`
4×	`associate-/l*`
3×	`tan-quot`
1×	`pow-to-exp` `frac-2neg` `associate-*l/` `clear-num` `associate-/r/`

Counts

4 → 66

Calls

4 calls:

2.0ms	(pow (/ k t) 2.0)
4.0ms	(* (pow t 3.0) (tan k))
12.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
7.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(pow (/ k t) 2.0)
233.0ms	(* (pow t 3.0) (tan k))
365.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
240.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify48.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	478	690
1	1920	679
2	5001	679

prune315.0ms

Filtered

78 candidates to 63 candidates (80.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	10	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 13.6b

Counts

80 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.5b	(* (pow k 2.0) (pow t 1.0))
15.5b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

25×	`sqr-pow`
23×	`associate-r`
16×	`times-frac` `unpow2`
9×	`associate-r/` `associate-/r` `*-commutative`
8×	`associate-/l*`
4×	`pow-to-exp` `associate-l` `clear-num` `div-inv`
3×	`frac-2neg`
2×	`prod-exp` `unswap-sqr`
1×	`unpow-prod-down` `rec-exp` `un-div-inv` `inv-pow`

Counts

4 → 54

Calls

4 calls:

5.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
4.0ms	(* (pow k 2.0) (pow t 1.0))
16.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

337.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
87.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms	(* (pow k 2.0) (pow t 1.0))
646.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify37.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	495	549
1	1213	547
2	5002	547

prune339.0ms

Filtered

66 candidates to 51 candidates (77.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	57	9	66
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	59	18	77

Merged error: 9.8b

Counts

77 → 18

localize24.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
3.9b	(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ l (pow (sin k) (/ 2 2))))
7.2b	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)
8.5b	(* (pow k 2.0) (pow t 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

39×	`associate-l`
36×	`frac-times`
30×	`associate-/l*`
24×	`sqr-pow`
17×	`clear-num`
16×	`frac-2neg`
15×	`associate-/r` `-commutative`
9×	`associate-*l/` `div-inv`
6×	`unpow-prod-down`
4×	`pow-to-exp` `associate-*r/`
3×	`associate-r`
2×	`prod-exp` `unswap-sqr`
1×	`rec-exp` `un-div-inv` `inv-pow`

Counts

4 → 73

Calls

4 calls:

6.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
15.0ms	(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ l (pow (sin k) (/ 2 2))))
9.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)
4.0ms	(* (pow k 2.0) (pow t 1.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

342.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
656.0ms	(* (/ (* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ l (pow (sin k) (/ 2 2))))
370.0ms	(* (* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (cos k)) l)
330.0ms	(* (pow k 2.0) (pow t 1.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	687	970
1	2766	903
2	5001	903

prune404.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	78	7	85
Fresh	7	9	16
Picked	1	0	1
Done	1	0	1
Total	87	16	103

Merged error: 6.2b

Counts

103 → 16

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (pow (sin k) (/ 2 2)))
0.5b	(/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k))
3.9b	(* (/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ l (pow (sin k) (/ 2 2))))
7.2b	(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

120×	`associate-l`
66×	`associate-/l*`
56×	`frac-times`
51×	`sqr-pow`
46×	`div-inv`
42×	`unpow-prod-down`
35×	`times-frac`
23×	`clear-num`
22×	`frac-2neg` `*-commutative`
16×	`associate-/r*`
14×	`associate-*l/`
8×	`associate-r`
7×	`unswap-sqr`
4×	`associate-*r/`
1×	`un-div-inv`

Counts

4 → 106

Calls

4 calls:

3.0ms	(/ l (pow (sin k) (/ 2 2)))
17.0ms	(/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k))
21.0ms	(* (/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ l (pow (sin k) (/ 2 2))))
14.0ms	(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

series1.5s

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ l (pow (sin k) (/ 2 2)))
465.0ms	(/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k))
651.0ms	(* (/ (* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l) (sin k)) (/ l (pow (sin k) (/ 2 2))))
373.0ms	(* (* (pow (/ (/ 1 (pow k (/ 2.0 2))) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (cos k)) l)

simplify109.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	689	1713
1	3817	1423
2	5003	1423

prune555.0ms

Filtered

118 candidates to 102 candidates (86.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	103	15	118
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	114	20	134

Merged error: 1.4b

Counts

134 → 20

regimes443.0ms

Accuracy

43.2% (1.7b remaining)

Error of 3.2b against oracle of 1.5b and baseline of 4.5b

bsearch258.0ms

Steps

Iters	Range		Point
8	4.6726263811760715e-57	2.203300482176494e-54	4.776207133394045e-56

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	44
1	51	44

end0.0ms

sample13.7s

Algorithm

intervals

Results

4.2s	970×	body	5120	valid
4.1s	2217×	body	2560	valid
3.1s	4155×	body	1280	valid
1.2s	2453×	body	640	valid
345.0ms	1027×	body	320	valid
226.0ms	2079×	body	80	valid
90.0ms	411×	body	160	valid