Details

sample225.0ms

Algorithm

intervals

Results

61.0ms	125×	body	1280	valid
47.0ms	78×	body	1280	nan
25.0ms	59×	body	640	nan
19.0ms	55×	body	640	valid
16.0ms	52×	body	10240	exit
10.0ms	242×	body	80	nan
8.0ms	31×	body	320	nan
8.0ms	33×	body	320	valid
5.0ms	94×	body	80	valid
3.0ms	21×	body	160	valid
2.0ms	15×	body	160	nan

simplify150.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	4996	6
6	5001	6

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: 35.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `flip--` `div-inv` `difference-of-squares`

Counts

2 → 8

Calls

2 calls:

2.0ms	(pow x (/ 1.0 n))
4.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series342.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(pow x (/ 1.0 n))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify96.0ms

Algorithm

egg-herbie

Counts

14 → 14

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	248	158
1	788	157
2	3833	145
3	5001	145

prune48.0ms

Filtered

14 candidates to 12 candidates (85.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	3	15

Merged error: 25.1b

Counts

15 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (log x) 1.0) (* x (pow n 2)))
1.5b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
9.6b	(* x (pow n 2))
9.9b	(/ (/ 0.5 n) (pow x 2))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

1156×	`frac-sub`
445×	`associate-/l/`
402×	`associate-/r*`
360×	`frac-2neg` `clear-num`
276×	`associate-/l*`
152×	`div-inv`
143×	`*-commutative`
142×	`unpow2`
135×	`associate-r`
132×	`sqr-pow`
10×	`times-frac` `sub-div`
8×	`flip3--` `flip--`
2×	`sub-neg` `associate--r+`
1×	`associate--r-`

Counts

4 → 628

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
49.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
3.0ms	(* x (pow n 2))
4.0ms	(/ (/ 0.5 n) (pow x 2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
66.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
35.0ms	(* x (pow n 2))
27.0ms	(/ (/ 0.5 n) (pow x 2))

simplify188.0ms

Algorithm

egg-herbie

Counts

640 → 640

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5002	16740

prune2.1s

Filtered

640 candidates to 503 candidates (78.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	635	5	640
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	635	8	643

Merged error: 25.0b

Counts

643 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (- 1.0 (- (* (/ (/ 0.5 n) x) n) (* x (/ (* (log x) 1.0) (* x n))))) (* x n))
0.9b	(/ (* (log x) 1.0) (* x n))
10.9b	(* x (/ (* (log x) 1.0) (* x n)))
11.1b	(* (/ (/ 0.5 n) x) n)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-commutative`
8×	`times-frac`
7×	`associate-r/` `associate-l/`
6×	`clear-num` `associate-/r*`
5×	`frac-2neg` `associate-r` `div-inv` `associate-/l/` `associate-/l*`
3×	`div-sub`
2×	`associate--r+`
1×	`sub-neg` `flip3--` `associate-l` `un-div-inv` `flip--`

Counts

4 → 44

Calls

4 calls:

4.0ms	(/ (- 1.0 (- (* (/ (/ 0.5 n) x) n) (* x (/ (* (log x) 1.0) (* x n))))) (* x n))
4.0ms	(/ (* (log x) 1.0) (* x n))
6.0ms	(* x (/ (* (log x) 1.0) (* x n)))
5.0ms	(* (/ (/ 0.5 n) x) n)

series244.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (- 1.0 (- (* (/ (/ 0.5 n) x) n) (* x (/ (* (log x) 1.0) (* x n))))) (* x n))
95.0ms	(/ (* (log x) 1.0) (* x n))
64.0ms	(* x (/ (* (log x) 1.0) (* x n)))
12.0ms	(* (/ (/ 0.5 n) x) n)

simplify46.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	313	283
1	1564	281
2	5002	261

prune172.0ms

Filtered

56 candidates to 47 candidates (83.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	5	5
Picked	1	0	1
Done	1	1	2
Total	56	8	64

Merged error: 25.0b

Counts

64 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (* (log x) 1.0) (* x n))
7.9b	(/ (/ (- 1.0 (- (* (/ (/ 0.5 n) x) n) (* x (/ (* (log x) 1.0) (* x n))))) x) n)
10.9b	(* x (/ (* (log x) 1.0) (* x n)))
11.1b	(* (/ (/ 0.5 n) x) n)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-commutative`
10×	`associate-/l/`
8×	`times-frac`
7×	`associate-r/` `associate-l/` `clear-num`
6×	`frac-2neg` `div-sub` `div-inv` `associate-/l*`
5×	`associate-r`
4×	`associate-/r*`
2×	`associate--r+`
1×	`sub-neg` `flip3--` `associate-l` `un-div-inv` `flip--`

Counts

4 → 46

Calls

4 calls:

4.0ms	(/ (* (log x) 1.0) (* x n))
5.0ms	(/ (/ (- 1.0 (- (* (/ (/ 0.5 n) x) n) (* x (/ (* (log x) 1.0) (* x n))))) x) n)
6.0ms	(* x (/ (* (log x) 1.0) (* x n)))
5.0ms	(* (/ (/ 0.5 n) x) n)

series245.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (* (log x) 1.0) (* x n))
73.0ms	(/ (/ (- 1.0 (- (* (/ (/ 0.5 n) x) n) (* x (/ (* (log x) 1.0) (* x n))))) x) n)
64.0ms	(* x (/ (* (log x) 1.0) (* x n)))
12.0ms	(* (/ (/ 0.5 n) x) n)

simplify47.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	323	277
1	1659	274
2	5001	257

prune158.0ms

Filtered

58 candidates to 48 candidates (82.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	58	8	66

Merged error: 25.0b

Counts

66 → 8

regimes258.0ms

Accuracy

84.7% (1.6b remaining)

Error of 24.0b against oracle of 22.4b and baseline of 33.0b

bsearch177.0ms

Steps

Iters	Range		Point
10	1.3631296947685654e-08	15668503.59854612	604142.6566243569
8	-2026836488009.5793	-630460809.4077591	-35447295026.760864

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	18
1	35	18

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	3903×	body	1280	valid
1.3s	2214×	body	1280	nan
761.0ms	1838×	body	640	nan
637.0ms	1815×	body	640	valid
581.0ms	1424×	body	10240	exit
289.0ms	6454×	body	80	nan
221.0ms	891×	body	320	nan
205.0ms	882×	body	320	valid
162.0ms	3121×	body	80	valid
77.0ms	502×	body	160	valid
65.0ms	448×	body	160	nan