Details

sample224.0ms

Algorithm

intervals

Results

61.0ms	125×	body	1280	valid
47.0ms	78×	body	1280	nan
25.0ms	59×	body	640	nan
18.0ms	55×	body	640	valid
15.0ms	52×	body	10240	exit
10.0ms	242×	body	80	nan
8.0ms	31×	body	320	nan
7.0ms	33×	body	320	valid
5.0ms	94×	body	80	valid
3.0ms	21×	body	160	valid
2.0ms	15×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	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

localize9.0ms

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

6×	`sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-unpow` `flip3--` `fma-neg` `prod-diff` `flip--` `div-inv` `difference-of-squares`

Counts

2 → 10

Calls

2 calls:

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

series339.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(pow x (/ 1.0 n))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify105.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	267	192
1	864	170
2	4257	158
3	5001	152

prune57.0ms

Filtered

16 candidates to 14 candidates (87.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	13	4	17

Merged error: 25.2b

Counts

17 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (log x) 1.0) (* x (pow n 2)))
0.5b	(/ 0.5 (pow x 2))
7.9b	(fma (/ 1 n) (- (/ 1.0 x) (/ 0.5 (pow x 2))) (/ (* (log x) 1.0) (* x (pow n 2))))
9.6b	(* x (pow n 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-commutative`
8×	`times-frac` `associate-r`
6×	`associate-/r*`
5×	`unpow2` `sqr-pow`
2×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`
1×	`fma-udef`

Counts

4 → 26

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
2.0ms	(/ 0.5 (pow x 2))
1.0ms	(fma (/ 1 n) (- (/ 1.0 x) (/ 0.5 (pow x 2))) (/ (* (log x) 1.0) (* x (pow n 2))))
3.0ms	(* x (pow n 2))

series208.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
28.0ms	(/ 0.5 (pow x 2))
63.0ms	(fma (/ 1 n) (- (/ 1.0 x) (/ 0.5 (pow x 2))) (/ (* (log x) 1.0) (* x (pow n 2))))
32.0ms	(* x (pow n 2))

simplify128.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	204	165
1	753	163
2	4664	156
3	5001	154

prune119.0ms

Filtered

38 candidates to 30 candidates (78.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	37	5	42

Merged error: 25.1b

Counts

42 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (log x) 1.0) (* x (pow n 2)))
0.5b	(/ 0.5 (pow x 2))
7.9b	(/ (- (/ 1.0 x) (/ 0.5 (pow x 2))) n)
9.6b	(* x (pow n 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-/l/`
15×	`frac-sub`
13×	`associate-/r*`
11×	`frac-2neg` `clear-num`
9×	`*-commutative` `unpow2`
8×	`times-frac` `associate-r` `sqr-pow`
3×	`div-inv`
2×	`associate-/l*`
1×	`flip3--` `div-sub` `flip--` `sub-div`

Counts

4 → 47

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
2.0ms	(/ 0.5 (pow x 2))
8.0ms	(/ (- (/ 1.0 x) (/ 0.5 (pow x 2))) n)
3.0ms	(* x (pow n 2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
24.0ms	(/ 0.5 (pow x 2))
51.0ms	(/ (- (/ 1.0 x) (/ 0.5 (pow x 2))) n)
29.0ms	(* x (pow n 2))

simplify32.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	294	225
1	1155	210
2	5002	207

prune196.0ms

Filtered

59 candidates to 49 candidates (83.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	56	8	64

Merged error: 25.1b

Counts

64 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (log (/ 1 x)) (pow n 2))
0.4b	(/ (- 0.5) (* (pow x 2) n))
2.7b	(fma (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))) (/ (- 0.5) (* (pow x 2) n)))
10.0b	(* (pow x 2) n)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`times-frac` `associate-l` `associate-/r*`
5×	`neg-mul-1` `unpow2` `sqr-pow`
4×	`div-sub` `clear-num`
3×	`log-div` `frac-2neg` `distribute-frac-neg` `log-pow` `*-commutative` `inv-pow`
2×	`log-rec` `div-inv` `associate-/l*`
1×	`neg-sub0` `fma-udef`

Counts

4 → 31

Calls

4 calls:

4.0ms	(/ (log (/ 1 x)) (pow n 2))
4.0ms	(/ (- 0.5) (* (pow x 2) n))
1.0ms	(fma (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))) (/ (- 0.5) (* (pow x 2) n)))
4.0ms	(* (pow x 2) n)

series188.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (log (/ 1 x)) (pow n 2))
22.0ms	(/ (- 0.5) (* (pow x 2) n))
82.0ms	(fma (/ 1.0 x) (- (/ 1 n) (/ (log (/ 1 x)) (pow n 2))) (/ (- 0.5) (* (pow x 2) n)))
18.0ms	(* (pow x 2) n)

simplify158.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	194	178
1	731	169
2	4563	160
3	5001	160

prune115.0ms

Filtered

43 candidates to 32 candidates (74.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	43	8	51

Merged error: 25.1b

Counts

51 → 8

regimes246.0ms

Accuracy

85.4% (1.5b remaining)

Error of 24.0b against oracle of 22.5b and baseline of 33.0b

bsearch174.0ms

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	42	29
1	42	29

end0.0ms

sample6.5s

Algorithm

intervals

Results

1.8s	3903×	body	1280	valid
1.3s	2214×	body	1280	nan
743.0ms	1838×	body	640	nan
615.0ms	1815×	body	640	valid
559.0ms	1424×	body	10240	exit
270.0ms	6454×	body	80	nan
230.0ms	891×	body	320	nan
194.0ms	882×	body	320	valid
157.0ms	3121×	body	80	valid
75.0ms	502×	body	160	valid
63.0ms	448×	body	160	nan