Details

analyze1.3s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample210.0ms

Algorithm

intervals

Results

65.0ms	119×	body	1280	valid
46.0ms	41×	body	1280	nan
22.0ms	30×	body	640	nan
21.0ms	49×	body	640	valid
13.0ms	76×	body	80	overflowed
7.0ms	26×	body	320	valid
5.0ms	52×	body	80	valid
4.0ms	10×	body	320	nan
4.0ms	6×	body	640	invalid
2.0ms	10×	body	160	valid
1.0ms	11×	body	80	invalid
1.0ms	6×	body	160	invalid
1.0ms	1×	body	1280	invalid
1.0ms	3×	body	320	invalid
1.0ms	17×	body	80	nan
1.0ms	3×	body	160	nan

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune7.0ms

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: 33.6b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 23

Calls

1 calls:

9.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series40.0ms

Counts

1 → 3

Calls

1 calls:

40.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify55.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4956	583
1	4956	583

prune78.0ms

Filtered

23 candidates to 26 candidates (-13.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	5	27

Merged error: 24.5b

Counts

27 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`unpow-prod-down`
18×	`*-un-lft-identity` `difference-of-squares`
15×	`log-prod` `exp-sum`
12×	`sqr-pow`
6×	`distribute-lft-out--`
4×	`add-cube-cbrt` `exp-prod` `add-log-exp`
3×	`pow1`
2×	`add-exp-log` `log-div` `flip3--` `exp-diff` `add-cbrt-cube` `flip--` `distribute-lft-out`
1×	`sub-neg` `diff-log` `log-pow` `rem-exp-log`

Counts

2 → 52

Calls

2 calls:

11.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify61.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4920	1245
1	4920	1245

prune136.0ms

Filtered

44 candidates to 58 candidates (-31.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	57	6	63

Merged error: 24.5b

Counts

63 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (pow (exp (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`unpow-prod-down`
29×	`*-un-lft-identity`
27×	`difference-of-squares`
20×	`sqr-pow`
10×	`add-log-exp`
9×	`distribute-lft-out--`
8×	`add-cube-cbrt`
7×	`pow-unpow`
5×	`pow1` `add-exp-log`
4×	`cbrt-prod` `pow-exp` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`
2×	`pow-to-exp`
1×	`pow-pow` `log-pow`

Counts

4 → 96

Calls

4 calls:

4.0ms	(pow (pow (exp (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

508.0ms	(pow (pow (exp (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))) (cbrt (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5066	3595

prune630.0ms

Filtered

91 candidates to 108 candidates (-18.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 24.5b

Counts

114 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
34×	`*-un-lft-identity`
24×	`sqr-pow`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `sub-neg` `log-prod` `add-cbrt-cube` `distribute-lft-out`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp` `exp-sum`

Counts

4 → 98

Calls

4 calls:

10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series154.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify73.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4942	2222
1	4942	2222

prune616.0ms

Filtered

95 candidates to 110 candidates (-15.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Merged error: 24.5b

Counts

116 → 7

regimes338.0ms

Accuracy

86.6% (1.5b remaining)

Error of 24.1b against oracle of 22.6b and baseline of 33.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	135
1	59	135

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.1s	3890×	body	1280	valid
1.2s	1116×	body	1280	nan
685.0ms	1545×	body	640	valid
644.0ms	920×	body	640	nan
492.0ms	2761×	body	80	overflowed
217.0ms	728×	body	320	valid
197.0ms	461×	body	320	nan
190.0ms	266×	body	640	invalid
136.0ms	106×	body	1280	invalid
135.0ms	1509×	body	80	valid
71.0ms	177×	body	320	invalid
64.0ms	328×	body	160	valid
48.0ms	213×	body	160	nan
33.0ms	545×	body	80	nan
30.0ms	244×	body	80	invalid
21.0ms	87×	body	160	invalid

Details

analyze1.3s

sample210.0ms

simplify48.0ms

prune7.0ms

localize9.0ms

rewrite10.0ms

series40.0ms

simplify55.0ms

prune78.0ms

localize10.0ms

rewrite22.0ms

series77.0ms

simplify61.0ms

prune136.0ms

localize15.0ms

rewrite36.0ms

series622.0ms

simplify59.0ms

prune630.0ms

localize19.0ms

rewrite45.0ms

series154.0ms

simplify73.0ms

prune616.0ms

regimes338.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling