Details

analyze1.1s

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

sample209.0ms

Algorithm

intervals

Results

69.0ms	123×	body	1280	valid
40.0ms	37×	body	1280	nan
22.0ms	52×	body	640	valid
18.0ms	27×	body	640	nan
14.0ms	85×	body	80	overflowed
8.0ms	27×	body	320	valid
7.0ms	18×	body	320	nan
6.0ms	8×	body	640	invalid
4.0ms	50×	body	80	valid
3.0ms	3×	body	1280	invalid
1.0ms	6×	body	160	nan
1.0ms	19×	body	80	nan
1.0ms	2×	body	320	invalid
1.0ms	4×	body	160	valid
0.0ms	4×	body	80	invalid
0.0ms	1×	body	160	invalid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune3.0ms

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: 31.5b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

1.9b	(- (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)))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4956	583
1	4956	583

prune72.0ms

Filtered

23 candidates to 26 candidates (-13.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	22	4	26
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	4	27

Merged error: 22.0b

Counts

27 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 52

Calls

2 calls:

9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series75.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
36.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4942	1056
1	4942	1056

prune200.0ms

Filtered

47 candidates to 58 candidates (-23.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	56	6	62

Merged error: 22.0b

Counts

62 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

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)))
12.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
10.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series239.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (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)))
82.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
81.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4925	2008
1	4925	2008

prune399.0ms

Filtered

80 candidates to 94 candidates (-17.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	92	8	100

Merged error: 21.9b

Counts

100 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.1b	(log (cbrt (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
2.1b	(log (cbrt (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

27×	`log-prod`
24×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
18×	`cbrt-prod`
12×	`add-cube-cbrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqrt-prod`
7×	`pow1` `add-exp-log`
6×	`log-pow` `add-log-exp` `sqr-pow`
4×	`sub-neg` `add-cbrt-cube`
3×	`log-div` `cbrt-div` `exp-diff` `pow1/3` `rem-log-exp` `exp-sum` `distribute-lft-out--`
2×	`sqrt-div`
1×	`flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 83

Calls

4 calls:

10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
11.0ms	(log (cbrt (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
11.0ms	(log (cbrt (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

series287.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
83.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
83.0ms	(log (cbrt (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))
85.0ms	(log (cbrt (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5044	2297

prune526.0ms

Filtered

76 candidates to 95 candidates (-25.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	96	7	103

Merged error: 21.8b

Counts

103 → 7

regimes362.0ms

Accuracy

79.2% (2.3b remaining)

Error of 24.4b against oracle of 22.1b and baseline of 33.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	110
1	72	110

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.1s	3797×	body	1280	valid
1.2s	1147×	body	1280	nan
691.0ms	1597×	body	640	valid
605.0ms	879×	body	640	nan
475.0ms	2736×	body	80	overflowed
224.0ms	749×	body	320	valid
189.0ms	438×	body	320	nan
178.0ms	257×	body	640	invalid
135.0ms	1557×	body	80	valid
128.0ms	101×	body	1280	invalid
78.0ms	199×	body	320	invalid
57.0ms	300×	body	160	valid
44.0ms	199×	body	160	nan
35.0ms	540×	body	80	nan
27.0ms	219×	body	80	invalid
18.0ms	78×	body	160	invalid

Details

analyze1.1s

sample209.0ms

simplify46.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series41.0ms

simplify53.0ms

prune72.0ms

localize10.0ms

rewrite24.0ms

series75.0ms

simplify58.0ms

prune200.0ms

localize14.0ms

rewrite42.0ms

series239.0ms

simplify98.0ms

prune399.0ms

localize19.0ms

rewrite46.0ms

series287.0ms

simplify48.0ms

prune526.0ms

regimes362.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling