Details

analyze1.2s

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

sample232.0ms

Algorithm

intervals

Results

73.0ms	128×	body	1280	valid
43.0ms	41×	body	1280	nan
22.0ms	46×	body	640	valid
17.0ms	26×	body	640	nan
17.0ms	99×	body	80	overflowed
10.0ms	15×	body	640	invalid
7.0ms	22×	body	320	valid
7.0ms	16×	body	320	nan
4.0ms	49×	body	80	valid
4.0ms	9×	body	320	invalid
4.0ms	3×	body	1280	invalid
2.0ms	11×	body	160	valid
2.0ms	8×	body	160	nan
2.0ms	26×	body	80	nan
1.0ms	6×	body	160	invalid
1.0ms	7×	body	80	invalid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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: 29.6b

Counts

2 → 1

localize11.0ms

Local error

Found 1 expressions with local error:

1.5b	(- (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)))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(- (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

prune82.0ms

Filtered

23 candidates to 26 candidates (-13.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 19.0b

Counts

27 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (sqrt x) (/ 1.0 n)) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))))
0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
1.8b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
48×	`sqrt-prod`
34×	`unpow-prod-down`
32×	`difference-of-squares`
20×	`-un-lft-identity` `associate-r*` `sqr-pow`
10×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `rem-sqrt-square` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `associate-l` `flip--`
3×	`sub-neg` `flip3-+` `flip-+` `distribute-lft-out`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `distribute-lft-out--`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

30.0ms	(* (+ (pow (sqrt x) (/ 1.0 n)) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))))
4.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
4.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
12.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (+ (pow (sqrt x) (/ 1.0 n)) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))))
31.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
31.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
69.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5093	3223

prune384.0ms

Filtered

97 candidates to 126 candidates (-29.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	126	6	132

Merged error: 19.0b

Counts

132 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
2.3b	(- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

68×	`sqrt-prod`
56×	`add-sqr-sqrt`
30×	`unpow-prod-down`
25×	`difference-of-squares`
14×	`*-un-lft-identity`
12×	`sqr-pow`
10×	`add-cube-cbrt`
9×	`sqrt-pow1`
8×	`pow1`
7×	`rem-sqrt-square`
6×	`add-log-exp`
5×	`pow1/2`
4×	`add-exp-log` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 95

Calls

4 calls:

4.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
16.0ms	(- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

series137.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
14.0ms	(sqrt (sqrt x))
16.0ms	(sqrt (sqrt x))
76.0ms	(- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

simplify41.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4956	1850
1	4956	1850

prune347.0ms

Filtered

67 candidates to 107 candidates (-59.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	106	7	113

Merged error: 18.9b

Counts

113 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n))) 3))
0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
2.3b	(- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

140×	`sqrt-prod`
135×	`add-sqr-sqrt`
104×	`unpow-prod-down`
75×	`difference-of-squares`
64×	`cbrt-prod`
31×	`sqr-pow`
29×	`cube-prod`
17×	`*-un-lft-identity`
11×	`add-cube-cbrt`
8×	`pow1` `sqrt-pow1`
6×	`add-log-exp`
4×	`add-exp-log` `rem-sqrt-square` `pow1/2` `add-cbrt-cube`
3×	`distribute-lft-out--`
2×	`cube-div` `cbrt-div` `flip3--` `flip--`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 150

Calls

4 calls:

21.0ms	(cbrt (pow (- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n))) 3))
2.0ms	(sqrt (sqrt x))
2.0ms	(sqrt (sqrt x))
16.0ms	(- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(cbrt (pow (- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n))) 3))
13.0ms	(sqrt (sqrt x))
14.0ms	(sqrt (sqrt x))
77.0ms	(- (sqrt (pow (sqrt (+ x 1.0)) (/ 1.0 n))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5047	4339

prune413.0ms

Filtered

74 candidates to 162 candidates (-118.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	162	7	169

Merged error: 18.9b

Counts

169 → 7

regimes324.0ms

Accuracy

85.4% (1.5b remaining)

Error of 23.6b against oracle of 22.2b and baseline of 32.3b

bsearch102.0ms

Steps

Iters	Range		Point
7	824213181560625.0	60723579848863384.0	1425461234759011.2
9	-2584110919.497428	-161.4807360789119	-2333063452.297904

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	55
1	61	55

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.1s	3776×	body	1280	valid
1.2s	1040×	body	1280	nan
665.0ms	1499×	body	640	valid
613.0ms	869×	body	640	nan
470.0ms	2645×	body	80	overflowed
227.0ms	736×	body	320	valid
195.0ms	451×	body	320	nan
163.0ms	235×	body	640	invalid
156.0ms	1601×	body	80	valid
117.0ms	92×	body	1280	invalid
76.0ms	388×	body	160	valid
71.0ms	175×	body	320	invalid
57.0ms	209×	body	160	nan
31.0ms	515×	body	80	nan
27.0ms	213×	body	80	invalid
17.0ms	72×	body	160	invalid

Details

analyze1.2s

sample232.0ms

simplify47.0ms

prune3.0ms

localize11.0ms

rewrite10.0ms

series39.0ms

simplify53.0ms

prune82.0ms

localize12.0ms

rewrite54.0ms

series305.0ms

simplify54.0ms

prune384.0ms

localize21.0ms

rewrite27.0ms

series137.0ms

simplify41.0ms

prune347.0ms

localize24.0ms

rewrite51.0ms

series180.0ms

simplify43.0ms

prune413.0ms

regimes324.0ms

bsearch102.0ms

simplify2.0ms

end0.0ms

sample6.5s

Profiling