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

sample208.0ms

Algorithm

intervals

Results

62.0ms	114×	body	1280	valid
29.0ms	29×	body	1280	nan
27.0ms	34×	body	640	nan
22.0ms	52×	body	640	valid
14.0ms	87×	body	80	overflowed
8.0ms	6×	body	1280	invalid
7.0ms	17×	body	320	nan
7.0ms	23×	body	320	valid
5.0ms	55×	body	80	valid
3.0ms	5×	body	640	invalid
3.0ms	13×	body	160	nan
3.0ms	7×	body	320	invalid
2.0ms	12×	body	160	valid
1.0ms	6×	body	160	invalid
1.0ms	23×	body	80	nan
1.0ms	8×	body	80	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 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 78

Calls

3 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series70.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4985	1250
1	4985	1250

prune186.0ms

Filtered

71 candidates to 87 candidates (-22.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	6	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	6	88

Merged error: 20.7b

Counts

88 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
0.6b	(cbrt n)
3.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
17×	`unpow-prod-down`
15×	`difference-of-squares`
11×	`sqr-pow`
9×	`cbrt-prod` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
1.0ms	(cbrt n)
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

series133.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt n)
20.0ms	(cbrt n)
21.0ms	(cbrt n)
70.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

simplify75.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4896	1305
1	4896	1305

prune149.0ms

Filtered

58 candidates to 72 candidates (-24.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 20.5b

Counts

78 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
0.3b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
3.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 125

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
12.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow x (/ 1.0 n))
37.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify37.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5416	2531

prune271.0ms

Filtered

95 candidates to 137 candidates (-44.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	134	9	143

Merged error: 20.5b

Counts

143 → 9

localize3.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ 1.0 (* x n))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`pow1` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

1 → 21

Calls

1 calls:

4.0ms

(/ 1.0 (* x n))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ 1.0 (* x n))

simplify121.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5668	152

prune24.0ms

Filtered

16 candidates to 24 candidates (-50.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	18	6	24
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	20	13	33

Merged error: 20.2b

Counts

33 → 13

regimes333.0ms

Accuracy

86.9% (1.4b remaining)

Error of 23.7b against oracle of 22.2b and baseline of 33.2b

bsearch104.0ms

Steps

Iters	Range		Point
7	0.09425071258236715	3.127112988043234	3.0876165420064856
8	-134430410879267.69	-353145784705.12695	-3526319384090.8047

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	42
1	36	42

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.1s	3843×	body	1280	valid
1.2s	1084×	body	1280	nan
660.0ms	1539×	body	640	valid
612.0ms	890×	body	640	nan
459.0ms	2697×	body	80	overflowed
218.0ms	733×	body	320	valid
186.0ms	459×	body	320	nan
155.0ms	230×	body	640	invalid
133.0ms	1553×	body	80	valid
133.0ms	106×	body	1280	invalid
79.0ms	200×	body	320	invalid
63.0ms	332×	body	160	valid
51.0ms	230×	body	160	nan
33.0ms	563×	body	80	nan
27.0ms	217×	body	80	invalid
15.0ms	65×	body	160	invalid

Details

analyze1.2s

sample208.0ms

simplify46.0ms

prune3.0ms

localize8.0ms

rewrite19.0ms

series70.0ms

simplify54.0ms

prune186.0ms

localize15.0ms

rewrite16.0ms

series133.0ms

simplify75.0ms

prune149.0ms

localize11.0ms

rewrite35.0ms

series105.0ms

simplify37.0ms

prune271.0ms

localize3.0ms

rewrite4.0ms

series3.0ms

simplify121.0ms

prune24.0ms

regimes333.0ms

bsearch104.0ms

simplify1.0ms

end0.0ms

sample6.4s

Profiling