Details

analyze1.3s (12.7%)

Algorithm

1×

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

sample235.0ms (2.3%)

Algorithm

1×

intervals

Results

69.0ms	130×	body	1280	valid
56.0ms	48×	body	1280	nan
22.0ms	47×	body	640	valid
21.0ms	31×	body	640	nan
18.0ms	105×	body	80	overflowed
7.0ms	22×	body	320	valid
5.0ms	13×	body	320	nan
4.0ms	49×	body	80	valid
4.0ms	6×	body	640	invalid
3.0ms	7×	body	320	invalid
2.0ms	2×	body	1280	invalid
2.0ms	10×	body	160	nan
2.0ms	8×	body	160	valid
1.0ms	9×	body	80	invalid
1.0ms	19×	body	80	nan
0.0ms	2×	body	160	invalid

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune7.0ms (0.1%)

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 (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms (0.2%)

Algorithm

1×	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:

10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))

series70.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))
15.0ms	(pow x (/ 1.0 n))

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4985	1250
1	4985	1250

prune197.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 19.9b

Counts

88 → 4

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt n)
0.5b	(cbrt n)
0.5b	(cbrt n)
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

rewrite17.0ms (0.2%)

Algorithm

1×	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:

12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
1.0ms	(cbrt n)
1.0ms	(cbrt n)
1.0ms	(cbrt n)

series140.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
22.0ms	(cbrt n)
21.0ms	(cbrt n)
21.0ms	(cbrt n)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4896	1305
1	4896	1305

prune184.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	71	5	76

Merged error: 19.6b

Counts

76 → 5

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt n)
0.5b	(cbrt n)
0.5b	(cbrt n)
0.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))

rewrite18.0ms (0.2%)

Algorithm

1×	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:

13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
1.0ms	(cbrt n)
1.0ms	(cbrt n)
1.0ms	(cbrt n)

series139.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ 1 (* (cbrt n) (cbrt n)))) (/ 1.0 (cbrt n))))
23.0ms	(cbrt n)
22.0ms	(cbrt n)
21.0ms	(cbrt n)

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4896	1305
1	4896	1305

prune212.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	71	6	77

Merged error: 19.6b

Counts

77 → 6

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.6b	(/ 1.0 (* x n))

rewrite4.0ms (0%)

Algorithm

1×	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 (0%)

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ 1.0 (* x n))

simplify138.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	5668	152

prune35.0ms (0.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	19	5	24
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	20	10	30

Merged error: 19.2b

Counts

30 → 10

regimes252.0ms (2.5%)

Accuracy

Total 1.3b remaining (5.8%)

Threshold costs 0b (0%)

bsearch147.0ms (1.4%)

Steps

Iters	Range		Point
11	2.433706907414182e-16	9641786123.138424	7243570702.27218
9	-33.446121995133495	-2.0450084948724234e-08	-32.48759670317301

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	45
1	39	45

end0.0ms (0%)

sample6.7s (66.1%)

Algorithm

1×

intervals

Results

2.2s	3809×	body	1280	valid
1.2s	1068×	body	1280	nan
709.0ms	1558×	body	640	valid
670.0ms	936×	body	640	nan
486.0ms	2687×	body	80	overflowed
241.0ms	739×	body	320	valid
182.0ms	429×	body	320	nan
179.0ms	240×	body	640	invalid
149.0ms	1551×	body	80	valid
117.0ms	90×	body	1280	invalid
86.0ms	201×	body	320	invalid
73.0ms	343×	body	160	valid
53.0ms	235×	body	160	nan
32.0ms	535×	body	80	nan
31.0ms	234×	body	80	invalid
16.0ms	67×	body	160	invalid

Details

analyze1.3s (12.7%)

sample235.0ms (2.3%)

simplify55.0ms (0.5%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite21.0ms (0.2%)

series70.0ms (0.7%)

simplify60.0ms (0.6%)

prune197.0ms (1.9%)

localize18.0ms (0.2%)

rewrite17.0ms (0.2%)

series140.0ms (1.4%)

simplify84.0ms (0.8%)

prune184.0ms (1.8%)

localize19.0ms (0.2%)

rewrite18.0ms (0.2%)

series139.0ms (1.4%)

simplify83.0ms (0.8%)

prune212.0ms (2.1%)

localize4.0ms (0%)

rewrite4.0ms (0%)

series3.0ms (0%)

simplify138.0ms (1.4%)

prune35.0ms (0.3%)

regimes252.0ms (2.5%)

bsearch147.0ms (1.4%)

simplify1.0ms (0%)

end0.0ms (0%)

sample6.7s (66.1%)

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