Details

analyze1.1s (10.3%)

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

sample211.0ms (1.9%)

Algorithm

1×

intervals

Results

60.0ms	115×	body	1280	valid
38.0ms	34×	body	1280	nan
23.0ms	57×	body	640	valid
20.0ms	27×	body	640	nan
16.0ms	97×	body	80	overflowed
8.0ms	51×	body	80	valid
6.0ms	21×	body	320	valid
6.0ms	13×	body	320	nan
5.0ms	4×	body	1280	invalid
5.0ms	8×	body	640	invalid
2.0ms	12×	body	160	valid
2.0ms	9×	body	160	nan
1.0ms	3×	body	320	invalid
1.0ms	19×	body	80	nan
1.0ms	4×	body	160	invalid
0.0ms	4×	body	80	invalid

simplify48.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4977	13
1	4977	13

prune6.0ms (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: 34.4b

Counts

2 → 1

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 50

Calls

2 calls:

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

series54.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(pow x (/ 1.0 n))

simplify38.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4980	932
1	4980	932

prune147.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	5	57

Merged error: 23.1b

Counts

57 → 5

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.4b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
23×	`unpow-prod-down`
18×	`difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
13×	`add-cube-cbrt` `pow-unpow` `sqr-pow`
9×	`times-frac`
6×	`distribute-lft-out--`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`add-cbrt-cube`
2×	`sub-neg` `distribute-lft-out`
1×	`pow-to-exp` `log-div` `flip3--` `pow-pow` `exp-diff` `diff-log` `rem-log-exp` `exp-sum` `pow-exp` `flip--` `div-inv`

Counts

3 → 79

Calls

3 calls:

11.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.0ms	(pow x (/ 1.0 n))

series92.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

41.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms	(pow x (/ 1.0 n))

simplify55.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	1460
1	4962	1460

prune241.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 23.0b

Counts

93 → 6

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(pow (sqrt x) (/ 1.0 n))
3.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
57×	`unpow-prod-down`
34×	`add-cube-cbrt` `*-un-lft-identity`
28×	`sqrt-prod`
26×	`pow-unpow`
18×	`add-exp-log` `times-frac`
16×	`unswap-sqr`
15×	`sqr-pow`
12×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`prod-exp`
8×	`pow1` `pow-to-exp` `pow-exp`
6×	`pow-pow` `add-cbrt-cube` `add-log-exp`
3×	`difference-of-squares`
2×	`sqrt-pow1` `pow1/2` `sqrt-pow2` `div-inv`
1×	`pow2` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod`

Counts

4 → 150

Calls

4 calls:

9.0ms	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
4.0ms	(pow (sqrt x) (/ 1.0 n))
4.0ms	(pow (sqrt x) (/ 1.0 n))

series165.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
41.0ms	(* (pow (sqrt x) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))
23.0ms	(pow (sqrt x) (/ 1.0 n))
23.0ms	(pow (sqrt x) (/ 1.0 n))

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	2153
1	4957	2153

prune377.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	162	6	168

Merged error: 23.0b

Counts

168 → 6

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.5b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite42.0ms (0.4%)

Algorithm

1×	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:

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

series249.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
86.0ms	(log (cbrt (exp (- (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)))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4925	2008
1	4925	2008

prune423.0ms (3.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	90	10	100

Merged error: 22.6b

Counts

100 → 10

regimes466.0ms (4.3%)

Accuracy

Total 2.5b remaining (10.2%)

Threshold costs 0b (0%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	198	108
1	198	108

end0.0ms (0%)

sample6.8s (62.9%)

Algorithm

1×

intervals

Results

2.1s	3816×	body	1280	valid
1.3s	1191×	body	1280	nan
725.0ms	1618×	body	640	valid
669.0ms	962×	body	640	nan
489.0ms	2793×	body	80	overflowed
204.0ms	654×	body	320	valid
187.0ms	436×	body	320	nan
174.0ms	253×	body	640	invalid
148.0ms	1589×	body	80	valid
143.0ms	113×	body	1280	invalid
72.0ms	178×	body	320	invalid
63.0ms	323×	body	160	valid
57.0ms	233×	body	160	nan
38.0ms	504×	body	80	nan
31.0ms	252×	body	80	invalid
20.0ms	82×	body	160	invalid

Details

analyze1.1s (10.3%)

sample211.0ms (1.9%)

simplify48.0ms (0.4%)

prune6.0ms (0.1%)

localize9.0ms (0.1%)

rewrite14.0ms (0.1%)

series54.0ms (0.5%)

simplify38.0ms (0.4%)

prune147.0ms (1.4%)

localize11.0ms (0.1%)

rewrite27.0ms (0.2%)

series92.0ms (0.9%)

simplify55.0ms (0.5%)

prune241.0ms (2.2%)

localize13.0ms (0.1%)

rewrite30.0ms (0.3%)

series165.0ms (1.5%)

simplify62.0ms (0.6%)

prune377.0ms (3.5%)

localize15.0ms (0.1%)

rewrite42.0ms (0.4%)

series249.0ms (2.3%)

simplify96.0ms (0.9%)

prune423.0ms (3.9%)

regimes466.0ms (4.3%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.8s (62.9%)

Profiling