Details

analyze14.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	23.7%	76.3%	0
0%	23.7%	76.3%	1
11.9%	11.9%	76.3%	2
17.8%	5.9%	76.3%	3
20.8%	3%	76.3%	4
22.2%	1.5%	76.3%	5
23%	0.7%	76.3%	6
23.3%	0.4%	76.3%	7
23.3%	0.4%	76.3%	8
23.4%	0.3%	76.3%	9
23.5%	0.2%	76.3%	10
23.5%	0.2%	76.3%	11
23.5%	0.2%	76.3%	12
23.6%	0.2%	76.3%	13
23.6%	0.1%	76.3%	14

Compiler

Compiled 18 to 14 computations (22.2% saved)

sample81.0ms (2.1%)

Algorithm

1×

intervals

Results

42.0ms	140×	body	1024	valid
16.0ms	62×	body	512	valid
8.0ms	15×	body	2048	valid
4.0ms	35×	body	256	valid
3.0ms	256×	pre	128	true
0.0ms	4×	body	128	valid

Compiler

Compiled 33 to 27 computations (18.2% saved)

simplify291.0ms (7.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	5238	23

prune3.0ms (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: 63.0b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
0.3b	(*.f64 n (log.f64 n))
6.1b	(-.f64 (.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (.f64 n (log.f64 n)))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`log-prod_binary64_497`
25×	`*-un-lft-identity_binary64_414`
19×	`add-sqr-sqrt_binary64_435`
15×	`add-cube-cbrt_binary64_446`
14×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366`
9×	`pow1_binary64_472`
8×	`associate--l+_binary64_353` `associate-r_binary64_356`
7×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `associate-l_binary64_357`
6×	`associate--r+_binary64_352`
5×	`add-log-exp_binary64_450` `distribute-lft-out_binary64_367`
2×	`associate-l/_binary64_359` `log-pow_binary64_500` `-commutative_binary64_347` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444`
1×	`flip3--_binary64_418` `flip3-+_binary64_417` `diff-log_binary64_503` `sub-neg_binary64_407` `flip-+_binary64_388` `flip--_binary64_389`

Counts

3 → 80

Calls

3 calls:

11.0ms	(-.f64 (.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (.f64 n (log.f64 n)))
9.0ms	(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
5.0ms	(*.f64 n (log.f64 n))

series268.0ms (7.1%)

Counts

3 → 9

Calls

3 calls:

124.0ms	(*.f64 n (log.f64 n))
108.0ms	(-.f64 (.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (.f64 n (log.f64 n)))
36.0ms	(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5073	1541

prune107.0ms (2.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	1	90

Merged error: 0.0b

Counts

90 → 1

Compiler

Compiled 1927 to 1216 computations (36.9% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n)))
0.0b	(-.f64 (-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n))) 1)
1.4b	(/.f64 1/6 (*.f64 n n))

rewrite57.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_414`
29×	`add-log-exp_binary64_450`
27×	`distribute-lft-out--_binary64_368`
17×	`diff-log_binary64_503`
11×	`add-sqr-sqrt_binary64_435`
8×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
7×	`pow1_binary64_472`
6×	`distribute-lft-out_binary64_367`
5×	`associate--l+_binary64_353` `add-cube-cbrt_binary64_446`
4×	`flip3--_binary64_418` `log-pow_binary64_500` `frac-sub_binary64_423` `sub-neg_binary64_407` `flip--_binary64_389` `sum-log_binary64_502`
3×	`times-frac_binary64_420` `difference-of-squares_binary64_383` `associate-/l*_binary64_361`
2×	`flip3-+_binary64_417` `cbrt-undiv_binary64_445` `flip-+_binary64_388` `associate--r-_binary64_355` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `associate--l-_binary64_354` `div-inv_binary64_411` `prod-exp_binary64_460` `associate--r+_binary64_352` `frac-2neg_binary64_425` `difference-of-sqr-1_binary64_384` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`

Counts

3 → 78

Calls

3 calls:

26.0ms	(-.f64 (-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n))) 1)
18.0ms	(-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n)))
5.0ms	(/.f64 1/6 (*.f64 n n))

series106.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n)))
35.0ms	(-.f64 (-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n))) 1)
33.0ms	(/.f64 1/6 (*.f64 n n))

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4997	2202
1	4997	2202

prune102.0ms (2.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	1	88

Merged error: 0b

Counts

88 → 1

Compiler

Compiled 2023 to 1338 computations (33.9% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

1.4b	(/.f64 1/6 (*.f64 n n))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
3×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446` `-un-lft-identity_binary64_414` `associate-/l_binary64_361` `add-sqr-sqrt_binary64_435`
2×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `pow1_binary64_472` `div-inv_binary64_411` `prod-exp_binary64_460` `add-log-exp_binary64_450` `frac-2neg_binary64_425` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`

Counts

1 → 21

Calls

1 calls:

7.0ms

(/.f64 1/6 (*.f64 n n))

series32.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

31.0ms

(/.f64 1/6 (*.f64 n n))

simplify93.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4794	212
1	4794	212

prune19.0ms (0.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	1	25

Merged error: 0b

Counts

25 → 1

Compiler

Compiled 369 to 230 computations (37.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	18
1	28	18

end0.0ms (0%)

sample2.4s (63%)

Algorithm

1×

intervals

Results

1.3s	4282×	body	1024	valid
398.0ms	2032×	body	512	valid
210.0ms	438×	body	2048	valid
136.0ms	1100×	body	256	valid
106.0ms	8000×	pre	128	true
9.0ms	148×	body	128	valid

Compiler

Compiled 66 to 53 computations (19.7% saved)

Details

analyze14.0ms (0.4%)

sample81.0ms (2.1%)

simplify291.0ms (7.7%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

rewrite33.0ms (0.9%)

series268.0ms (7.1%)

simplify74.0ms (2%)

prune107.0ms (2.8%)

localize11.0ms (0.3%)

rewrite57.0ms (1.5%)

series106.0ms (2.8%)

simplify71.0ms (1.9%)

prune102.0ms (2.7%)

localize8.0ms (0.2%)

rewrite8.0ms (0.2%)

series32.0ms (0.8%)

simplify93.0ms (2.5%)

prune19.0ms (0.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.4s (63%)

Profiling