Details

analyze19.0ms (0.5%)

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)

sample70.0ms (1.8%)

Algorithm

1×

intervals

Results

37.0ms	129×	body	1024	valid
12.0ms	64×	body	512	valid
5.0ms	46×	body	256	valid
5.0ms	11×	body	2048	valid
3.0ms	256×	pre	128	true
0.0ms	6×	body	128	valid

Compiler

Compiled 33 to 27 computations (18.2% saved)

simplify153.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	5237	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)

localize9.0ms (0.2%)

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))
5.6b	(-.f64 (.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (.f64 n (log.f64 n)))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`log-prod_binary64`
25×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
14×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
9×	`pow1_binary64`
8×	`associate-r_binary64` `associate--l+_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
6×	`associate--r+_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 81

Calls

3 calls:

12.0ms	(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))
11.0ms	(-.f64 (.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (.f64 n (log.f64 n)))
5.0ms	(*.f64 n (log.f64 n))

series262.0ms (6.6%)

Counts

3 → 9

Calls

3 calls:

119.0ms	(*.f64 n (log.f64 n))
104.0ms	(-.f64 (.f64 (+.f64 n 1) (log.f64 (+.f64 n 1))) (.f64 n (log.f64 n)))
39.0ms	(*.f64 (+.f64 n 1) (log.f64 (+.f64 n 1)))

simplify70.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5070	1539

prune408.0ms (10.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	1	91

Merged error: 0.0b

Counts

91 → 1

Compiler

Compiled 7734 to 5403 computations (30.1% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n))) 1)
0.4b	(/.f64 1/6 (*.f64 n n))

rewrite36.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
19×	`distribute-lft-out--_binary64`
18×	`add-log-exp_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`diff-log_binary64` `associate--l+_binary64`
10×	`cancel-sign-sub-inv_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`difference-of-squares_binary64` `times-frac_binary64`
3×	`distribute-lft-out_binary64` `log-pow_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sum-log_binary64`
1×	`associate-/r*_binary64` `flip3--_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `associate--r-_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64`

Counts

2 → 60

Calls

2 calls:

25.0ms	(-.f64 (-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n))) 1)
5.0ms	(/.f64 1/6 (*.f64 n n))

series72.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

40.0ms	(-.f64 (-.f64 (+.f64 1 (/.f64 1/2 n)) (-.f64 (/.f64 1/6 (*.f64 n n)) (log.f64 n))) 1)
32.0ms	(/.f64 1/6 (*.f64 n n))

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4895	1139
1	4895	1139

prune69.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	2	67

Merged error: 0b

Counts

67 → 2

Compiler

Compiled 1336 to 867 computations (35.1% saved)

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(/.f64 -1/6 (*.f64 n n))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `associate-/l_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

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

series32.0ms (0.8%)

Counts

1 → 3

Calls

1 calls:

32.0ms

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

simplify101.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4794	212
1	4794	212

prune22.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	24	2	26

Merged error: 0b

Counts

26 → 2

Compiler

Compiled 393 to 277 computations (29.5% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.4b	(/.f64 1/6 (*.f64 n n))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `associate-/l_binary64` `times-frac_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

1 → 21

Calls

1 calls:

5.0ms

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

series38.0ms (1%)

Counts

1 → 3

Calls

1 calls:

38.0ms

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

simplify95.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4794	212
1	4794	212

prune21.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	24	2	26

Merged error: 0b

Counts

26 → 2

Compiler

Compiled 357 to 221 computations (38.1% saved)

regimes8.0ms (0.2%)

Compiler: Compiled 27 to 21 computations (22.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	18
1	106	18

end0.0ms (0%)

sample2.3s (58.4%)

Algorithm

1×

intervals

Results

1.2s	4172×	body	1024	valid
402.0ms	2128×	body	512	valid
209.0ms	450×	body	2048	valid
130.0ms	1096×	body	256	valid
105.0ms	8000×	pre	128	true
9.0ms	154×	body	128	valid

Compiler

Compiled 79 to 63 computations (20.3% saved)

Details

analyze19.0ms (0.5%)

sample70.0ms (1.8%)

simplify153.0ms (3.9%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite35.0ms (0.9%)

series262.0ms (6.6%)

simplify70.0ms (1.8%)

prune408.0ms (10.3%)

localize11.0ms (0.3%)

rewrite36.0ms (0.9%)

series72.0ms (1.8%)

simplify77.0ms (1.9%)

prune69.0ms (1.7%)

localize9.0ms (0.2%)

rewrite6.0ms (0.2%)

series32.0ms (0.8%)

simplify101.0ms (2.6%)

prune22.0ms (0.6%)

localize8.0ms (0.2%)

rewrite6.0ms (0.2%)

series38.0ms (1%)

simplify95.0ms (2.4%)

prune21.0ms (0.5%)

regimes8.0ms (0.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.3s (58.4%)

Profiling