Details

analyze18.0ms (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

sample83.0ms (2.4%)

Algorithm

1×

intervals

Results

43.0ms	115×	body	1280	valid
22.0ms	87×	body	640	valid
7.0ms	41×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	13×	body	160	valid

simplify135.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	5997	15

prune4.0ms (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

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(*.f64 (+.f64 n 1.0) (log.f64 (+.f64 n 1.0)))
0.3b	(*.f64 n (log.f64 n))
6.1b	(-.f64 (.f64 (+.f64 n 1.0) (log.f64 (+.f64 n 1.0))) (.f64 n (log.f64 n)))

rewrite29.0ms (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` `flip--_binary64` `flip-+_binary64`

Counts

3 → 80

Calls

3 calls:

13.0ms	(-.f64 (.f64 (+.f64 n 1.0) (log.f64 (+.f64 n 1.0))) (.f64 n (log.f64 n)))
9.0ms	(*.f64 (+.f64 n 1.0) (log.f64 (+.f64 n 1.0)))
5.0ms	(*.f64 n (log.f64 n))

series33.0ms (1%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(-.f64 (.f64 (+.f64 n 1.0) (log.f64 (+.f64 n 1.0))) (.f64 n (log.f64 n)))
13.0ms	(*.f64 n (log.f64 n))
5.0ms	(*.f64 (+.f64 n 1.0) (log.f64 (+.f64 n 1.0)))

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4924	1044
1	4924	1044

prune124.0ms (3.7%)

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

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (-.f64 (+.f64 1.0 (/.f64 0.5 n)) (/.f64 0.16666666666666669 (*.f64 n n))) (*.f64 1.0 (log.f64 n)))

0.0b

(-.f64 (+.f64 (-.f64 (+.f64 1.0 (/.f64 0.5 n)) (/.f64 0.16666666666666669 (*.f64 n n))) (*.f64 1.0 (log.f64 n))) 1.0)

0.9b

(/.f64 0.16666666666666669 (*.f64 n n))

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sum-log_binary64`
7×	`add-cube-cbrt_binary64`
6×	`log-prod_binary64` `associate-+r+_binary64`
3×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`sub-neg_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 61

Calls

3 calls:

17.0ms

(-.f64 (+.f64 (-.f64 (+.f64 1.0 (/.f64 0.5 n)) (/.f64 0.16666666666666669 (*.f64 n n))) (*.f64 1.0 (log.f64 n))) 1.0)

15.0ms

(+.f64 (-.f64 (+.f64 1.0 (/.f64 0.5 n)) (/.f64 0.16666666666666669 (*.f64 n n))) (*.f64 1.0 (log.f64 n)))

5.0ms

(/.f64 0.16666666666666669 (*.f64 n n))

series16.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

6.0ms

(+.f64 (-.f64 (+.f64 1.0 (/.f64 0.5 n)) (/.f64 0.16666666666666669 (*.f64 n n))) (*.f64 1.0 (log.f64 n)))

6.0ms

(-.f64 (+.f64 (-.f64 (+.f64 1.0 (/.f64 0.5 n)) (/.f64 0.16666666666666669 (*.f64 n n))) (*.f64 1.0 (log.f64 n))) 1.0)

4.0ms

(/.f64 0.16666666666666669 (*.f64 n n))

simplify57.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4961	1105
1	4961	1105

prune93.0ms (2.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	1	71

Merged error: 0b

Counts

71 → 1

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.9b	(/.f64 0.16666666666666669 (*.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 0.16666666666666669 (*.f64 n n))

series4.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

4.0ms

(/.f64 0.16666666666666669 (*.f64 n n))

simplify44.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5024	152

prune28.0ms (0.8%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms (0%)

sample2.5s (75.3%)

Algorithm

1×

intervals

Results

1.4s	3589×	body	1280	valid
681.0ms	2636×	body	640	valid
241.0ms	1349×	body	320	valid
90.0ms	8000×	pre	80	true
47.0ms	426×	body	160	valid

Details

analyze18.0ms (0.5%)

sample83.0ms (2.4%)

simplify135.0ms (4%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

rewrite29.0ms (0.9%)

series33.0ms (1%)

simplify86.0ms (2.6%)

prune124.0ms (3.7%)

localize11.0ms (0.3%)

rewrite39.0ms (1.2%)

series16.0ms (0.5%)

simplify57.0ms (1.7%)

prune93.0ms (2.8%)

localize9.0ms (0.3%)

rewrite6.0ms (0.2%)

series4.0ms (0.1%)

simplify44.0ms (1.3%)

prune28.0ms (0.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.5s (75.3%)

Profiling