Details

analyze974.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
12.5%	37.5%	50%	5
15.6%	31.2%	53.2%	6
17.2%	26.5%	56.3%	7
18%	22.6%	59.4%	8
18.3%	19.9%	61.8%	9
18.5%	17.8%	63.7%	10
18.6%	16.3%	65.1%	11
18.7%	15.2%	66.1%	12
18.7%	14.4%	66.9%	13
18.7%	13.8%	67.4%	14

Compiler

Compiled 19 to 16 computations (15.8% saved)

sample180.0ms (1.2%)

Algorithm

1×

intervals

Results

54.0ms	51×	body	1024	nan
46.0ms	256×	body	128	valid
29.0ms	81×	body	128	overflowed
13.0ms	19×	body	512	nan
6.0ms	15×	body	256	nan
4.0ms	30×	body	128	nan
2.0ms	10×	body	128	invalid

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

788×	`neg-mul-1_binary64`
672×	`associate-/l*_binary64`
625×	`associate-/r*_binary64`
480×	`div-sub_binary64`
445×	`distribute-frac-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	32	22
2	65	22
3	128	22
4	277	22
5	623	22
6	1296	22
7	3024	22
8	4691	22
9	4933	22

prune7.0ms (0%)

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

Error

0.3b

Counts

2 → 2

Alt Table

Status	Error	Program
	0.5b	(.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
▶	0.4b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

Compiler

Compiled 84 to 69 computations (17.9% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.3b	(.f64 (.f64 2 PI.f64) n)
0.3b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))

rewrite295.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

48×	`times-frac_binary64`
42×	`*-un-lft-identity_binary64`
42×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
26×	`add-exp-log_binary64`

Counts

3 → 115

Calls

3 calls:

15.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
9.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
7.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2467 to 1670 computations (32.3% saved)

series147.0ms (1%)

Error

0.2b

Counts

3 → 18

Calls

3 calls:

59.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
54.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
11.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 1081 to 812 computations (24.9% saved)

simplify233.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

504×	`distribute-rgt-in_binary64`
500×	`distribute-lft-in_binary64`
249×	`associate-/l*_binary64`
207×	`associate-/l/_binary64`
169×	`associate-l_binary64`

Counts

133 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	3840
1	532	3659
2	1642	3458
3	4828	3454
4	4985	3454

prune174.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	7	124

Error

0.0b

Counts

124 → 7

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
	22.0b	(/.f64 (sqrt.f64 (.f64 n PI.f64)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) (sqrt.f64 2))) -1/2))))
	0.6b	(/.f64 (.f64 (pow.f64 (.f64 n (.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4)))) (sqrt.f64 k))
	0.5b	(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	0.4b	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
	0.9b	(/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (.f64 1/2 (-.f64 1 k)))))
	0.5b	(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))))

Compiler

Compiled 2050 to 1416 computations (30.9% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
0.2b	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
0.3b	(.f64 n (.f64 2 PI.f64))
0.3b	(.f64 (.f64 2 PI.f64) n)

rewrite288.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

127×	`add-exp-log_binary64`
67×	`prod-exp_binary64`
36×	`pow-exp_binary64`
30×	`div-exp_binary64`
20×	`pow1_binary64`

Counts

4 → 118

Calls

4 calls:

14.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
10.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
9.0ms	(.f64 n (.f64 2 PI.f64))
7.0ms	(.f64 (.f64 2 PI.f64) n)

Compiler

Compiled 2942 to 2066 computations (29.8% saved)

series116.0ms (0.8%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

51.0ms	(/.f64 (pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2)) (.f64 (sqrt.f64 k) (pow.f64 (.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))
29.0ms	(pow.f64 (.f64 (.f64 2 PI.f64) n) (/.f64 1 2))
14.0ms	(.f64 (.f64 2 PI.f64) n)
12.0ms	(.f64 n (.f64 2 PI.f64))

Compiler

Compiled 969 to 747 computations (22.9% saved)

simplify197.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/r*_binary64`
457×	`*-commutative_binary64`
270×	`associate-*l/_binary64`
228×	`associate-*r/_binary64`
221×	`exp-sum_binary64`

Counts

133 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	3252
1	431	2962
2	1560	2717
3	4465	2717
4	5080	2717

prune140.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	123	5	128

Error

Counts

128 → 5

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
	0.4b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))))
	0.5b	(/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 1 2)) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
	0.5b	(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	22.0b	(/.f64 (sqrt.f64 (.f64 n PI.f64)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) (sqrt.f64 2))) -1/2))))

Compiler

Compiled 1710 to 1128 computations (34% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1 k))
0.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
0.2b	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
0.3b	(.f64 n (.f64 2 PI.f64))

rewrite353.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

56×	`add-sqr-sqrt_binary64`
37×	`sqrt-prod_binary64`
33×	`*-un-lft-identity_binary64`
26×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`

Counts

4 → 132

Calls

4 calls:

22.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
11.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
7.0ms	(.f64 n (.f64 2 PI.f64))
4.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 2814 to 2074 computations (26.3% saved)

series133.0ms (0.9%)

Error

Counts

4 → 21

Calls

4 calls:

50.0ms	(pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k))
49.0ms	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
11.0ms	(.f64 n (.f64 2 PI.f64))
9.0ms	(sqrt.f64 (/.f64 1 k))

Compiler

Compiled 1384 to 1023 computations (26.1% saved)

simplify451.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

927×	`times-frac_binary64`
538×	`*-commutative_binary64`
224×	`sqr-pow_binary64`
206×	`associate-r_binary64`
203×	`associate-l_binary64`

Counts

153 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	3587
1	465	3476
2	1431	3428
3	3157	3416
4	4865	3416
5	4992	3416
6	4997	3416
7	4997	3416
8	4913	3416

prune189.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
▶	0.4b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))))
	0.5b	(/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 1 2)) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
	0.5b	(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	22.0b	(/.f64 (sqrt.f64 (.f64 n PI.f64)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) (sqrt.f64 2))) -1/2))))

Compiler

Compiled 1955 to 1340 computations (31.5% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)
0.3b	(*.f64 n PI.f64)
0.3b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))))

rewrite374.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

44×	`add-sqr-sqrt_binary64`
42×	`sqrt-prod_binary64`
25×	`pow1_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 123

Calls

4 calls:

38.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))))
6.0ms	(*.f64 n PI.f64)
6.0ms	(*.f64 n PI.f64)
6.0ms	(*.f64 n PI.f64)

Compiler

Compiled 5255 to 2956 computations (43.7% saved)

series113.0ms (0.8%)

Error

Counts

4 → 15

Calls

4 calls:

65.0ms	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))))
15.0ms	(*.f64 n PI.f64)
15.0ms	(*.f64 n PI.f64)
14.0ms	(*.f64 n PI.f64)

Compiler

Compiled 1267 to 884 computations (30.2% saved)

simplify308.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

367×	`unswap-sqr_binary64`
365×	`exp-sum_binary64`
341×	`times-frac_binary64`
306×	`associate-/l*_binary64`
221×	`*-commutative_binary64`

Counts

138 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	169	4287
1	324	3805
2	980	3604
3	3045	3471
4	4577	3434
5	5262	3434

prune158.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	95	5	100

Error

Counts

100 → 5

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (pow.f64 (sqrt.f64 (.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (/.f64 1 k)))
✓	0.4b	(.f64 (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (.f64 n PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (.f64 2 (.f64 n PI.f64))) (.f64 (sqrt.f64 k) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))))
	0.5b	(/.f64 (pow.f64 (.f64 2 PI.f64) (/.f64 1 2)) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 n) (pow.f64 (.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
	0.5b	(/.f64 (/.f64 (pow.f64 (sqrt.f64 (.f64 n (.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
	22.0b	(/.f64 (sqrt.f64 (.f64 n PI.f64)) (/.f64 (sqrt.f64 k) (+.f64 (sqrt.f64 2) (.f64 (.f64 k (.f64 (log.f64 (.f64 n (.f64 2 PI.f64))) (sqrt.f64 2))) -1/2))))

Compiler

Compiled 2149 to 1351 computations (37.1% saved)

regimes3.5s (24%)

Accuracy

Total 0.3b remaining (73.1%)

Threshold costs 0.3b (73.1%)

Compiler

Compiled 31140 to 24316 computations (21.9% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	30	35
2	32	35
3	33	35
4	32	35

end1.0ms (0%)

Compiler: Compiled 23 to 18 computations (21.7% saved)

sample6.1s (41.7%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	128	valid
1.6s	1298×	body	1024	nan
909.0ms	2403×	body	128	overflowed
540.0ms	647×	body	512	nan
153.0ms	345×	body	256	nan
130.0ms	929×	body	128	nan
51.0ms	233×	body	128	invalid

Compiler

Compiled 175 to 133 computations (24% saved)

Details

analyze974.0ms (6.7%)

sample180.0ms (1.2%)

simplify72.0ms (0.5%)

prune7.0ms (0%)

localize20.0ms (0.1%)

rewrite295.0ms (2%)

series147.0ms (1%)

simplify233.0ms (1.6%)

prune174.0ms (1.2%)

localize30.0ms (0.2%)

rewrite288.0ms (2%)

series116.0ms (0.8%)

simplify197.0ms (1.3%)

prune140.0ms (1%)

localize22.0ms (0.1%)

rewrite353.0ms (2.4%)

series133.0ms (0.9%)

simplify451.0ms (3.1%)

prune189.0ms (1.3%)

localize30.0ms (0.2%)

rewrite374.0ms (2.6%)

series113.0ms (0.8%)

simplify308.0ms (2.1%)

prune158.0ms (1.1%)

regimes3.5s (24%)

simplify10.0ms (0.1%)

end1.0ms (0%)

sample6.1s (41.7%)

Profiling