Details

analyze780.0ms (2.7%)

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
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample155.0ms (0.5%)

Algorithm

1×

intervals

Results

62.0ms	53×	body	2048	valid
51.0ms	90×	body	1024	valid
8.0ms	34×	body	512	valid
5.0ms	2×	body	4096	valid
5.0ms	7×	body	1024	invalid
3.0ms	57×	body	128	valid
3.0ms	20×	body	256	valid
2.0ms	6×	body	512	invalid
2.0ms	17×	body	128	invalid
1.0ms	6×	body	256	invalid
0.0ms	9×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify165.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5036	22

prune3.0ms (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

47.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

8.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
8.0b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
1.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.6b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite181.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2408`
486×	`add-sqr-sqrt_binary64_2424`
367×	`*-un-lft-identity_binary64_2402`
225×	`add-cube-cbrt_binary64_2437`
174×	`associate-r_binary64_2342`
168×	`difference-of-squares_binary64_2371`
88×	`unpow-prod-down_binary64_2481`
85×	`sqr-pow_binary64_2374`
84×	`difference-of-sqr-1_binary64_2372`
29×	`div-inv_binary64_2399`
28×	`distribute-lft-out--_binary64_2354`
19×	`add-exp-log_binary64_2440`
18×	`add-cbrt-cube_binary64_2438`
13×	`associate-/r_binary64_2346` `associate-/l_binary64_2347`
7×	`pow1_binary64_2463`
6×	`cbrt-undiv_binary64_2436` `div-exp_binary64_2453` `add-log-exp_binary64_2441`
3×	`unswap-sqr_binary64_2370` `cbrt-unprod_binary64_2435` `associate-l_binary64_2343` `cancel-sign-sub-inv_binary64_2368` `pow-unpow_binary64_2479` `prod-exp_binary64_2451`
2×	`associate-/l/_binary64_2349` `flip--_binary64_2377` `flip3--_binary64_2406` `associate-/r/_binary64_2348`
1×	`clear-num_binary64_2401` `pow-prod-down_binary64_2473` `-commutative_binary64_2333` `frac-2neg_binary64_2413` `div-sub_binary64_2407` `pow-to-exp_binary64_2471` `diff-log_binary64_2494` `associate-r/_binary64_2344` `pow-pow_binary64_2474` `sub-neg_binary64_2395` `pow-exp_binary64_2470` `distribute-lft-out_binary64_2353`

Counts

4 → 451

Calls

8 calls:

65.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
24.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
12.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
0.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))

series1.6s (5.5%)

Counts

4 → 60

Calls

4 calls:

583.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
571.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
273.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
149.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 4342 to 3245 computations (25.3% saved)

simplify212.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

511 → 511

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4940	18028
1	4940	18028

prune1.1s (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	499	12	511
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	500	12	512

Error

0.6b

Counts

512 → 12

Compiler

Compiled 16701 to 8949 computations (46.4% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i)))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))
0.0b	(+.f64 i (*.f64 i i))
0.0b	(+.f64 (.f64 i 1/2) (.f64 1/6 (*.f64 i i)))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.2b	(.f64 1/6 (.f64 i i))
0.3b	(*.f64 1/3 (/.f64 i (/.f64 n i)))
2.8b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i))))) (.f64 -1/2 (+.f64 i (*.f64 i i))))
4.3b	(.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i))))

rewrite69.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`times-frac_binary64_2408`
55×	`add-sqr-sqrt_binary64_2424`
48×	`associate-r_binary64_2342`
43×	`*-un-lft-identity_binary64_2402` `add-cube-cbrt_binary64_2437`
23×	`associate-*r/_binary64_2344`
20×	`add-exp-log_binary64_2440` `add-cbrt-cube_binary64_2438` `frac-add_binary64_2410`
18×	`flip3-+_binary64_2405` `flip-+_binary64_2376`
13×	`pow1_binary64_2463` `add-log-exp_binary64_2441`
9×	`associate-l_binary64_2343`
7×	`cbrt-unprod_binary64_2435` `prod-exp_binary64_2451`
6×	`sum-log_binary64_2493`
5×	`pow-prod-down_binary64_2473` `unswap-sqr_binary64_2370`
4×	`div-inv_binary64_2399`
3×	`cbrt-undiv_binary64_2436` `*-commutative_binary64_2333` `div-exp_binary64_2453`
2×	`associate-+r+_binary64_2334` `distribute-rgt-in_binary64_2352` `distribute-lft-in_binary64_2351`
1×	`+-commutative_binary64_2332` `associate-+l+_binary64_2335` `associate-/r/_binary64_2348`

Counts

4 → 135

Calls

8 calls:

17.0ms	(*.f64 1/3 (/.f64 i (/.f64 n i)))
14.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i))))) (.f64 -1/2 (+.f64 i (*.f64 i i))))
7.0ms	(.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i))))
6.0ms	(.f64 1/6 (.f64 i i))
0.0ms	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))

series643.0ms (2.2%)

Counts

4 → 36

Calls

4 calls:

398.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i))))) (.f64 -1/2 (+.f64 i (*.f64 i i))))
138.0ms	(.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i))))
78.0ms	(*.f64 1/3 (/.f64 i (/.f64 n i)))
29.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 1669 to 1277 computations (23.5% saved)

simplify74.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5031	5453

prune343.0ms (1.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	169	14	183

Error

0.6b

Counts

183 → 14

Compiler

Compiled 7884 to 4151 computations (47.3% saved)

localize235.0ms (0.8%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 1/2 (*.f64 i 1/6))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
4.3b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))

rewrite94.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`associate-*r/_binary64_2344`
60×	`frac-add_binary64_2410`
52×	`flip3-+_binary64_2405` `flip-+_binary64_2376`
42×	`cbrt-div_binary64_2434`
9×	`pow1_binary64_2463` `add-exp-log_binary64_2440` `add-cbrt-cube_binary64_2438` `cbrt-prod_binary64_2433`
8×	`*-un-lft-identity_binary64_2402` `add-sqr-sqrt_binary64_2424` `add-cube-cbrt_binary64_2437`
4×	`distribute-rgt-in_binary64_2352` `distribute-lft-in_binary64_2351` `add-log-exp_binary64_2441`
3×	`pow-prod-down_binary64_2473` `cbrt-unprod_binary64_2435` `associate-l_binary64_2343` `prod-exp_binary64_2451` `pow1/3_binary64_2484`
1×	`-commutative_binary64_2333` `associate-r*_binary64_2342`

Counts

4 → 99

Calls

8 calls:

16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
7.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
0.0ms	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))

series3.4s (11.8%)

Counts

4 → 54

Calls

4 calls:

1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
142.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

Compiler

Compiled 14486 to 11066 computations (23.6% saved)

simplify134.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5000	14359

prune1.2s (4.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	152	15	167

Error

0.6b

Counts

167 → 15

Compiler

Compiled 20294 to 11384 computations (43.9% saved)

localize50.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))

rewrite122.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`associate-*r/_binary64_2344`
80×	`frac-add_binary64_2410`
68×	`flip3-+_binary64_2405` `flip-+_binary64_2376`
56×	`cbrt-div_binary64_2434`
12×	`cbrt-prod_binary64_2433`
8×	`*-un-lft-identity_binary64_2402` `add-sqr-sqrt_binary64_2424` `add-cube-cbrt_binary64_2437`
4×	`pow1_binary64_2463` `add-exp-log_binary64_2440` `add-cbrt-cube_binary64_2438` `add-log-exp_binary64_2441` `pow1/3_binary64_2484`

Counts

4 → 100

Calls

8 calls:

21.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
0.0ms	(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))

series4.5s (15.6%)

Counts

4 → 60

Calls

4 calls:

1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s	(cbrt.f64 (+.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6)))) (+.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 1/3 (/.f64 i (/.f64 n i)))))))

Compiler

Compiled 22652 to 16464 computations (27.3% saved)

simplify168.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5199	18528

prune2.1s (7.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	0	12	12
Picked	1	0	1
Done	0	2	2
Total	160	15	175

Error

0.6b

Counts

175 → 15

Compiler

Compiled 32016 to 17817 computations (44.3% saved)

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	1155	3619
1	1155	3619

regimes790.0ms (2.7%)

Accuracy

Total 10.6b remaining (95.9%)

Threshold costs 0b (0%)

Compiler

Compiled 9733 to 6375 computations (34.5% saved)

bsearch240.0ms (0.8%)

Steps

Iters	Range		Point
12	13.435813393928033	8.677803220342494e+40	13.565025160760564
9	-4.357261029441336	-7.481267210665203e-06	-0.00011156580364168401

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	384	309
1	384	309

end0.0ms (0%)

sample10.4s (36%)

Algorithm

1×

intervals

Results

2.1s	1744×	body	2048	valid
1.4s	2702×	body	1024	valid
294.0ms	1160×	body	512	valid
115.0ms	1806×	body	128	valid
109.0ms	179×	body	1024	invalid
82.0ms	228×	body	512	invalid
81.0ms	567×	body	256	valid
47.0ms	471×	body	128	invalid
43.0ms	21×	body	4096	valid
32.0ms	153×	body	256	invalid
21.0ms	22×	body	2048	invalid
13.0ms	288×	body	128	nan

Compiler

Compiled 7585 to 4934 computations (35% saved)

Pareto

-0.4185389396438231

Details

analyze780.0ms (2.7%)

sample155.0ms (0.5%)

simplify165.0ms (0.6%)

prune3.0ms (0%)

localize9.0ms (0%)

rewrite181.0ms (0.6%)

series1.6s (5.5%)

simplify212.0ms (0.7%)

prune1.1s (3.9%)

localize20.0ms (0.1%)

rewrite69.0ms (0.2%)

series643.0ms (2.2%)

simplify74.0ms (0.3%)

prune343.0ms (1.2%)

localize235.0ms (0.8%)

rewrite94.0ms (0.3%)

series3.4s (11.8%)

simplify134.0ms (0.5%)

prune1.2s (4.1%)

localize50.0ms (0.2%)

rewrite122.0ms (0.4%)

series4.5s (15.6%)

simplify168.0ms (0.6%)

prune2.1s (7.2%)

simplify66.0ms (0.2%)

regimes790.0ms (2.7%)

bsearch240.0ms (0.8%)

simplify10.0ms (0%)

end0.0ms (0%)

sample10.4s (36%)

Profiling