Details

analyze745.0ms (6.3%)

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)

sample162.0ms (1.4%)

Algorithm

1×

intervals

Results

74.0ms	60×	body	2048	valid
49.0ms	90×	body	1024	valid
9.0ms	35×	body	512	valid
3.0ms	54×	body	128	valid
3.0ms	9×	body	512	invalid
3.0ms	5×	body	1024	invalid
3.0ms	1×	body	4096	valid
2.0ms	16×	body	256	valid
2.0ms	19×	body	128	invalid
1.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	invalid
0.0ms	7×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify163.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

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

Merged error: 50.0b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
0.9b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.6b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
11.2b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite175.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_3494`
486×	`add-sqr-sqrt_binary64_3510`
367×	`*-un-lft-identity_binary64_3488`
225×	`add-cube-cbrt_binary64_3523`
174×	`associate-r_binary64_3428`
168×	`difference-of-squares_binary64_3457`
88×	`unpow-prod-down_binary64_3567`
85×	`sqr-pow_binary64_3460`
84×	`difference-of-sqr-1_binary64_3458`
29×	`div-inv_binary64_3485`
28×	`distribute-lft-out--_binary64_3440`
19×	`add-exp-log_binary64_3526`
18×	`add-cbrt-cube_binary64_3524`
13×	`associate-/r_binary64_3432` `associate-/l_binary64_3433`
7×	`pow1_binary64_3549`
6×	`add-log-exp_binary64_3527` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
3×	`unswap-sqr_binary64_3456` `cancel-sign-sub-inv_binary64_3454` `associate-l_binary64_3429` `cbrt-unprod_binary64_3521` `pow-unpow_binary64_3565` `prod-exp_binary64_3537`
2×	`flip3--_binary64_3492` `associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `flip--_binary64_3463`
1×	`pow-exp_binary64_3556` `distribute-lft-out_binary64_3439` `clear-num_binary64_3487` `diff-log_binary64_3580` `pow-to-exp_binary64_3557` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `frac-2neg_binary64_3499` `-commutative_binary64_3419` `div-sub_binary64_3493` `pow-pow_binary64_3560` `sub-neg_binary64_3481`

Counts

4 → 451

Calls

4 calls:

60.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
23.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series938.0ms (7.9%)

Counts

4 → 51

Calls

4 calls:

320.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
301.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
198.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
119.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 2781 to 2046 computations (26.4% saved)

simplify174.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4958	16164
1	4958	16164

prune1.1s (9.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	493	9	502
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	494	9	503

Merged error: 0.4b

Counts

503 → 9

Compiler

Compiled 15181 to 7916 computations (47.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 1/3 (.f64 i (/.f64 i n)))
0.2b	(.f64 1/6 (.f64 i 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 i n))))) (.f64 -1/2 (+.f64 (.f64 i i) i)))
3.5b	(.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i))))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`associate-*r/_binary64_3430`
20×	`frac-add_binary64_3496` `add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
18×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
16×	`pow1_binary64_3549`
13×	`add-log-exp_binary64_3527`
11×	`add-sqr-sqrt_binary64_3510`
9×	`associate-l_binary64_3429` `cbrt-unprod_binary64_3521` `prod-exp_binary64_3537`
8×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
7×	`pow-prod-down_binary64_3559`
6×	`sum-log_binary64_3579`
5×	`associate-r_binary64_3428`
3×	`*-commutative_binary64_3419`
2×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `unswap-sqr_binary64_3456` `associate-+r+_binary64_3420`
1×	`+-commutative_binary64_3418` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `associate-+l+_binary64_3421`

Counts

4 → 90

Calls

4 calls:

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

series426.0ms (3.6%)

Counts

4 → 30

Calls

4 calls:

226.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 (.f64 i i) i)))
91.0ms	(.f64 n (+.f64 (.f64 i 1/2) (.f64 1/6 (.f64 i i))))
84.0ms	(.f64 1/3 (.f64 i (/.f64 i n)))
25.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 1499 to 1153 computations (23.1% saved)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4967	4631
1	4967	4631

prune238.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	119	10	129

Merged error: 0.4b

Counts

129 → 10

Compiler

Compiled 5568 to 3062 computations (45% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
0.1b	(.f64 n (+.f64 100 (.f64 i 50)))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_3510`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-cube-cbrt_binary64_3523` `add-log-exp_binary64_3527` `*-un-lft-identity_binary64_3488` `pow1_binary64_3549`
3×	`associate-l_binary64_3429` `associate-r_binary64_3428`
2×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `associate-*r/_binary64_3430` `associate--l+_binary64_3425`
1×	`unswap-sqr_binary64_3456` `flip3--_binary64_3492` `flip-+_binary64_3462` `diff-log_binary64_3580` `flip3-+_binary64_3491` `cancel-sign-sub-inv_binary64_3454` `cbrt-unprod_binary64_3521` `pow-prod-down_binary64_3559` `flip--_binary64_3463` `*-commutative_binary64_3419` `prod-exp_binary64_3537` `sub-neg_binary64_3481`

Counts

2 → 36

Calls

2 calls:

6.0ms	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
5.0ms	(.f64 n (+.f64 100 (.f64 i 50)))

series210.0ms (1.8%)

Counts

2 → 20

Calls

2 calls:

127.0ms	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
82.0ms	(.f64 n (+.f64 100 (.f64 i 50)))

Compiler

Compiled 368 to 328 computations (10.9% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5042	785

prune58.0ms (0.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	55	11	66

Merged error: 0.3b

Counts

66 → 11

Compiler

Compiled 1019 to 747 computations (26.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 100 (*.f64 i 50))
0.1b	(.f64 i (.f64 i 2500))
3.6b	(.f64 n (-.f64 10000 (.f64 i (*.f64 i 2500))))
3.9b	(/.f64 (.f64 n (-.f64 10000 (.f64 i (.f64 i 2500)))) (-.f64 100 (.f64 i 50)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
11×	`add-sqr-sqrt_binary64_3510` `pow1_binary64_3549`
9×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
6×	`associate-l_binary64_3429` `add-log-exp_binary64_3527`
5×	`cbrt-unprod_binary64_3521` `prod-exp_binary64_3537`
4×	`flip3--_binary64_3492` `associate-r/_binary64_3430` `associate-r*_binary64_3428` `pow-prod-down_binary64_3559` `flip--_binary64_3463`
3×	`associate-/r*_binary64_3432` `cancel-sign-sub-inv_binary64_3454` `times-frac_binary64_3494` `sub-neg_binary64_3481`
2×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `associate-/l/_binary64_3435` `associate-/r/_binary64_3434` `*-commutative_binary64_3419` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
1×	`clear-num_binary64_3487` `unswap-sqr_binary64_3456` `diff-log_binary64_3580` `associate-/l*_binary64_3433` `frac-2neg_binary64_3499` `div-inv_binary64_3485`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/.f64 (.f64 n (-.f64 10000 (.f64 i (.f64 i 2500)))) (-.f64 100 (.f64 i 50)))
6.0ms	(.f64 n (-.f64 10000 (.f64 i (*.f64 i 2500))))
5.0ms	(.f64 i (.f64 i 2500))
3.0ms	(-.f64 100 (*.f64 i 50))

series337.0ms (2.9%)

Counts

4 → 24

Calls

4 calls:

188.0ms	(/.f64 (.f64 n (-.f64 10000 (.f64 i (.f64 i 2500)))) (-.f64 100 (.f64 i 50)))
106.0ms	(.f64 n (-.f64 10000 (.f64 i (*.f64 i 2500))))
26.0ms	(.f64 i (.f64 i 2500))
18.0ms	(-.f64 100 (*.f64 i 50))

Compiler

Compiled 734 to 644 computations (12.3% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4919	1502
1	4919	1502

prune116.0ms (1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	103	11	114

Merged error: 0.3b

Counts

114 → 11

Compiler

Compiled 2317 to 1727 computations (25.5% saved)

regimes698.0ms (5.9%)

Compiler: Compiled 5764 to 4035 computations (30% saved)

bsearch150.0ms (1.3%)

Steps

Iters	Range		Point
9	8.138446179073379e-06	642.7386542852148	0.24071237325819259
10	-756.228122680952	-3.6453730515185725e-16	-0.00014267079397400185

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	228	170
1	228	170

end0.0ms (0%)

sample5.8s (49.1%)

Algorithm

1×

intervals

Results

2.2s	1796×	body	2048	valid
1.4s	2663×	body	1024	valid
287.0ms	1166×	body	512	valid
116.0ms	195×	body	1024	invalid
112.0ms	1785×	body	128	valid
92.0ms	245×	body	512	invalid
76.0ms	555×	body	256	valid
68.0ms	35×	body	4096	valid
41.0ms	447×	body	128	invalid
35.0ms	155×	body	256	invalid
19.0ms	20×	body	2048	invalid
14.0ms	334×	body	128	nan

Compiler

Compiled 1564 to 1084 computations (30.7% saved)

Details

analyze745.0ms (6.3%)

sample162.0ms (1.4%)

simplify163.0ms (1.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite175.0ms (1.5%)

series938.0ms (7.9%)

simplify174.0ms (1.5%)

prune1.1s (9.1%)

localize18.0ms (0.2%)

rewrite49.0ms (0.4%)

series426.0ms (3.6%)

simplify77.0ms (0.7%)

prune238.0ms (2%)

localize6.0ms (0.1%)

rewrite14.0ms (0.1%)

series210.0ms (1.8%)

simplify66.0ms (0.6%)

prune58.0ms (0.5%)

localize12.0ms (0.1%)

rewrite31.0ms (0.3%)

series337.0ms (2.9%)

simplify61.0ms (0.5%)

prune116.0ms (1%)

regimes698.0ms (5.9%)

bsearch150.0ms (1.3%)

simplify6.0ms (0%)

end0.0ms (0%)

sample5.8s (49.1%)

Profiling