Details

analyze1.3s (6.8%)

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%	36%	19.4%	13
45.5%	34.5%	20%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample259.0ms (1.3%)

Algorithm

1×

intervals

Results

120.0ms	57×	body	2048	valid
68.0ms	83×	body	1024	valid
13.0ms	4×	body	4096	valid
11.0ms	32×	body	512	valid
10.0ms	58×	body	128	valid
4.0ms	10×	body	512	invalid
4.0ms	22×	body	256	valid
4.0ms	5×	body	1024	invalid
4.0ms	2×	body	2048	invalid
3.0ms	9×	body	256	invalid
2.0ms	14×	body	128	invalid
1.0ms	9×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify298.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4939	22
1	4939	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

Merged error: 49.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0%)

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)))
2.9b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
6.8b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
10.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite246.0ms (1.3%)

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:

99.0ms	(*.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))
13.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
9.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series2.5s (12.8%)

Counts

4 → 12

Calls

4 calls:

794.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
725.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
554.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
401.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify212.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5117	14771

prune1.0s (5.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	455	8	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	456	8	464

Merged error: 20.8b

Counts

464 → 8

Compiler

Compiled 14041 to 7387 computations (47.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
18.8b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite99.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_3494`
97×	`add-sqr-sqrt_binary64_3510`
85×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
50×	`associate-r_binary64_3428`
25×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
13×	`associate-/r*_binary64_3432` `pow1_binary64_3549`
9×	`div-inv_binary64_3485`
7×	`associate-l_binary64_3429` `cbrt-unprod_binary64_3521` `prod-exp_binary64_3537`
6×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
5×	`unswap-sqr_binary64_3456` `pow-prod-down_binary64_3559`
4×	`add-log-exp_binary64_3527`
3×	`associate-/l_binary64_3433` `associate-r/_binary64_3430` `*-commutative_binary64_3419`
2×	`associate-/l/_binary64_3435` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434`
1×	`distribute-lft-in_binary64_3437` `clear-num_binary64_3487` `distribute-rgt-in_binary64_3438` `frac-2neg_binary64_3499`

Counts

4 → 179

Calls

4 calls:

20.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
17.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
15.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
8.0ms	(*.f64 1/6 i)

series363.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
115.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
100.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
21.0ms	(*.f64 1/6 i)

simplify174.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4928	5462
1	4928	5462

prune421.0ms (2.2%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	177	14	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	178	21	199

Merged error: 10.2b

Counts

199 → 21

Compiler

Compiled 6053 to 3351 computations (44.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i))))
0.1b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
4.0b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3510`
10×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488` `pow1_binary64_3549`
9×	`associate-l_binary64_3429` `associate-r_binary64_3428`
6×	`add-log-exp_binary64_3527`
4×	`associate-*r/_binary64_3430`
3×	`distribute-lft-in_binary64_3437` `distribute-rgt-in_binary64_3438` `unswap-sqr_binary64_3456` `flip-+_binary64_3462` `flip3-+_binary64_3491` `cbrt-unprod_binary64_3521` `pow-prod-down_binary64_3559` `*-commutative_binary64_3419` `prod-exp_binary64_3537`
2×	`associate-+r+_binary64_3420`
1×	`+-commutative_binary64_3418` `sum-log_binary64_3579`

Counts

4 → 75

Calls

4 calls:

7.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
6.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
4.0ms	(*.f64 50/3 i)
4.0ms	(+.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i))))

series267.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
96.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
27.0ms	(+.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i))))
24.0ms	(*.f64 50/3 i)

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4864	1188
1	4864	1188

prune125.0ms (0.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	5	15	20
Picked	0	1	1
Done	0	0	0
Total	89	19	108

Merged error: 10.2b

Counts

108 → 19

Compiler

Compiled 1884 to 1396 computations (25.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 n)
0.6b	(cbrt.f64 n)
1.3b	(.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))) (cbrt.f64 n))
3.1b	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))) (cbrt.f64 n)))

rewrite45.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_3526` `pow1_binary64_3549`
13×	`add-sqr-sqrt_binary64_3510`
11×	`add-cbrt-cube_binary64_3524`
10×	`cbrt-prod_binary64_3519`
9×	`cbrt-unprod_binary64_3521` `pow-prod-down_binary64_3559` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488` `prod-exp_binary64_3537`
7×	`associate-r_binary64_3428`
4×	`associate-l/_binary64_3431` `associate-l*_binary64_3429` `add-log-exp_binary64_3527`
2×	`unswap-sqr_binary64_3456` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-r/_binary64_3430` `-commutative_binary64_3419` `pow1/3_binary64_3570`

Counts

4 → 70

Calls

4 calls:

28.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))) (cbrt.f64 n)))
8.0ms	(.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))) (cbrt.f64 n))
1.0ms	(cbrt.f64 n)
1.0ms	(cbrt.f64 n)

series662.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt.f64 n)
195.0ms	(cbrt.f64 n)
135.0ms	(.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))) (cbrt.f64 n))
126.0ms	(.f64 (.f64 (cbrt.f64 n) (cbrt.f64 n)) (.f64 (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))) (cbrt.f64 n)))

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5105	1270

prune107.0ms (0.6%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	3	14	17
Picked	0	1	1
Done	0	1	1
Total	80	21	101

Merged error: 10.2b

Counts

101 → 21

Compiler

Compiled 1757 to 1064 computations (39.4% saved)

regimes1.6s (8.2%)

Compiler: Compiled 13284 to 9102 computations (31.5% saved)

bsearch196.0ms (1%)

Steps

Iters	Range		Point
9	2.222736542749049e-22	2.0731149164510275e-16	2.0516285899980936e-16
7	-0.023808464819877157	-0.000677853492854564	-0.022241235268148037

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	51
1	36	51

end0.0ms (0%)

sample9.2s (47.5%)

Algorithm

1×

intervals

Results

3.4s	1785×	body	2048	valid
1.9s	2598×	body	1024	valid
418.0ms	1190×	body	512	valid
157.0ms	1805×	body	128	valid
154.0ms	47×	body	4096	valid
121.0ms	160×	body	1024	invalid
116.0ms	575×	body	256	valid
102.0ms	224×	body	512	invalid
57.0ms	480×	body	128	invalid
40.0ms	158×	body	256	invalid
25.0ms	14×	body	2048	invalid
18.0ms	327×	body	128	nan

Compiler

Compiled 3329 to 2279 computations (31.5% saved)

Details

analyze1.3s (6.8%)

sample259.0ms (1.3%)

simplify298.0ms (1.5%)

prune7.0ms (0%)

localize9.0ms (0%)

rewrite246.0ms (1.3%)

series2.5s (12.8%)

simplify212.0ms (1.1%)

prune1.0s (5.2%)

localize25.0ms (0.1%)

rewrite99.0ms (0.5%)

series363.0ms (1.9%)

simplify174.0ms (0.9%)

prune421.0ms (2.2%)

localize15.0ms (0.1%)

rewrite27.0ms (0.1%)

series267.0ms (1.4%)

simplify99.0ms (0.5%)

prune125.0ms (0.6%)

localize12.0ms (0.1%)

rewrite45.0ms (0.2%)

series662.0ms (3.4%)

simplify83.0ms (0.4%)

prune107.0ms (0.6%)

regimes1.6s (8.2%)

bsearch196.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.2s (47.5%)

Profiling