Details

analyze1.1s (3.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4977	44
1	4977	44
0	2	2
1	2	2

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)

sample156.0ms (0.5%)

Algorithm

1×

intervals

Results

74.0ms	56×	body	2048	valid
39.0ms	73×	body	1024	valid
10.0ms	34×	body	512	valid
5.0ms	71×	body	128	valid
3.0ms	4×	body	1024	invalid
3.0ms	22×	body	256	valid
3.0ms	8×	body	512	invalid
2.0ms	19×	body	128	invalid
2.0ms	7×	body	256	invalid
1.0ms	12×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify131.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

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

45.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.7b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.2b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
10.4b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite1.2s (4%)

Algorithm

1×	rewrite-expression-head

Error

45.0b

Rules

584×	`times-frac_binary64_2471`
486×	`add-sqr-sqrt_binary64_2487`
367×	`*-un-lft-identity_binary64_2465`
225×	`add-cube-cbrt_binary64_2500`
174×	`associate-r_binary64_2405`
168×	`difference-of-squares_binary64_2434`
88×	`unpow-prod-down_binary64_2544`
85×	`sqr-pow_binary64_2437`
84×	`difference-of-sqr-1_binary64_2435`
29×	`div-inv_binary64_2462`
28×	`distribute-lft-out--_binary64_2417`
19×	`add-exp-log_binary64_2503`
18×	`add-cbrt-cube_binary64_2501`
13×	`associate-/l_binary64_2410` `associate-/r_binary64_2409`
7×	`pow1_binary64_2526`
6×	`div-exp_binary64_2516` `add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499`
3×	`pow-unpow_binary64_2542` `cancel-sign-sub-inv_binary64_2431` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `unswap-sqr_binary64_2433` `associate-l_binary64_2406`
2×	`flip3--_binary64_2469` `associate-/l/_binary64_2412` `flip--_binary64_2440` `associate-/r/_binary64_2411`
1×	`frac-2neg_binary64_2476` `div-sub_binary64_2470` `clear-num_binary64_2464` `distribute-lft-out_binary64_2416` `pow-pow_binary64_2537` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `diff-log_binary64_2557` `sub-neg_binary64_2458` `pow-prod-down_binary64_2536` `associate-r/_binary64_2407` `-commutative_binary64_2396`

Counts

4 → 451

Calls

4 calls:

61.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
31.0ms	(/.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)

Compiler

Compiled 14661 to 7953 computations (45.8% saved)

series2.1s (6.8%)

Error

1.6b

Counts

4 → 71

Calls

4 calls:

689.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
683.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
346.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
194.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 8026 to 5601 computations (30.2% saved)

simplify235.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

522 → 522

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5302	19293

prune1.2s (3.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	508	14	522
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	509	14	523

Error

0.6b

Counts

523 → 14

Compiler

Compiled 17716 to 9378 computations (47.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/6 (.f64 i i))
2.9b	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
3.8b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
6.5b	(/.f64 (*.f64 i i) n)

rewrite306.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

22×	`associate-*r/_binary64_2407`
20×	`frac-add_binary64_2473`
18×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
16×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
13×	`add-log-exp_binary64_2504`
12×	`add-sqr-sqrt_binary64_2487`
11×	`pow1_binary64_2526`
9×	`add-cube-cbrt_binary64_2500` `*-un-lft-identity_binary64_2465`
6×	`sum-log_binary64_2556` `associate-l_binary64_2406`
5×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
4×	`pow-prod-down_binary64_2536` `associate-r_binary64_2405`
3×	`times-frac_binary64_2471` `associate-/r*_binary64_2409`
2×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `distribute-rgt-in_binary64_2415` `associate-+r+_binary64_2397` `distribute-lft-in_binary64_2414` `unswap-sqr_binary64_2433` `*-commutative_binary64_2396`
1×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `associate-/l*_binary64_2410` `associate-+l+_binary64_2398` `+-commutative_binary64_2395`

Counts

4 → 90

Calls

4 calls:

13.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
6.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
6.0ms	(.f64 1/6 (.f64 i i))
5.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 5383 to 2602 computations (51.7% saved)

series730.0ms (2.3%)

Error

0.6b

Counts

4 → 34

Calls

4 calls:

394.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
149.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
77.0ms	(/.f64 (*.f64 i i) n)
38.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 2517 to 1776 computations (29.4% saved)

simplify106.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5436	4614

prune318.0ms (1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	123	15	138

Error

0.6b

Counts

138 → 15

Compiler

Compiled 6067 to 3322 computations (45.2% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.7b	(+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)
7.2b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
7.2b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
7.2b	(pow.f64 (+.f64 1 (/.f64 i n)) n)

rewrite199.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

18×	`*-un-lft-identity_binary64_2465`
13×	`unpow-prod-down_binary64_2544`
12×	`add-sqr-sqrt_binary64_2487`
10×	`add-cube-cbrt_binary64_2500`
9×	`pow-unpow_binary64_2542`
7×	`pow1_binary64_2526` `add-exp-log_binary64_2503`
6×	`add-log-exp_binary64_2504`
4×	`distribute-lft-out_binary64_2416` `add-cbrt-cube_binary64_2501` `sqr-pow_binary64_2437`
3×	`pow-pow_binary64_2537` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533` `difference-of-sqr--1_binary64_2436`
1×	`sum-log_binary64_2556` `flip3-+_binary64_2468` `flip-+_binary64_2439` `+-commutative_binary64_2395`

Counts

4 → 69

Calls

4 calls:

10.0ms	(+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 3143 to 1993 computations (36.6% saved)

series1.0s (3.3%)

Error

0.6b

Counts

4 → 56

Calls

4 calls:

299.0ms	(+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)
206.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
193.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)
147.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 7608 to 5341 computations (29.8% saved)

simplify99.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5085	3338

prune390.0ms (1.2%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	125	15	140

Error

0.6b

Counts

140 → 15

Compiler

Compiled 6784 to 4184 computations (38.3% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

1.6b	(+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n)) -1)
7.2b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
7.2b	(pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n))
10.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n)) -1) (+.f64 1 (pow.f64 (+.f64 1 (/.f64 i n)) n))) (/.f64 i n))

rewrite3.0s (9.4%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

1149×	`times-frac_binary64_2471`
734×	`*-un-lft-identity_binary64_2465`
534×	`add-sqr-sqrt_binary64_2487`
420×	`add-cube-cbrt_binary64_2500`
171×	`difference-of-sqr--1_binary64_2436`
157×	`distribute-lft-out_binary64_2416`
65×	`unpow-prod-down_binary64_2544`
59×	`sqr-pow_binary64_2437`
50×	`div-inv_binary64_2462`
34×	`associate-/l*_binary64_2410`
29×	`associate-/r/_binary64_2411`
18×	`add-exp-log_binary64_2503`
16×	`add-cbrt-cube_binary64_2501`
15×	`flip3-+_binary64_2468` `flip-+_binary64_2439`
13×	`associate-/r*_binary64_2409`
8×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
6×	`pow1_binary64_2526` `add-log-exp_binary64_2504`
4×	`pow-unpow_binary64_2542`
2×	`pow-pow_binary64_2537` `pow-to-exp_binary64_2534` `pow-exp_binary64_2533`
1×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/l/_binary64_2412` `sum-log_binary64_2556` `+-commutative_binary64_2395`

Counts

4 → 558

Calls

4 calls:

78.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n)) -1) (+.f64 1 (pow.f64 (+.f64 1 (/.f64 i n)) n))) (/.f64 i n))
10.0ms	(+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n)) -1)
9.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n))
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 29955 to 17904 computations (40.2% saved)

series3.0s (9.7%)

Error

0.5b

Counts

4 → 65

Calls

4 calls:

2.1s	(/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n)) -1) (+.f64 1 (pow.f64 (+.f64 1 (/.f64 i n)) n))) (/.f64 i n))
350.0ms	(+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n)) -1)
220.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) (*.f64 2 n))
142.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 11213 to 7655 computations (31.7% saved)

simplify406.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

623 → 623

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5073	42752

prune2.8s (9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	620	3	623
Fresh	2	10	12
Picked	1	0	1
Done	1	1	2
Total	624	14	638

Error

0.5b

Counts

638 → 14

Compiler

Compiled 32257 to 18665 computations (42.1% saved)

regimes2.5s (7.9%)

Accuracy

Total 11.1b remaining (95.8%)

Threshold costs 0b (0%)

Compiler

Compiled 23856 to 15947 computations (33.2% saved)

bsearch257.0ms (0.8%)

Steps

Iters	Range		Point
9	1.0595037285931264e-09	0.00011921198232038432	5.60806670825752e-06
10	-0.0004427596338495568	-1.0894686701799286e-16	-0.00018629600656972037

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	377	279
1	377	279

end0.0ms (0%)

sample10.0s (31.7%)

Algorithm

1×

intervals

Results

2.5s	1701×	body	2048	valid
1.7s	2651×	body	1024	valid
334.0ms	1169×	body	512	valid
134.0ms	1858×	body	128	valid
108.0ms	157×	body	1024	invalid
102.0ms	228×	body	512	invalid
91.0ms	589×	body	256	valid
84.0ms	32×	body	4096	valid
47.0ms	448×	body	128	invalid
39.0ms	147×	body	256	invalid
25.0ms	21×	body	2048	invalid
15.0ms	292×	body	128	nan

Compiler

Compiled 6067 to 4046 computations (33.3% saved)

Details

analyze1.1s (3.4%)

sample156.0ms (0.5%)

simplify131.0ms (0.4%)

prune3.0ms (0%)

localize8.0ms (0%)

rewrite1.2s (4%)

series2.1s (6.8%)

simplify235.0ms (0.7%)

prune1.2s (3.9%)

localize24.0ms (0.1%)

rewrite306.0ms (1%)

series730.0ms (2.3%)

simplify106.0ms (0.3%)

prune318.0ms (1%)

localize24.0ms (0.1%)

rewrite199.0ms (0.6%)

series1.0s (3.3%)

simplify99.0ms (0.3%)

prune390.0ms (1.2%)

localize15.0ms (0%)

rewrite3.0s (9.4%)

series3.0s (9.7%)

simplify406.0ms (1.3%)

prune2.8s (9%)

regimes2.5s (7.9%)

bsearch257.0ms (0.8%)

simplify11.0ms (0%)

end0.0ms (0%)

sample10.0s (31.7%)

Profiling