Details

analyze858.0ms (6.5%)

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)

sample184.0ms (1.4%)

Algorithm

1×

intervals

Results

81.0ms	53×	body	2048	valid
60.0ms	94×	body	1024	valid
9.0ms	34×	body	512	valid
7.0ms	2×	body	4096	valid
4.0ms	56×	body	128	valid
3.0ms	17×	body	256	valid
2.0ms	21×	body	128	invalid
2.0ms	1×	body	2048	invalid
2.0ms	5×	body	512	invalid
1.0ms	2×	body	1024	invalid
1.0ms	3×	body	256	invalid
0.0ms	9×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify182.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4966	22
1	4966	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: 45.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (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)))
0.8b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite177.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_2442`
485×	`add-sqr-sqrt_binary64_2457`
366×	`*-un-lft-identity_binary64_2436`
224×	`add-cube-cbrt_binary64_2468`
174×	`associate-r_binary64_2378`
168×	`difference-of-squares_binary64_2405`
88×	`unpow-prod-down_binary64_2512`
85×	`sqr-pow_binary64_2408`
84×	`difference-of-sqr-1_binary64_2406`
29×	`div-inv_binary64_2433`
28×	`distribute-lft-out--_binary64_2390`
19×	`add-exp-log_binary64_2471`
18×	`add-cbrt-cube_binary64_2469`
13×	`associate-/l_binary64_2383` `associate-/r_binary64_2382`
7×	`pow1_binary64_2494`
6×	`cbrt-undiv_binary64_2467` `add-log-exp_binary64_2472` `div-exp_binary64_2484`
3×	`prod-exp_binary64_2482` `pow-unpow_binary64_2510` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404` `associate-l_binary64_2379`
2×	`associate-/r/_binary64_2384` `flip3--_binary64_2440` `associate-/l/_binary64_2385` `flip--_binary64_2411`
1×	`distribute-lft-out_binary64_2389` `-commutative_binary64_2369` `diff-log_binary64_2525` `pow-prod-down_binary64_2504` `associate-r/_binary64_2380` `pow-to-exp_binary64_2502` `clear-num_binary64_2435` `pow-exp_binary64_2501` `pow-pow_binary64_2505` `div-sub_binary64_2441` `frac-2neg_binary64_2447` `sub-neg_binary64_2429`

Counts

4 → 448

Calls

4 calls:

57.0ms	(*.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))
15.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series1.9s (14.2%)

Counts

4 → 12

Calls

4 calls:

629.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
579.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
350.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
311.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify155.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

460 → 460

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5097	14768

prune984.0ms (7.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	453	7	460
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	454	7	461

Merged error: 17.4b

Counts

461 → 7

Compiler

Compiled 13967 to 7341 computations (47.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.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)))
0.4b	(*.f64 1/6 i)
16.4b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_2442`
97×	`add-sqr-sqrt_binary64_2457`
85×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
50×	`associate-r_binary64_2378`
25×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
13×	`associate-/r*_binary64_2382` `pow1_binary64_2494`
9×	`div-inv_binary64_2433`
7×	`prod-exp_binary64_2482` `cbrt-unprod_binary64_2466` `associate-l_binary64_2379`
6×	`cbrt-undiv_binary64_2467` `div-exp_binary64_2484`
5×	`pow-prod-down_binary64_2504` `unswap-sqr_binary64_2404`
4×	`add-log-exp_binary64_2472`
3×	`-commutative_binary64_2369` `associate-/l_binary64_2383` `associate-*r/_binary64_2380`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r/_binary64_2384` `associate-/l/_binary64_2385`
1×	`distribute-rgt-in_binary64_2388` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387`

Counts

4 → 179

Calls

4 calls:

18.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
9.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
8.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series292.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
91.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
86.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
24.0ms	(*.f64 1/6 i)

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5624	5462

prune323.0ms (2.4%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	181	10	191
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	182	16	198

Merged error: 7.1b

Counts

198 → 16

Compiler

Compiled 5794 to 3185 computations (45% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 50 (*.f64 50/3 i))
0.0b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
3.1b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2457`
10×	`add-exp-log_binary64_2471` `add-cube-cbrt_binary64_2468` `add-cbrt-cube_binary64_2469` `*-un-lft-identity_binary64_2436` `pow1_binary64_2494`
9×	`associate-r_binary64_2378` `associate-l_binary64_2379`
6×	`add-log-exp_binary64_2472`
4×	`associate-*r/_binary64_2380`
3×	`flip3-+_binary64_2439` `prod-exp_binary64_2482` `flip-+_binary64_2410` `*-commutative_binary64_2369` `pow-prod-down_binary64_2504` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404`
2×	`distribute-rgt-in_binary64_2388` `distribute-lft-in_binary64_2387`
1×	`sum-log_binary64_2524` `+-commutative_binary64_2368`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.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)
3.0ms	(+.f64 50 (*.f64 50/3 i))

series235.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
82.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
42.0ms	(+.f64 50 (*.f64 50/3 i))
22.0ms	(*.f64 50/3 i)

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5747	1060

prune106.0ms (0.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	84	17	101

Merged error: 7.1b

Counts

101 → 17

Compiler

Compiled 1690 to 1269 computations (24.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.4b	(*.f64 1/6 i)
1.6b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 1 n))
11.9b	(.f64 (/.f64 100 i) (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 1 n)))

rewrite78.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`times-frac_binary64_2442`
122×	`add-sqr-sqrt_binary64_2457`
93×	`*-un-lft-identity_binary64_2436`
91×	`add-cube-cbrt_binary64_2468`
55×	`add-exp-log_binary64_2471`
50×	`associate-r_binary64_2378`
37×	`add-cbrt-cube_binary64_2469`
23×	`div-exp_binary64_2484`
17×	`associate-l_binary64_2379`
14×	`prod-exp_binary64_2482`
13×	`associate-/r*_binary64_2382` `pow1_binary64_2494`
12×	`cbrt-undiv_binary64_2467`
10×	`div-inv_binary64_2433` `cbrt-unprod_binary64_2466` `unswap-sqr_binary64_2404`
5×	`pow-prod-down_binary64_2504`
4×	`add-log-exp_binary64_2472`
3×	`-commutative_binary64_2369` `rec-exp_binary64_2483` `associate-/l_binary64_2383` `1-exp_binary64_2477` `associate-*r/_binary64_2380`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-/r/_binary64_2384` `associate-/l/_binary64_2385`
1×	`distribute-rgt-in_binary64_2388` `clear-num_binary64_2435` `frac-2neg_binary64_2447` `associate-*l/_binary64_2381` `frac-times_binary64_2446` `distribute-lft-in_binary64_2387`

Counts

4 → 208

Calls

4 calls:

29.0ms	(.f64 (/.f64 100 i) (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 1 n)))
10.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 1 n))
8.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series277.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(.f64 (/.f64 100 i) (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 1 n)))
90.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
59.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 1 n))
27.0ms	(*.f64 1/6 i)

simplify102.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4936	6290
1	4936	6290

prune367.0ms (2.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	218	2	220
Fresh	4	11	15
Picked	0	1	1
Done	0	1	1
Total	222	15	237

Merged error: 7.1b

Counts

237 → 15

Compiler

Compiled 6377 to 4033 computations (36.8% saved)

regimes194.0ms (1.5%)

Compiler: Compiled 1010 to 747 computations (26% saved)

bsearch292.0ms (2.2%)

Steps

Iters	Range		Point
9	1.7348189760282097e-23	3.3746085799148312e-18	3.344734511806178e-18
8	7.446584598917272e-186	4.022749768151908e-183	1.206767779907382e-183
7	-53582.71594587509	-1566.8462726361977	-1587.2666382638245

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	63	103
1	63	103

end0.0ms (0%)

sample6.2s (47.3%)

Algorithm

1×

intervals

Results

2.9s	1794×	body	2048	valid
1.6s	2622×	body	1024	valid
338.0ms	1130×	body	512	valid
137.0ms	1822×	body	128	valid
125.0ms	200×	body	1024	invalid
106.0ms	603×	body	256	valid
89.0ms	29×	body	4096	valid
85.0ms	221×	body	512	invalid
49.0ms	485×	body	128	invalid
34.0ms	149×	body	256	invalid
25.0ms	18×	body	2048	invalid
17.0ms	361×	body	128	nan

Compiler

Compiled 438 to 315 computations (28.1% saved)

Details

analyze858.0ms (6.5%)

sample184.0ms (1.4%)

simplify182.0ms (1.4%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite177.0ms (1.3%)

series1.9s (14.2%)

simplify155.0ms (1.2%)

prune984.0ms (7.5%)

localize12.0ms (0.1%)

rewrite66.0ms (0.5%)

series292.0ms (2.2%)

simplify79.0ms (0.6%)

prune323.0ms (2.4%)

localize8.0ms (0.1%)

rewrite23.0ms (0.2%)

series235.0ms (1.8%)

simplify51.0ms (0.4%)

prune106.0ms (0.8%)

localize13.0ms (0.1%)

rewrite78.0ms (0.6%)

series277.0ms (2.1%)

simplify102.0ms (0.8%)

prune367.0ms (2.8%)

regimes194.0ms (1.5%)

bsearch292.0ms (2.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.2s (47.3%)

Profiling