Details

analyze787.0ms (5.9%)

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)

sample172.0ms (1.3%)

Algorithm

1×

intervals

Results

75.0ms	57×	body	2048	valid
46.0ms	87×	body	1024	valid
13.0ms	44×	body	512	valid
10.0ms	4×	body	4096	valid
4.0ms	6×	body	1024	invalid
3.0ms	50×	body	128	valid
2.0ms	6×	body	512	invalid
2.0ms	2×	body	2048	invalid
2.0ms	14×	body	256	valid
2.0ms	19×	body	128	invalid
1.0ms	6×	body	256	invalid
1.0ms	12×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify164.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5036	22

prune2.0ms (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:

0.1b	(*.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)
5.1b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
10.2b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite163.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

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-/r_binary64_2409` `associate-/l_binary64_2410`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
3×	`unswap-sqr_binary64_2433` `cancel-sign-sub-inv_binary64_2431` `prod-exp_binary64_2514` `pow-unpow_binary64_2542` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
2×	`flip--_binary64_2440` `associate-/l/_binary64_2412` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`-commutative_binary64_2396` `associate-r/_binary64_2407` `clear-num_binary64_2464` `div-sub_binary64_2470` `pow-exp_binary64_2533` `sub-neg_binary64_2458` `pow-to-exp_binary64_2534` `diff-log_binary64_2557` `pow-pow_binary64_2537` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 451

Calls

4 calls:

58.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
25.0ms	(/.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)

series941.0ms (7%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
297.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
169.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
150.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify192.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune960.0ms (7.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	454	9	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	455	9	464

Merged error: 19.8b

Counts

464 → 9

Compiler

Compiled 14058 to 7380 computations (47.5% saved)

localize10.0ms (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)
15.6b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_2471`
97×	`add-sqr-sqrt_binary64_2487`
85×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
50×	`associate-r_binary64_2405`
25×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
13×	`associate-/r*_binary64_2409` `pow1_binary64_2526`
9×	`div-inv_binary64_2462`
7×	`prod-exp_binary64_2514` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
6×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
5×	`unswap-sqr_binary64_2433` `pow-prod-down_binary64_2536`
4×	`add-log-exp_binary64_2504`
3×	`-commutative_binary64_2396` `associate-r/_binary64_2407` `associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `associate-/r/_binary64_2411`
1×	`distribute-lft-in_binary64_2414` `clear-num_binary64_2464` `distribute-rgt-in_binary64_2415` `frac-2neg_binary64_2476`

Counts

4 → 179

Calls

4 calls:

17.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
10.0ms	(/.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)

series153.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
48.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
45.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
10.0ms	(*.f64 1/6 i)

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune298.0ms (2.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	179	12	191
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	180	20	200

Merged error: 9.0b

Counts

200 → 20

Compiler

Compiled 6000 to 3300 computations (45% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 50 (*.f64 50/3 i))
0.1b	(.f64 i (+.f64 50 (.f64 50/3 i)))
0.5b	(*.f64 50/3 i)
2.6b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2487`
10×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
9×	`associate-r_binary64_2405` `associate-l_binary64_2406`
6×	`add-log-exp_binary64_2504`
4×	`associate-*r/_binary64_2407`
3×	`flip3-+_binary64_2468` `*-commutative_binary64_2396` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
2×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 50/3 i)
5.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
5.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
3.0ms	(+.f64 50 (*.f64 50/3 i))

series109.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
37.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
19.0ms	(+.f64 50 (*.f64 50/3 i))
10.0ms	(*.f64 50/3 i)

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4938	1060
1	4938	1060

prune102.0ms (0.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	85	20	105

Merged error: 9.0b

Counts

105 → 20

Compiler

Compiled 1886 to 1378 computations (26.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 i 50/3)
0.5b	(*.f64 i 50/3)
1.0b	(.f64 n (-.f64 10000 (.f64 (.f64 i (+.f64 50 (.f64 i 50/3))) (.f64 i (+.f64 50 (.f64 i 50/3))))))
12.8b	(/.f64 (.f64 n (-.f64 10000 (.f64 (.f64 i (+.f64 50 (.f64 i 50/3))) (.f64 i (+.f64 50 (.f64 i 50/3)))))) (-.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i)))))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_2487`
15×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
12×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
10×	`pow1_binary64_2526` `associate-r_binary64_2405`
9×	`associate-l_binary64_2406`
4×	`add-log-exp_binary64_2504` `associate-*r/_binary64_2407` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
3×	`-commutative_binary64_2396` `times-frac_binary64_2471` `associate-/r_binary64_2409` `flip--_binary64_2440` `unswap-sqr_binary64_2433` `pow-prod-down_binary64_2536` `flip3--_binary64_2469`
2×	`distribute-lft-in_binary64_2414` `associate-/l/_binary64_2412` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `distribute-rgt-in_binary64_2415` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516` `associate-/r/_binary64_2411`
1×	`difference-of-squares_binary64_2434` `clear-num_binary64_2464` `div-inv_binary64_2462` `frac-2neg_binary64_2476` `associate-/l*_binary64_2410`

Counts

4 → 86

Calls

4 calls:

12.0ms	(/.f64 (.f64 n (-.f64 10000 (.f64 (.f64 i (+.f64 50 (.f64 i 50/3))) (.f64 i (+.f64 50 (.f64 i 50/3)))))) (-.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i)))))
7.0ms	(.f64 n (-.f64 10000 (.f64 (.f64 i (+.f64 50 (.f64 i 50/3))) (.f64 i (+.f64 50 (.f64 i 50/3))))))
4.0ms	(*.f64 i 50/3)
4.0ms	(*.f64 i 50/3)

series252.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (.f64 n (-.f64 10000 (.f64 (.f64 i (+.f64 50 (.f64 i 50/3))) (.f64 i (+.f64 50 (.f64 i 50/3)))))) (-.f64 100 (.f64 i (+.f64 50 (.f64 50/3 i)))))
73.0ms	(.f64 n (-.f64 10000 (.f64 (.f64 i (+.f64 50 (.f64 i 50/3))) (.f64 i (+.f64 50 (.f64 i 50/3))))))
11.0ms	(*.f64 i 50/3)
10.0ms	(*.f64 i 50/3)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5001	1844

prune169.0ms (1.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	4	14	18
Picked	1	0	1
Done	0	1	1
Total	100	18	118

Merged error: 9.0b

Counts

118 → 18

Compiler

Compiled 3154 to 2447 computations (22.4% saved)

regimes1.2s (8.9%)

Compiler: Compiled 14273 to 9746 computations (31.7% saved)

bsearch158.0ms (1.2%)

Steps

Iters	Range		Point
11	0.00023260871939406952	2.452610184317742e+16	0.05443781441738046
7	-1876383395416300.2	-68572938835656.58	-69221321268138.08

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	40	48
1	40	48

end0.0ms (0%)

sample7.2s (53.8%)

Algorithm

1×

intervals

Results

2.2s	1767×	body	2048	valid
1.4s	2562×	body	1024	valid
315.0ms	1233×	body	512	valid
124.0ms	1811×	body	128	valid
95.0ms	155×	body	1024	invalid
86.0ms	601×	body	256	valid
82.0ms	225×	body	512	invalid
56.0ms	26×	body	4096	valid
41.0ms	438×	body	128	invalid
34.0ms	155×	body	256	invalid
22.0ms	20×	body	2048	invalid
14.0ms	316×	body	128	nan

Compiler

Compiled 3582 to 2443 computations (31.8% saved)

Details

analyze787.0ms (5.9%)

sample172.0ms (1.3%)

simplify164.0ms (1.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite163.0ms (1.2%)

series941.0ms (7%)

simplify192.0ms (1.4%)

prune960.0ms (7.2%)

localize10.0ms (0.1%)

rewrite58.0ms (0.4%)

series153.0ms (1.1%)

simplify95.0ms (0.7%)

prune298.0ms (2.2%)

localize7.0ms (0.1%)

rewrite24.0ms (0.2%)

series109.0ms (0.8%)

simplify64.0ms (0.5%)

prune102.0ms (0.8%)

localize15.0ms (0.1%)

rewrite36.0ms (0.3%)

series252.0ms (1.9%)

simplify68.0ms (0.5%)

prune169.0ms (1.3%)

regimes1.2s (8.9%)

bsearch158.0ms (1.2%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.2s (53.8%)

Profiling