Details

analyze776.0ms (5.8%)

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%	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
45.0ms	87×	body	1024	valid
11.0ms	44×	body	512	valid
11.0ms	4×	body	4096	valid
4.0ms	19×	body	128	invalid
3.0ms	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
1.0ms	6×	body	256	invalid
1.0ms	12×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify170.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

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:

0.1b	(*.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))

rewrite173.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

584×	`times-frac_binary64_1789`
486×	`add-sqr-sqrt_binary64_1805`
367×	`*-un-lft-identity_binary64_1783`
225×	`add-cube-cbrt_binary64_1818`
174×	`associate-r_binary64_1723`
168×	`difference-of-squares_binary64_1752`
88×	`unpow-prod-down_binary64_1862`
85×	`sqr-pow_binary64_1755`
84×	`difference-of-sqr-1_binary64_1753`
29×	`div-inv_binary64_1780`
28×	`distribute-lft-out--_binary64_1735`
19×	`add-exp-log_binary64_1821`
18×	`add-cbrt-cube_binary64_1819`
13×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
7×	`pow1_binary64_1844`
6×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `add-log-exp_binary64_1822`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-unpow_binary64_1860` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `unswap-sqr_binary64_1751`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip--_binary64_1758`
1×	`div-sub_binary64_1788` `associate-r/_binary64_1725` `distribute-lft-out_binary64_1734` `diff-log_binary64_1875` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `pow-pow_binary64_1855` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 451

Calls

4 calls:

62.0ms	(*.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)
8.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

series946.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
306.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
179.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
148.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify190.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune1.1s (8.2%)

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))

rewrite60.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64_1789`
97×	`add-sqr-sqrt_binary64_1805`
85×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
50×	`associate-r_binary64_1723`
25×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
13×	`associate-/r*_binary64_1727` `pow1_binary64_1844`
9×	`div-inv_binary64_1780`
7×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-l_binary64_1724`
6×	`cbrt-undiv_binary64_1817` `div-exp_binary64_1834`
5×	`pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`
4×	`add-log-exp_binary64_1822`
3×	`associate-r/_binary64_1725` `associate-/l_binary64_1728` `*-commutative_binary64_1714`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786`
1×	`distribute-lft-in_binary64_1732` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `clear-num_binary64_1782`

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)))
11.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
7.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
4.0ms	(*.f64 1/6 i)

series154.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
49.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
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)

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune292.0ms (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)

localize9.0ms (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)))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1805`
10×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
9×	`associate-l_binary64_1724` `associate-r_binary64_1723`
6×	`add-log-exp_binary64_1822`
4×	`associate-*r/_binary64_1725`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`
2×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
1×	`+-commutative_binary64_1713` `sum-log_binary64_1874`

Counts

4 → 73

Calls

4 calls:

6.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
5.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
4.0ms	(*.f64 50/3 i)
3.0ms	(+.f64 50 (*.f64 50/3 i))

series105.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
34.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
20.0ms	(+.f64 50 (*.f64 50/3 i))
11.0ms	(*.f64 50/3 i)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4938	1060
1	4938	1060

prune99.0ms (0.7%)

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)

localize17.0ms (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)))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_1805`
15×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
12×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`associate-r_binary64_1723` `pow1_binary64_1844`
9×	`associate-l_binary64_1724`
4×	`associate-*r/_binary64_1725` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `add-log-exp_binary64_1822`
3×	`flip3--_binary64_1787` `associate-/r_binary64_1727` `times-frac_binary64_1789` `-commutative_binary64_1714` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `flip--_binary64_1758`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `distribute-lft-in_binary64_1732` `cancel-sign-sub-inv_binary64_1749` `cbrt-undiv_binary64_1817` `distribute-rgt-in_binary64_1733` `div-exp_binary64_1834` `sub-neg_binary64_1776`
1×	`difference-of-squares_binary64_1752` `associate-/l*_binary64_1728` `div-inv_binary64_1780` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 86

Calls

4 calls:

9.0ms	(/.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)

series249.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(/.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)))))
74.0ms	(.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 (45.0ms)

Iter	Nodes	Cost
0	5001	1844

prune161.0ms (1.2%)

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)

bsearch151.0ms (1.1%)

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%)

sample7.0s (52.6%)

Algorithm

1×

intervals

Results

2.2s	1767×	body	2048	valid
1.4s	2562×	body	1024	valid
304.0ms	1233×	body	512	valid
117.0ms	1811×	body	128	valid
96.0ms	155×	body	1024	invalid
87.0ms	601×	body	256	valid
84.0ms	225×	body	512	invalid
54.0ms	26×	body	4096	valid
41.0ms	438×	body	128	invalid
33.0ms	155×	body	256	invalid
20.0ms	20×	body	2048	invalid
15.0ms	316×	body	128	nan

Compiler

Compiled 3582 to 2443 computations (31.8% saved)

Details

analyze776.0ms (5.8%)

sample172.0ms (1.3%)

simplify170.0ms (1.3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite173.0ms (1.3%)

series946.0ms (7.1%)

simplify190.0ms (1.4%)

prune1.1s (8.2%)

localize10.0ms (0.1%)

rewrite60.0ms (0.5%)

series154.0ms (1.2%)

simplify97.0ms (0.7%)

prune292.0ms (2.2%)

localize9.0ms (0.1%)

rewrite22.0ms (0.2%)

series105.0ms (0.8%)

simplify66.0ms (0.5%)

prune99.0ms (0.7%)

localize17.0ms (0.1%)

rewrite33.0ms (0.2%)

series249.0ms (1.9%)

simplify68.0ms (0.5%)

prune161.0ms (1.2%)

regimes1.2s (8.9%)

bsearch151.0ms (1.1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.0s (52.6%)

Profiling