Details

analyze781.0ms (6%)

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)

sample151.0ms (1.2%)

Algorithm

1×

intervals

Results

67.0ms	54×	body	2048	valid
41.0ms	77×	body	1024	valid
12.0ms	48×	body	512	valid
6.0ms	3×	body	4096	valid
4.0ms	51×	body	128	valid
3.0ms	23×	body	256	valid
3.0ms	8×	body	512	invalid
2.0ms	4×	body	1024	invalid
2.0ms	20×	body	128	invalid
1.0ms	1×	body	2048	invalid
1.0ms	4×	body	256	invalid
0.0ms	6×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify164.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

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: 47.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize12.0ms (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)))
1.2b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
2.7b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.9b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite171.0ms (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)))
21.0ms	(/.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)

series950.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

322.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
303.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
172.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
153.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify184.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune794.0ms (6.1%)

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: 19.9b

Counts

464 → 8

Compiler

Compiled 14014 to 7357 computations (47.5% 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)))
0.1b	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
0.3b	(*.f64 1/6 i)
13.7b	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))

rewrite57.0ms (0.4%)

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:

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)

series151.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
50.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
40.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
11.0ms	(*.f64 1/6 i)

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune301.0ms (2.3%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	176	15	191
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	177	22	199

Merged error: 10.3b

Counts

199 → 22

Compiler

Compiled 6036 to 3348 computations (44.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
0.1b	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
0.3b	(*.f64 i 1/6)
1.7b	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_1805`
15×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `pow1_binary64_1844`
12×	`associate-l_binary64_1724`
11×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
10×	`associate-r_binary64_1723`
8×	`associate-*r/_binary64_1725`
6×	`distribute-lft-in_binary64_1732` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `distribute-rgt-in_binary64_1733` `pow-prod-down_binary64_1854`
4×	`*-commutative_binary64_1714` `add-log-exp_binary64_1822`
3×	`flip-+_binary64_1757` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751`

Counts

4 → 86

Calls

4 calls:

7.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
6.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
6.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
4.0ms	(*.f64 i 1/6)

series135.0ms (1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 100 (+.f64 n (.f64 n (.f64 i (+.f64 1/2 (.f64 i 1/6))))))
41.0ms	(.f64 n (.f64 i (+.f64 1/2 (*.f64 i 1/6))))
34.0ms	(.f64 i (+.f64 1/2 (.f64 i 1/6)))
11.0ms	(*.f64 i 1/6)

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4993	1381
1	4993	1381

prune126.0ms (1%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	97	23	120

Merged error: 10.3b

Counts

120 → 23

Compiler

Compiled 2377 to 1710 computations (28.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 i)
0.6b	(cbrt.f64 i)
0.6b	(cbrt.f64 i)
1.7b	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 1/6 (cbrt.f64 i))))))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `cbrt-prod_binary64_1814` `pow1_binary64_1844`
8×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
4×	`associate-*r/_binary64_1725` `distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733` `add-log-exp_binary64_1822`
3×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `associate-l_binary64_1724` `pow1/3_binary64_1865` `pow-prod-down_binary64_1854`
1×	`flip-+_binary64_1757` `-commutative_binary64_1714` `flip3-+_binary64_1786` `associate-r*_binary64_1723`

Counts

4 → 57

Calls

4 calls:

8.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 1/6 (cbrt.f64 i))))))
1.0ms	(cbrt.f64 i)
1.0ms	(cbrt.f64 i)
1.0ms	(cbrt.f64 i)

series319.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt.f64 i)
83.0ms	(cbrt.f64 i)
77.0ms	(cbrt.f64 i)
72.0ms	(.f64 n (.f64 i (+.f64 1/2 (.f64 (.f64 (cbrt.f64 i) (cbrt.f64 i)) (*.f64 1/6 (cbrt.f64 i))))))

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4953	652
1	4953	652

prune68.0ms (0.5%)

Pruning

23 alts after pruning (22 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	22	22
Picked	0	1	1
Done	0	0	0
Total	69	23	92

Merged error: 10.3b

Counts

92 → 23

Compiler

Compiled 1496 to 862 computations (42.4% saved)

regimes1.2s (9.2%)

Compiler: Compiled 13672 to 9392 computations (31.3% saved)

bsearch214.0ms (1.6%)

Steps

Iters	Range		Point
8	2.583888434164659e-14	3.162209622168923e-11	8.787233895042543e-13
8	6.143035921151748e-177	2.460506998119988e-172	1.5181636956965362e-175
6	-15399.725079770662	-3572.7575854044167	-3606.923004814872

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	66	103
1	66	103

end0.0ms (0%)

sample7.0s (53.6%)

Algorithm

1×

intervals

Results

2.1s	1763×	body	2048	valid
1.4s	2556×	body	1024	valid
309.0ms	1255×	body	512	valid
128.0ms	1831×	body	128	valid
97.0ms	160×	body	1024	invalid
84.0ms	567×	body	256	valid
75.0ms	208×	body	512	invalid
61.0ms	28×	body	4096	valid
46.0ms	493×	body	128	invalid
32.0ms	150×	body	256	invalid
17.0ms	17×	body	2048	invalid
14.0ms	307×	body	128	nan

Compiler

Compiled 3469 to 2378 computations (31.4% saved)

Details

analyze781.0ms (6%)

sample151.0ms (1.2%)

simplify164.0ms (1.3%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite171.0ms (1.3%)

series950.0ms (7.3%)

simplify184.0ms (1.4%)

prune794.0ms (6.1%)

localize13.0ms (0.1%)

rewrite57.0ms (0.4%)

series151.0ms (1.2%)

simplify95.0ms (0.7%)

prune301.0ms (2.3%)

localize9.0ms (0.1%)

rewrite28.0ms (0.2%)

series135.0ms (1%)

simplify55.0ms (0.4%)

prune126.0ms (1%)

localize15.0ms (0.1%)

rewrite16.0ms (0.1%)

series319.0ms (2.4%)

simplify44.0ms (0.3%)

prune68.0ms (0.5%)

regimes1.2s (9.2%)

bsearch214.0ms (1.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.0s (53.6%)

Profiling