Details

analyze775.0ms (5.7%)

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)

sample143.0ms (1%)

Algorithm

1×

intervals

Results

65.0ms	56×	body	2048	valid
41.0ms	78×	body	1024	valid
9.0ms	35×	body	512	valid
4.0ms	63×	body	128	valid
3.0ms	23×	body	256	valid
3.0ms	5×	body	1024	invalid
3.0ms	1×	body	4096	valid
2.0ms	5×	body	512	invalid
2.0ms	17×	body	128	invalid
1.0ms	4×	body	256	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify166.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

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

Error

46.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.9b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
10.2b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite165.0ms (1.2%)

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:

58.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
20.0ms	(/.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)

series911.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
289.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
171.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
137.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify192.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

463 → 463

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4954	14743
1	4954	14743

prune809.0ms (5.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	453	10	463
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	454	10	464

Error

20.0b

Counts

464 → 10

Compiler

Compiled 14070 to 7393 computations (47.5% saved)

localize13.0ms (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)))
0.0b	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
0.3b	(*.f64 1/6 i)
17.1b	(/.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:

17.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
8.0ms	(/.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)

series147.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))) (/.f64 i n))
47.0ms	(.f64 100 (/.f64 (+.f64 i (.f64 (.f64 i i) (+.f64 1/2 (.f64 1/6 i)))) (/.f64 i n)))
41.0ms	(.f64 (.f64 i i) (+.f64 1/2 (*.f64 1/6 i)))
10.0ms	(*.f64 1/6 i)

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4971	5462
1	4971	5462

prune303.0ms (2.2%)

Pruning

25 alts after pruning (25 fresh and 0 done)

	Pruned	Kept	Total
New	175	16	191
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	176	25	201

Error

9.4b

Counts

201 → 25

Compiler

Compiled 6106 to 3394 computations (44.4% 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)))))

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

series111.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 50/3 i)))))
37.0ms	(.f64 i (+.f64 50 (.f64 50/3 i)))
24.0ms	(+.f64 50 (*.f64 50/3 i))
10.0ms	(*.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

prune103.0ms (0.8%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	2	22	24
Picked	0	1	1
Done	0	0	0
Total	86	24	110

Error

9.4b

Counts

110 → 24

Compiler

Compiled 1950 to 1446 computations (25.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.1b	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))
14.5b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
14.5b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
14.5b	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-*r/_binary64_1725` `add-sqr-sqrt_binary64_1805`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `cbrt-div_binary64_1815` `*-un-lft-identity_binary64_1783` `pow1_binary64_1844`
4×	`flip-+_binary64_1757` `flip3-+_binary64_1786` `add-log-exp_binary64_1822`
3×	`cbrt-prod_binary64_1814` `associate-l_binary64_1724` `pow1/3_binary64_1865` `associate-r_binary64_1723`
1×	`distribute-lft-in_binary64_1732` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

4 → 55

Calls

4 calls:

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

series408.0ms (3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
123.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
119.0ms	(cbrt.f64 (.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3))))))
43.0ms	(.f64 n (+.f64 100 (.f64 i (+.f64 50 (*.f64 i 50/3)))))

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4865	1667
1	4865	1667

prune145.0ms (1.1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	62	5	67
Fresh	6	16	22
Picked	1	0	1
Done	0	1	1
Total	69	22	91

Error

9.4b

Counts

91 → 22

Compiler

Compiled 3147 to 2387 computations (24.1% saved)

regimes1.4s (10.2%)

Accuracy

Total 6.2b remaining (41.8%)

Threshold costs 0b (0%)

Compiler

Compiled 15457 to 10801 computations (30.1% saved)

bsearch180.0ms (1.3%)

Steps

Iters	Range		Point
12	6.737482278960457e-05	3.999257534622798e+38	0.9976863218325943
8	-36.4752059562282	-0.003479041501636987	-0.06789254273176702

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	53	76
1	53	76

end0.0ms (0%)

sample7.3s (53.4%)

Algorithm

1×

intervals

Results

2.1s	1723×	body	2048	valid
1.4s	2676×	body	1024	valid
293.0ms	1156×	body	512	valid
122.0ms	1827×	body	128	valid
106.0ms	174×	body	1024	invalid
95.0ms	43×	body	4096	valid
86.0ms	575×	body	256	valid
78.0ms	214×	body	512	invalid
45.0ms	479×	body	128	invalid
29.0ms	135×	body	256	invalid
14.0ms	14×	body	2048	invalid
13.0ms	277×	body	128	nan

Compiler

Compiled 3924 to 2734 computations (30.3% saved)

Details

analyze775.0ms (5.7%)

sample143.0ms (1%)

simplify166.0ms (1.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite165.0ms (1.2%)

series911.0ms (6.7%)

simplify192.0ms (1.4%)

prune809.0ms (5.9%)

localize13.0ms (0.1%)

rewrite57.0ms (0.4%)

series147.0ms (1.1%)

simplify99.0ms (0.7%)

prune303.0ms (2.2%)

localize8.0ms (0.1%)

rewrite22.0ms (0.2%)

series111.0ms (0.8%)

simplify66.0ms (0.5%)

prune103.0ms (0.8%)

localize14.0ms (0.1%)

rewrite23.0ms (0.2%)

series408.0ms (3%)

simplify95.0ms (0.7%)

prune145.0ms (1.1%)

regimes1.4s (10.2%)

bsearch180.0ms (1.3%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.3s (53.4%)

Profiling