Details

analyze776.0ms (8.4%)

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
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample58.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	106×	body	1024	valid
17.0ms	42×	body	2048	valid
7.0ms	46×	body	512	valid
2.0ms	47×	body	128	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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: 37.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.3b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`tan-quot_binary64_1942` `add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `tan-sum_binary64_1918` `frac-sub_binary64_1792` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 27

Calls

2 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series187.0ms (2%)

Counts

2 → 6

Calls

2 calls:

119.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
68.0ms	(tan.f64 (+.f64 x eps))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4834	544
1	4834	544

prune39.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Merged error: 14.2b

Counts

34 → 8

Compiler

Compiled 556 to 179 computations (67.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805`
16×	`add-cube-cbrt_binary64_1818`
13×	`times-frac_binary64_1789`
9×	`tan-quot_binary64_1942`
8×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
6×	`pow1_binary64_1844`
5×	`distribute-lft-out_binary64_1734`
4×	`associate-/l*_binary64_1728`
3×	`associate-/l/_binary64_1730` `cancel-sign-sub-inv_binary64_1749` `associate-/r_binary64_1727` `associate-l_binary64_1724` `associate-r*_binary64_1723`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `difference-of-squares_binary64_1752` `frac-add_binary64_1791` `flip-+_binary64_1757` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `distribute-lft-out--_binary64_1735` `associate-l/_binary64_1726` `diff-log_binary64_1875` `frac-sub_binary64_1792` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `frac-times_binary64_1793` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`

Counts

4 → 88

Calls

4 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.0s (11.4%)

Counts

4 → 12

Calls

4 calls:

536.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
297.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
109.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
106.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify86.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5619	2567

prune135.0ms (1.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	87	13	100
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	92	16	108

Merged error: 14.0b

Counts

108 → 16

Compiler

Compiled 2953 to 1010 computations (65.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))))
0.2b	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 eps) (sin.f64 x))
3.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

rewrite62.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_1783`
43×	`add-sqr-sqrt_binary64_1805`
28×	`times-frac_binary64_1789`
21×	`add-cube-cbrt_binary64_1818`
13×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
12×	`difference-of-squares_binary64_1752`
9×	`associate-/r*_binary64_1727`
7×	`distribute-lft-out_binary64_1734`
6×	`distribute-lft-out--_binary64_1735` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`tan-quot_binary64_1942` `associate-/l*_binary64_1728`
4×	`associate-/l/_binary64_1730`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `associate-r_binary64_1723`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `associate-*l/_binary64_1726` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `flip--_binary64_1758`
1×	`frac-add_binary64_1791` `flip-+_binary64_1757` `diff-log_binary64_1875` `frac-sub_binary64_1792` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`

Counts

4 → 110

Calls

4 calls:

26.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
12.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))))
6.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))

series1.0s (11.1%)

Counts

4 → 12

Calls

4 calls:

544.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
299.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))))
110.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
69.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5021	3719

prune145.0ms (1.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	122	16	138

Merged error: 14.0b

Counts

138 → 16

Compiler

Compiled 3976 to 1207 computations (69.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
5.9b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite83.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`times-frac_binary64_1789`
105×	`*-un-lft-identity_binary64_1783`
84×	`add-sqr-sqrt_binary64_1805`
68×	`add-cube-cbrt_binary64_1818`
23×	`associate-/r*_binary64_1727`
19×	`add-exp-log_binary64_1821`
16×	`associate-/r/_binary64_1729` `distribute-lft-out_binary64_1734`
15×	`tan-quot_binary64_1942`
13×	`add-cbrt-cube_binary64_1819`
8×	`div-exp_binary64_1834`
7×	`div-inv_binary64_1780` `pow1_binary64_1844`
6×	`associate-/l*_binary64_1728` `add-log-exp_binary64_1822`
5×	`difference-of-squares_binary64_1752` `frac-add_binary64_1791` `flip-+_binary64_1757` `flip3-+_binary64_1786`
4×	`cbrt-undiv_binary64_1817`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `associate-r_binary64_1723`
2×	`flip3--_binary64_1787` `associate-/l/_binary64_1730` `1-exp_binary64_1827` `distribute-lft-out--_binary64_1735` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `flip--_binary64_1758` `rec-exp_binary64_1833`
1×	`div-sub_binary64_1788` `associate-r/_binary64_1725` `inv-pow_binary64_1868` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-flip_binary64_1857` `associate-l/_binary64_1726` `diff-log_binary64_1875` `frac-sub_binary64_1792` `*-commutative_binary64_1714` `frac-times_binary64_1793` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`

Counts

4 → 180

Calls

4 calls:

32.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
12.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
9.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series1.2s (13.5%)

Counts

4 → 12

Calls

4 calls:

530.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
317.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
298.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
103.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4966	6518
1	4966	6518

prune232.0ms (2.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	193	15	208

Merged error: 14.0b

Counts

208 → 15

Compiler

Compiled 5576 to 1957 computations (64.9% saved)

regimes417.0ms (4.5%)

Compiler: Compiled 4833 to 2683 computations (44.5% saved)

bsearch65.0ms (0.7%)

Steps

Iters	Range		Point
6	6.000980334080563e-148	7.475396277707629e-147	7.335594256652865e-147
10	-1.2199136045795702e-08	-1.803382996670263e-21	-2.5888280122113803e-20

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	90	87
1	90	87

end0.0ms (0%)

sample3.1s (33.9%)

Algorithm

1×

intervals

Results

851.0ms	3484×	body	1024	valid
557.0ms	1257×	body	2048	valid
208.0ms	1336×	body	512	valid
62.0ms	1327×	body	128	valid
59.0ms	594×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1656 to 921 computations (44.4% saved)

Details

analyze776.0ms (8.4%)

sample58.0ms (0.6%)

simplify100.0ms (1.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite13.0ms (0.1%)

series187.0ms (2%)

simplify91.0ms (1%)

prune39.0ms (0.4%)

localize10.0ms (0.1%)

rewrite41.0ms (0.4%)

series1.0s (11.4%)

simplify86.0ms (0.9%)

prune135.0ms (1.5%)

localize15.0ms (0.2%)

rewrite62.0ms (0.7%)

series1.0s (11.1%)

simplify76.0ms (0.8%)

prune145.0ms (1.6%)

localize11.0ms (0.1%)

rewrite83.0ms (0.9%)

series1.2s (13.5%)

simplify120.0ms (1.3%)

prune232.0ms (2.5%)

regimes417.0ms (4.5%)

bsearch65.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.1s (33.9%)

Profiling