Details

analyze796.0ms (6.1%)

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)

sample80.0ms (0.6%)

Algorithm

1×

intervals

Results

32.0ms	107×	body	1024	valid
24.0ms	35×	body	2048	valid
9.0ms	55×	body	512	valid
5.0ms	48×	body	128	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify168.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 35.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0b	(tan.f64 (+.f64 x eps))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1821` `*-un-lft-identity_binary64_1799`
4×	`add-log-exp_binary64_1838` `tan-quot_binary64_1958`
3×	`add-cube-cbrt_binary64_1834` `cancel-sign-sub-inv_binary64_1765`
2×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `frac-sub_binary64_1808` `add-exp-log_binary64_1837` `tan-sum_binary64_1934`
1×	`sub-neg_binary64_1792` `diff-log_binary64_1891` `flip--_binary64_1774` `difference-of-squares_binary64_1768` `flip3--_binary64_1803` `distribute-lft-out--_binary64_1751`

Counts

2 → 27

Calls

2 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series336.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

213.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
122.0ms	(tan.f64 (+.f64 x eps))

simplify126.0ms (1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4851	544
1	4851	544

prune98.0ms (0.8%)

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: 15.6b

Counts

34 → 8

Compiler

Compiled 1427 to 766 computations (46.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1799`
23×	`add-sqr-sqrt_binary64_1821`
16×	`add-cube-cbrt_binary64_1834`
13×	`times-frac_binary64_1805`
9×	`tan-quot_binary64_1958`
8×	`add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
6×	`pow1_binary64_1860`
5×	`distribute-lft-out_binary64_1750`
4×	`associate-/l*_binary64_1744`
3×	`associate-/r_binary64_1743` `associate-l_binary64_1740` `associate-/l/_binary64_1746` `cancel-sign-sub-inv_binary64_1765` `associate-r*_binary64_1739`
2×	`flip--_binary64_1774` `difference-of-squares_binary64_1768` `associate-/r/_binary64_1745` `flip3--_binary64_1803` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `clear-num_binary64_1798` `div-exp_binary64_1850` `+-commutative_binary64_1729` `prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `frac-2neg_binary64_1810` `associate-r/_binary64_1741` `diff-log_binary64_1891` `cbrt-undiv_binary64_1833` `frac-sub_binary64_1808` `cbrt-unprod_binary64_1832` `-commutative_binary64_1730` `div-inv_binary64_1796` `pow-prod-down_binary64_1870` `distribute-lft-out--_binary64_1751` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 88

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
10.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.9s (14.3%)

Counts

4 → 12

Calls

4 calls:

953.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
544.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
187.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
185.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4949	2567
1	4949	2567

prune543.0ms (4.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	88	12	100
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	92	16	108

Merged error: 15.5b

Counts

108 → 16

Compiler

Compiled 11389 to 5510 computations (51.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.7b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

rewrite56.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1821`
22×	`tan-quot_binary64_1958`
20×	`*-un-lft-identity_binary64_1799`
18×	`associate-r_binary64_1739`
15×	`add-cube-cbrt_binary64_1834` `add-exp-log_binary64_1837`
11×	`add-cbrt-cube_binary64_1835` `times-frac_binary64_1805`
8×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `frac-sub_binary64_1808`
7×	`associate-l_binary64_1740` `frac-times_binary64_1809` `associate-*l/_binary64_1742`
5×	`prod-exp_binary64_1848` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`
4×	`unswap-sqr_binary64_1767`
3×	`associate-*r/_binary64_1741` `cbrt-unprod_binary64_1832` `cancel-sign-sub-inv_binary64_1765`
2×	`div-exp_binary64_1850` `un-div-inv_binary64_1797` `flip--_binary64_1774` `associate-/r/_binary64_1745` `flip3--_binary64_1803` `*-commutative_binary64_1730` `pow-prod-down_binary64_1870` `distribute-lft-out_binary64_1750`
1×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `1-exp_binary64_1843` `diff-log_binary64_1891` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796`

Counts

4 → 101

Calls

4 calls:

16.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
16.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.9s (14.6%)

Counts

4 → 12

Calls

4 calls:

986.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
538.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
193.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
188.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4981	2972
1	4981	2972

prune303.0ms (2.3%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	2	13	15
Picked	0	1	1
Done	0	0	0
Total	110	19	129

Merged error: 15.5b

Counts

129 → 19

Compiler

Compiled 7088 to 3129 computations (55.9% saved)

localize12.0ms (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)))
0.3b	(*.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))))
4.9b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite97.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`times-frac_binary64_1805`
105×	`*-un-lft-identity_binary64_1799`
84×	`add-sqr-sqrt_binary64_1821`
68×	`add-cube-cbrt_binary64_1834`
23×	`associate-/r*_binary64_1743`
19×	`add-exp-log_binary64_1837`
16×	`associate-/r/_binary64_1745` `distribute-lft-out_binary64_1750`
15×	`tan-quot_binary64_1958`
13×	`add-cbrt-cube_binary64_1835`
8×	`div-exp_binary64_1850`
7×	`pow1_binary64_1860` `div-inv_binary64_1796`
6×	`associate-/l*_binary64_1744` `add-log-exp_binary64_1838`
5×	`difference-of-squares_binary64_1768` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`
4×	`cbrt-undiv_binary64_1833`
3×	`associate-l_binary64_1740` `cancel-sign-sub-inv_binary64_1765` `associate-r_binary64_1739`
2×	`clear-num_binary64_1798` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `1-exp_binary64_1843` `flip--_binary64_1774` `flip3--_binary64_1803` `associate-/l/_binary64_1746` `distribute-lft-out--_binary64_1751`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `pow-flip_binary64_1873` `associate-r/_binary64_1741` `diff-log_binary64_1891` `frac-sub_binary64_1808` `cbrt-unprod_binary64_1832` `-commutative_binary64_1730` `pow-prod-down_binary64_1870` `inv-pow_binary64_1884` `frac-times_binary64_1809` `associate-*l/_binary64_1742`

Counts

4 → 180

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
14.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
10.0ms	(/.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))

series2.3s (17.4%)

Counts

4 → 12

Calls

4 calls:

953.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
583.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
537.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
196.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4950	6518
1	4950	6518

prune761.0ms (5.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	186	6	192
Fresh	8	9	17
Picked	1	0	1
Done	0	1	1
Total	195	16	211

Merged error: 15.5b

Counts

211 → 16

Compiler

Compiled 12785 to 5820 computations (54.5% saved)

regimes106.0ms (0.8%)

Compiler: Compiled 1080 to 586 computations (45.7% saved)

bsearch88.0ms (0.7%)

Steps

Iters	Range		Point
9	6.507665245367461e-50	7.896910684262039e-45	8.297387541937686e-47
8	-6.630095118248346e-23	-2.4063805024122417e-26	-4.960934173966239e-23

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	276	113
1	276	113

end0.0ms (0%)

sample3.1s (23.4%)

Algorithm

1×

intervals

Results

1.1s	3506×	body	1024	valid
938.0ms	1228×	body	2048	valid
235.0ms	1339×	body	512	valid
71.0ms	1353×	body	128	valid
64.0ms	572×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 627 to 340 computations (45.8% saved)

Details

analyze796.0ms (6.1%)

sample80.0ms (0.6%)

simplify168.0ms (1.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series336.0ms (2.6%)

simplify126.0ms (1%)

prune98.0ms (0.8%)

localize11.0ms (0.1%)

rewrite49.0ms (0.4%)

series1.9s (14.3%)

simplify85.0ms (0.7%)

prune543.0ms (4.2%)

localize14.0ms (0.1%)

rewrite56.0ms (0.4%)

series1.9s (14.6%)

simplify70.0ms (0.5%)

prune303.0ms (2.3%)

localize12.0ms (0.1%)

rewrite97.0ms (0.7%)

series2.3s (17.4%)

simplify105.0ms (0.8%)

prune761.0ms (5.8%)

regimes106.0ms (0.8%)

bsearch88.0ms (0.7%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.1s (23.4%)

Profiling