Details

analyze773.0ms (5.1%)

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)

sample78.0ms (0.5%)

Algorithm

1×

intervals

Results

34.0ms	111×	body	1024	valid
25.0ms	37×	body	2048	valid
8.0ms	47×	body	512	valid
2.0ms	20×	body	256	valid
2.0ms	41×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify168.0ms (1.1%)

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: 38.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.8b	(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))
4.0ms	(tan.f64 (+.f64 x eps))

series331.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

210.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
120.0ms	(tan.f64 (+.f64 x eps))

simplify126.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4851	544
1	4851	544

prune107.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Merged error: 14.7b

Counts

34 → 7

Compiler

Compiled 1588 to 841 computations (47% saved)

localize11.0ms (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))
2.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite48.0ms (0.3%)

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:

18.0ms	(-.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 (12.3%)

Counts

4 → 12

Calls

4 calls:

945.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
537.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
196.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
187.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4949	2567
1	4949	2567

prune913.0ms (6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	85	15	100
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	90	17	107

Merged error: 14.5b

Counts

107 → 17

Compiler

Compiled 18935 to 9551 computations (49.6% saved)

localize12.0ms (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)))))
0.1b	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1821`
26×	`*-un-lft-identity_binary64_1799`
23×	`add-cube-cbrt_binary64_1834`
20×	`times-frac_binary64_1805` `tan-quot_binary64_1958`
19×	`add-exp-log_binary64_1837`
18×	`associate-r_binary64_1739`
13×	`add-cbrt-cube_binary64_1835`
9×	`pow1_binary64_1860`
8×	`frac-sub_binary64_1808`
7×	`associate-l_binary64_1740` `frac-times_binary64_1809` `associate-*l/_binary64_1742`
6×	`add-log-exp_binary64_1838`
5×	`prod-exp_binary64_1848`
4×	`div-exp_binary64_1850` `unswap-sqr_binary64_1767` `associate-/r/_binary64_1745` `flip3-+_binary64_1802` `frac-add_binary64_1807` `flip-+_binary64_1773`
3×	`associate-/l_binary64_1744` `associate-/r_binary64_1743` `associate-*r/_binary64_1741` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-unprod_binary64_1832` `cancel-sign-sub-inv_binary64_1765`
2×	`un-div-inv_binary64_1797` `rec-exp_binary64_1849` `1-exp_binary64_1843` `cbrt-undiv_binary64_1833` `*-commutative_binary64_1730` `div-inv_binary64_1796` `pow-prod-down_binary64_1870`
1×	`sub-neg_binary64_1792` `clear-num_binary64_1798` `frac-2neg_binary64_1810` `pow-flip_binary64_1873` `diff-log_binary64_1891` `distribute-lft-out_binary64_1750` `inv-pow_binary64_1884`

Counts

4 → 121

Calls

4 calls:

18.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
15.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

series2.0s (13.4%)

Counts

4 → 12

Calls

4 calls:

984.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
558.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
303.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
198.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5152	3463

prune382.0ms (2.5%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	3	13	16
Picked	0	1	1
Done	0	0	0
Total	130	20	150

Merged error: 14.5b

Counts

150 → 20

Compiler

Compiled 8917 to 4026 computations (54.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
2.2b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`pow1_binary64_1860`
45×	`tan-quot_binary64_1958`
21×	`frac-times_binary64_1809`
20×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
19×	`pow-prod-down_binary64_1870`
15×	`associate-*r/_binary64_1741`
14×	`associate-*l/_binary64_1742`
13×	`add-sqr-sqrt_binary64_1821`
10×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832`
9×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
7×	`associate-l_binary64_1740` `associate-r_binary64_1739`
6×	`add-log-exp_binary64_1838`
5×	`frac-sub_binary64_1808`
4×	`pow-sqr_binary64_1772` `pow-prod-up_binary64_1869`
3×	`*-commutative_binary64_1730` `cancel-sign-sub-inv_binary64_1765`
2×	`unswap-sqr_binary64_1767` `associate--l+_binary64_1736` `pow-plus_binary64_1862` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`pow2_binary64_1880` `distribute-rgt-in_binary64_1749` `sub-neg_binary64_1792` `distribute-lft-in_binary64_1748` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `swap-sqr_binary64_1766`

Counts

4 → 112

Calls

4 calls:

17.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
12.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series4.3s (28%)

Counts

4 → 12

Calls

4 calls:

3.6s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
283.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
188.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
187.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5350	3156

prune423.0ms (2.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	118	6	124
Fresh	4	14	18
Picked	1	0	1
Done	0	1	1
Total	123	21	144

Merged error: 14.4b

Counts

144 → 21

Compiler

Compiled 10530 to 4425 computations (58% saved)

regimes170.0ms (1.1%)

Compiler: Compiled 1720 to 882 computations (48.7% saved)

bsearch94.0ms (0.6%)

Steps

Iters	Range		Point
9	3.762858264550735e-32	1.2920571637587814e-22	1.455759342729981e-31
8	-1.042520220496204e-72	-6.001693946064188e-76	-2.5520522219363244e-74

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	460	136
1	460	136

end0.0ms (0%)

sample3.0s (19.9%)

Algorithm

1×

intervals

Results

1.1s	3519×	body	1024	valid
809.0ms	1170×	body	2048	valid
230.0ms	1382×	body	512	valid
67.0ms	1355×	body	128	valid
60.0ms	573×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 961 to 491 computations (48.9% saved)

Details

analyze773.0ms (5.1%)

sample78.0ms (0.5%)

simplify168.0ms (1.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series331.0ms (2.2%)

simplify126.0ms (0.8%)

prune107.0ms (0.7%)

localize11.0ms (0.1%)

rewrite48.0ms (0.3%)

series1.9s (12.3%)

simplify81.0ms (0.5%)

prune913.0ms (6%)

localize12.0ms (0.1%)

rewrite59.0ms (0.4%)

series2.0s (13.4%)

simplify76.0ms (0.5%)

prune382.0ms (2.5%)

localize15.0ms (0.1%)

rewrite58.0ms (0.4%)

series4.3s (28%)

simplify56.0ms (0.4%)

prune423.0ms (2.8%)

regimes170.0ms (1.1%)

bsearch94.0ms (0.6%)

simplify21.0ms (0.1%)

end0.0ms (0%)

sample3.0s (19.9%)

Profiling