Details

analyze760.0ms (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
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)

sample81.0ms (0.6%)

Algorithm

1×

intervals

Results

38.0ms	113×	body	1024	valid
22.0ms	34×	body	2048	valid
8.0ms	47×	body	512	valid
3.0ms	27×	body	256	valid
2.0ms	35×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify174.0ms (1.4%)

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: 39.0b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.4b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.9b	(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:

9.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series339.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

221.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
118.0ms	(tan.f64 (+.f64 x eps))

simplify128.0ms (1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4851	544
1	4851	544

prune142.0ms (1.1%)

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: 14.6b

Counts

34 → 7

Compiler

Compiled 2164 to 1142 computations (47.2% 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 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite46.0ms (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 (15.1%)

Counts

4 → 12

Calls

4 calls:

979.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
541.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
193.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
184.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4949	2567
1	4949	2567

prune645.0ms (5.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	90	10	100
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	93	14	107

Merged error: 14.5b

Counts

107 → 14

Compiler

Compiled 13431 to 6505 computations (51.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (tan.f64 x))
0.3b	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
3.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
4.1b	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1821`
13×	`*-un-lft-identity_binary64_1799`
11×	`add-cube-cbrt_binary64_1834`
7×	`log-prod_binary64_1885` `add-log-exp_binary64_1838`
6×	`unpow-prod-down_binary64_1878` `exp-prod_binary64_1851`
5×	`pow1_binary64_1860` `add-exp-log_binary64_1837`
4×	`add-cbrt-cube_binary64_1835` `pow-pow_binary64_1871`
3×	`pow-unpow_binary64_1876` `cancel-sign-sub-inv_binary64_1765` `rem-log-exp_binary64_1840`
2×	`pow-to-exp_binary64_1868` `difference-of-squares_binary64_1768` `pow-exp_binary64_1867` `sqr-pow_binary64_1771`
1×	`sub-neg_binary64_1792` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `times-frac_binary64_1805` `rem-exp-log_binary64_1839` `frac-sub_binary64_1808` `tan-quot_binary64_1958` `log-pow_binary64_1888` `distribute-lft-out--_binary64_1751`

Counts

4 → 67

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
4.0ms	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
3.0ms	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
3.0ms	(exp.f64 (tan.f64 x))

series2.1s (16.4%)

Counts

4 → 12

Calls

4 calls:

1.3s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))))) (tan.f64 x))
403.0ms	(log.f64 (pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps)))
334.0ms	(pow.f64 (exp.f64 (tan.f64 x)) (tan.f64 eps))
68.0ms	(exp.f64 (tan.f64 x))

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4929	1535
1	4929	1535

prune115.0ms (0.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	79	14	93

Merged error: 14.5b

Counts

93 → 14

Compiler

Compiled 2626 to 987 computations (62.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
0.2b	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
6.3b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite93.0ms (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:

36.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
16.0ms	(/.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))

series2.4s (18.7%)

Counts

4 → 12

Calls

4 calls:

972.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
624.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
559.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
195.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify101.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4950	6518
1	4950	6518

prune312.0ms (2.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	2	9	11
Picked	1	0	1
Done	0	2	2
Total	191	15	206

Merged error: 14.5b

Counts

206 → 15

Compiler

Compiled 7202 to 2837 computations (60.6% saved)

regimes108.0ms (0.9%)

Compiler: Compiled 770 to 426 computations (44.7% saved)

bsearch80.0ms (0.6%)

Steps

Iters	Range		Point
10	1.8737204710143123e-13	1334.6439698398303	1.902949990538939e-13
8	-2.1948635434279864e-12	-4.3566971565286763e-16	-4.409799457837537e-16

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	59	53
1	59	53

end0.0ms (0%)

sample2.9s (22.8%)

Algorithm

1×

intervals

Results

1.1s	3511×	body	1024	valid
870.0ms	1281×	body	2048	valid
220.0ms	1314×	body	512	valid
63.0ms	1315×	body	128	valid
60.0ms	576×	body	256	valid
5.0ms	3×	body	4096	valid

Compiler

Compiled 435 to 247 computations (43.2% saved)

Details

analyze760.0ms (6%)

sample81.0ms (0.6%)

simplify174.0ms (1.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series339.0ms (2.7%)

simplify128.0ms (1%)

prune142.0ms (1.1%)

localize12.0ms (0.1%)

rewrite46.0ms (0.4%)

series1.9s (15.1%)

simplify82.0ms (0.7%)

prune645.0ms (5.1%)

localize16.0ms (0.1%)

rewrite38.0ms (0.3%)

series2.1s (16.4%)

simplify90.0ms (0.7%)

prune115.0ms (0.9%)

localize12.0ms (0.1%)

rewrite93.0ms (0.7%)

series2.4s (18.7%)

simplify101.0ms (0.8%)

prune312.0ms (2.5%)

regimes108.0ms (0.9%)

bsearch80.0ms (0.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (22.8%)

Profiling