Details

analyze766.0ms (6.8%)

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)

sample77.0ms (0.7%)

Algorithm

1×

intervals

Results

35.0ms	111×	body	1024	valid
22.0ms	34×	body	2048	valid
8.0ms	49×	body	512	valid
2.0ms	21×	body	256	valid
2.0ms	41×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify165.0ms (1.5%)

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: 36.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.7b	(tan.f64 (+.f64 x eps))

rewrite15.0ms (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))

series340.0ms (3%)

Counts

2 → 6

Calls

2 calls:

214.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
126.0ms	(tan.f64 (+.f64 x eps))

simplify133.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4851	544
1	4851	544

prune39.0ms (0.3%)

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: 12.2b

Counts

34 → 8

Compiler

Compiled 562 to 180 computations (68% saved)

localize12.0ms (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))
2.6b	(-.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_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:

15.0ms	(-.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 (16.8%)

Counts

4 → 12

Calls

4 calls:

967.0ms	(-.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))))
200.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
188.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify84.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4949	2567
1	4949	2567

prune141.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	88	12	100
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 12.1b

Counts

108 → 14

Compiler

Compiled 2923 to 990 computations (66.1% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
7.2b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`associate-*l/_binary64_1726`
16×	`add-sqr-sqrt_binary64_1805`
14×	`tan-quot_binary64_1942`
12×	`*-un-lft-identity_binary64_1783`
10×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-cube-cbrt_binary64_1818` `associate-l_binary64_1724` `pow1_binary64_1844`
9×	`associate-r_binary64_1723`
6×	`frac-sub_binary64_1792` `add-log-exp_binary64_1822`
4×	`flip3--_binary64_1787` `flip--_binary64_1758`
3×	`frac-add_binary64_1791` `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×	`associate-*r/_binary64_1725` `frac-times_binary64_1793`
1×	`distribute-lft-out_binary64_1734` `cancel-sign-sub-inv_binary64_1749` `diff-log_binary64_1875` `sub-neg_binary64_1776`

Counts

4 → 82

Calls

4 calls:

11.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
9.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series1.1s (10%)

Counts

4 → 12

Calls

4 calls:

496.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x)))
246.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
198.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
192.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4997	2284
1	4997	2284

prune161.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	100	8	108

Merged error: 0.1b

Counts

108 → 8

Compiler

Compiled 4018 to 1252 computations (68.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(pow.f64 (sin.f64 x) 2)

rewrite54.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_1805`
26×	`*-un-lft-identity_binary64_1783`
24×	`add-cube-cbrt_binary64_1818`
19×	`times-frac_binary64_1789`
16×	`associate-l_binary64_1724`
14×	`add-exp-log_binary64_1821`
13×	`add-cbrt-cube_binary64_1819`
9×	`pow1_binary64_1844`
7×	`associate-r_binary64_1723`
4×	`tan-quot_binary64_1942` `add-log-exp_binary64_1822`
3×	`associate-r/_binary64_1725` `associate-/l_binary64_1728` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-unpow_binary64_1860` `unpow-prod-down_binary64_1862` `associate-/r*_binary64_1727` `frac-times_binary64_1793` `unswap-sqr_binary64_1751`
2×	`flip-+_binary64_1757` `div-inv_binary64_1780` `associate-l/_binary64_1726` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `div-exp_binary64_1834` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854`
1×	`quot-tan_binary64_1943` `sqr-pow_binary64_1755` `distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `unpow2_binary64_1848` `frac-2neg_binary64_1794` `distribute-rgt-in_binary64_1733` `pow-pow_binary64_1855` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

4 → 106

Calls

4 calls:

26.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
4.0ms	(pow.f64 (sin.f64 x) 2)

series617.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

349.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)))
193.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
50.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
25.0ms	(pow.f64 (sin.f64 x) 2)

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4940	2185
1	4940	2185

prune167.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	106	12	118
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Merged error: 0.0b

Counts

126 → 14

Compiler

Compiled 3928 to 1402 computations (64.3% saved)

regimes660.0ms (5.8%)

Compiler: Compiled 8767 to 4901 computations (44.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	39
1	47	39

end0.0ms (0%)

sample4.6s (40.1%)

Algorithm

1×

intervals

Results

1.1s	3479×	body	1024	valid
845.0ms	1244×	body	2048	valid
229.0ms	1395×	body	512	valid
61.0ms	1322×	body	128	valid
57.0ms	555×	body	256	valid
9.0ms	5×	body	4096	valid

Compiler

Compiled 2948 to 1651 computations (44% saved)

Details

analyze766.0ms (6.8%)

sample77.0ms (0.7%)

simplify165.0ms (1.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series340.0ms (3%)

simplify133.0ms (1.2%)

prune39.0ms (0.3%)

localize12.0ms (0.1%)

rewrite46.0ms (0.4%)

series1.9s (16.8%)

simplify84.0ms (0.7%)

prune141.0ms (1.2%)

localize19.0ms (0.2%)

rewrite46.0ms (0.4%)

series1.1s (10%)

simplify67.0ms (0.6%)

prune161.0ms (1.4%)

localize24.0ms (0.2%)

rewrite54.0ms (0.5%)

series617.0ms (5.4%)

simplify107.0ms (0.9%)

prune167.0ms (1.5%)

regimes660.0ms (5.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.6s (40.1%)

Profiling