Details

analyze766.0ms (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)

sample64.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	95×	body	1024	valid
18.0ms	44×	body	2048	valid
6.0ms	45×	body	512	valid
2.0ms	26×	body	256	valid
2.0ms	46×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify99.0ms (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: 35.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.4b	(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))

series180.0ms (2%)

Counts

2 → 6

Calls

2 calls:

111.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
69.0ms	(tan.f64 (+.f64 x eps))

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4834	544
1	4834	544

prune38.0ms (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: 17.4b

Counts

34 → 8

Compiler

Compiled 567 to 180 computations (68.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.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))
3.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite42.0ms (0.5%)

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:

13.0ms	(-.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 (10.9%)

Counts

4 → 12

Calls

4 calls:

515.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
285.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
104.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
96.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5619	2567

prune132.0ms (1.4%)

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: 17.3b

Counts

108 → 16

Compiler

Compiled 2947 to 1001 computations (66% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
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))
3.7b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_1805`
26×	`*-un-lft-identity_binary64_1783`
23×	`add-cube-cbrt_binary64_1818`
20×	`tan-quot_binary64_1942` `times-frac_binary64_1789`
19×	`add-exp-log_binary64_1821`
18×	`associate-r_binary64_1723`
13×	`add-cbrt-cube_binary64_1819`
9×	`pow1_binary64_1844`
8×	`frac-sub_binary64_1792`
7×	`associate-l_binary64_1724` `associate-*l/_binary64_1726` `frac-times_binary64_1793`
6×	`add-log-exp_binary64_1822`
5×	`prod-exp_binary64_1832`
4×	`associate-/r/_binary64_1729` `frac-add_binary64_1791` `flip-+_binary64_1757` `div-exp_binary64_1834` `flip3-+_binary64_1786` `unswap-sqr_binary64_1751`
3×	`flip3--_binary64_1787` `associate-r/_binary64_1725` `associate-/l_binary64_1728` `cbrt-unprod_binary64_1816` `cancel-sign-sub-inv_binary64_1749` `associate-/r*_binary64_1727` `flip--_binary64_1758`
2×	`un-div-inv_binary64_1781` `1-exp_binary64_1827` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `pow-prod-down_binary64_1854` `rec-exp_binary64_1833`
1×	`inv-pow_binary64_1868` `distribute-lft-out_binary64_1734` `pow-flip_binary64_1857` `diff-log_binary64_1875` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `sub-neg_binary64_1776`

Counts

4 → 121

Calls

4 calls:

15.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
14.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

series1.1s (11.7%)

Counts

4 → 12

Calls

4 calls:

516.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
279.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
172.0ms	(/.f64 1 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
103.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4975	3463
1	4975	3463

prune159.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	128	5	133
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	134	15	149

Merged error: 17.3b

Counts

149 → 15

Compiler

Compiled 4033 to 1503 computations (62.7% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 (cos.f64 x) (-.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(.f64 (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x)))
3.7b	(-.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (cos.f64 eps)))

rewrite56.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
13×	`cbrt-unprod_binary64_1816` `prod-exp_binary64_1832`
11×	`pow1_binary64_1844`
9×	`add-sqr-sqrt_binary64_1805`
7×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
6×	`associate-r/_binary64_1725` `associate-l*_binary64_1724` `cbrt-undiv_binary64_1817` `div-exp_binary64_1834` `add-log-exp_binary64_1822`
4×	`tan-quot_binary64_1942` `pow-prod-down_binary64_1854` `associate-r_binary64_1723`
3×	`associate-/l/_binary64_1730`
2×	`flip3--_binary64_1787` `cos-mult_binary64_1937` `sin-cos-mult_binary64_1939` `frac-sub_binary64_1792` `*-commutative_binary64_1714` `flip--_binary64_1758`
1×	`associate-/r/_binary64_1729` `associate-/l_binary64_1728` `div-inv_binary64_1780` `cancel-sign-sub-inv_binary64_1749` `associate-/r_binary64_1727` `associate-*l/_binary64_1726` `diff-log_binary64_1875` `times-frac_binary64_1789` `frac-2neg_binary64_1794` `frac-times_binary64_1793` `clear-num_binary64_1782` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`

Counts

4 → 82

Calls

4 calls:

21.0ms	(/.f64 (.f64 (cos.f64 x) (-.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))))
13.0ms	(-.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (cos.f64 eps)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(.f64 (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x)))

series1.3s (13.9%)

Counts

4 → 12

Calls

4 calls:

613.0ms	(/.f64 (.f64 (cos.f64 x) (-.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (cos.f64 eps)))) (.f64 (cos.f64 x) (*.f64 (cos.f64 eps) (cos.f64 x))))
504.0ms	(-.f64 (/.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (sin.f64 x) (cos.f64 eps)))
103.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
53.0ms	(.f64 (cos.f64 x) (.f64 (cos.f64 eps) (cos.f64 x)))

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4974	3227
1	4974	3227

prune126.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 15.1b

Counts

109 → 8

Compiler

Compiled 4056 to 934 computations (77% saved)

regimes365.0ms (4%)

Compiler: Compiled 5248 to 2760 computations (47.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	79
1	59	79

end0.0ms (0%)

sample3.3s (36.3%)

Algorithm

1×

intervals

Results

803.0ms	3448×	body	1024	valid
602.0ms	1267×	body	2048	valid
190.0ms	1365×	body	512	valid
62.0ms	1285×	body	128	valid
60.0ms	631×	body	256	valid
3.0ms	4×	body	4096	valid

Compiler

Compiled 1785 to 936 computations (47.6% saved)

Details

analyze766.0ms (8.4%)

sample64.0ms (0.7%)

simplify99.0ms (1.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite13.0ms (0.1%)

series180.0ms (2%)

simplify92.0ms (1%)

prune38.0ms (0.4%)

localize11.0ms (0.1%)

rewrite42.0ms (0.5%)

series1.0s (10.9%)

simplify83.0ms (0.9%)

prune132.0ms (1.4%)

localize11.0ms (0.1%)

rewrite51.0ms (0.6%)

series1.1s (11.7%)

simplify91.0ms (1%)

prune159.0ms (1.7%)

localize24.0ms (0.3%)

rewrite56.0ms (0.6%)

series1.3s (13.9%)

simplify74.0ms (0.8%)

prune126.0ms (1.4%)

regimes365.0ms (4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.3s (36.3%)

Profiling