Details

analyze779.0ms (6.2%)

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)

sample76.0ms (0.6%)

Algorithm

1×

intervals

Results

32.0ms	107×	body	1024	valid
23.0ms	35×	body	2048	valid
9.0ms	55×	body	512	valid
2.0ms	48×	body	128	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify169.0ms (1.3%)

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: 35.4b

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))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64_1798` `add-sqr-sqrt_binary64_1783` `*-un-lft-identity_binary64_1762` `tan-quot_binary64_1918`
2×	`frac-sub_binary64_1771` `add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `tan-sum_binary64_1894` `add-exp-log_binary64_1797` `pow1_binary64_1820`
1×	`flip3--_binary64_1766` `diff-log_binary64_1851` `distribute-lft-out--_binary64_1716` `difference-of-squares_binary64_1731` `flip--_binary64_1737` `sub-neg_binary64_1755`

Counts

2 → 24

Calls

2 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series334.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

215.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
119.0ms	(tan.f64 (+.f64 x eps))

simplify86.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4932	529
1	4932	529

prune35.0ms (0.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 15.6b

Counts

31 → 8

Compiler

Compiled 543 to 180 computations (66.9% 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))

rewrite48.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_1762`
22×	`add-sqr-sqrt_binary64_1783`
15×	`add-cube-cbrt_binary64_1794`
13×	`times-frac_binary64_1768`
9×	`tan-quot_binary64_1918`
8×	`add-log-exp_binary64_1798` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
6×	`pow1_binary64_1820`
5×	`distribute-lft-out_binary64_1715`
4×	`associate-/l*_binary64_1709`
3×	`associate-/l/_binary64_1711` `associate-/r_binary64_1708` `associate-l_binary64_1705` `associate-r*_binary64_1704`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `flip3-+_binary64_1765` `flip-+_binary64_1736` `difference-of-squares_binary64_1731` `flip--_binary64_1737` `frac-add_binary64_1770`
1×	`frac-2neg_binary64_1773` `diff-log_binary64_1851` `frac-times_binary64_1772` `pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `clear-num_binary64_1761` `div-inv_binary64_1759` `unswap-sqr_binary64_1730` `associate-l/_binary64_1707` `+-commutative_binary64_1694` `cbrt-undiv_binary64_1793` `distribute-lft-out--_binary64_1716` `div-exp_binary64_1810` `associate-r/_binary64_1706` `frac-sub_binary64_1771` `cbrt-unprod_binary64_1792` `sub-neg_binary64_1755` `*-commutative_binary64_1695` `sum-log_binary64_1850`

Counts

4 → 85

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))
12.0ms	(/.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 (14.6%)

Counts

4 → 12

Calls

4 calls:

961.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
525.0ms	(/.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))
179.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5065	2549

prune134.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	86	11	97
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	90	15	105

Merged error: 15.5b

Counts

105 → 15

Compiler

Compiled 2873 to 972 computations (66.2% 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))

rewrite92.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`times-frac_binary64_1768`
104×	`*-un-lft-identity_binary64_1762`
83×	`add-sqr-sqrt_binary64_1783`
67×	`add-cube-cbrt_binary64_1794`
23×	`associate-/r*_binary64_1708`
19×	`add-exp-log_binary64_1797`
16×	`associate-/r/_binary64_1710` `distribute-lft-out_binary64_1715`
15×	`tan-quot_binary64_1918`
13×	`add-cbrt-cube_binary64_1795`
8×	`div-exp_binary64_1810`
7×	`div-inv_binary64_1759` `pow1_binary64_1820`
6×	`add-log-exp_binary64_1798` `associate-/l*_binary64_1709`
5×	`flip3-+_binary64_1765` `flip-+_binary64_1736` `difference-of-squares_binary64_1731` `frac-add_binary64_1770`
4×	`cbrt-undiv_binary64_1793`
3×	`associate-l_binary64_1705` `associate-r_binary64_1704`
2×	`flip3--_binary64_1766` `frac-2neg_binary64_1773` `associate-/l/_binary64_1711` `clear-num_binary64_1761` `distribute-lft-out--_binary64_1716` `flip--_binary64_1737` `1-exp_binary64_1803` `rec-exp_binary64_1809`
1×	`diff-log_binary64_1851` `frac-times_binary64_1772` `div-sub_binary64_1767` `inv-pow_binary64_1844` `pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `associate-l/_binary64_1707` `pow-flip_binary64_1833` `associate-r/_binary64_1706` `frac-sub_binary64_1771` `cbrt-unprod_binary64_1792` `sub-neg_binary64_1755` `*-commutative_binary64_1695`

Counts

4 → 177

Calls

4 calls:

39.0ms	(-.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))))
9.0ms	(/.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 (18.5%)

Counts

4 → 12

Calls

4 calls:

982.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
598.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
558.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps))))
197.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5404	6503

prune241.0ms (1.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	190	14	204

Merged error: 15.5b

Counts

204 → 14

Compiler

Compiled 5935 to 2167 computations (63.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
8.5b	(-.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)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`associate-*l/_binary64_1707`
16×	`add-sqr-sqrt_binary64_1783`
14×	`tan-quot_binary64_1918`
12×	`*-un-lft-identity_binary64_1762`
10×	`add-cube-cbrt_binary64_1794` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820` `associate-l_binary64_1705`
9×	`associate-r_binary64_1704`
6×	`add-log-exp_binary64_1798` `frac-sub_binary64_1771`
4×	`flip3--_binary64_1766` `flip--_binary64_1737`
3×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `flip3-+_binary64_1765` `flip-+_binary64_1736` `unswap-sqr_binary64_1730` `cbrt-unprod_binary64_1792` `frac-add_binary64_1770` `*-commutative_binary64_1695`
2×	`frac-times_binary64_1772` `associate-*r/_binary64_1706`
1×	`diff-log_binary64_1851` `sub-neg_binary64_1755` `distribute-lft-out_binary64_1715`

Counts

4 → 81

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 (8.5%)

Counts

4 → 12

Calls

4 calls:

464.0ms	(-.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)))
224.0ms	(*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x))
196.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
194.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4982	2268
1	4982	2268

prune144.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	99	8	107

Merged error: 0.1b

Counts

107 → 8

Compiler

Compiled 3649 to 1074 computations (70.6% saved)

regimes550.0ms (4.3%)

Compiler: Compiled 7920 to 4120 computations (48% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	44
1	50	44

end0.0ms (0%)

sample4.3s (34.1%)

Algorithm

1×

intervals

Results

1.1s	3506×	body	1024	valid
925.0ms	1228×	body	2048	valid
221.0ms	1339×	body	512	valid
64.0ms	1353×	body	128	valid
59.0ms	572×	body	256	valid
4.0ms	2×	body	4096	valid

Compiler

Compiled 2669 to 1394 computations (47.8% saved)

Details

analyze779.0ms (6.2%)

sample76.0ms (0.6%)

simplify169.0ms (1.3%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.1%)

series334.0ms (2.6%)

simplify86.0ms (0.7%)

prune35.0ms (0.3%)

localize11.0ms (0.1%)

rewrite48.0ms (0.4%)

series1.9s (14.6%)

simplify79.0ms (0.6%)

prune134.0ms (1.1%)

localize12.0ms (0.1%)

rewrite92.0ms (0.7%)

series2.3s (18.5%)

simplify118.0ms (0.9%)

prune241.0ms (1.9%)

localize18.0ms (0.1%)

rewrite43.0ms (0.3%)

series1.1s (8.5%)

simplify76.0ms (0.6%)

prune144.0ms (1.1%)

regimes550.0ms (4.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.3s (34.1%)

Profiling