Details

analyze784.0ms (6.7%)

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)

sample82.0ms (0.7%)

Algorithm

1×

intervals

Results

35.0ms	106×	body	1024	valid
27.0ms	42×	body	2048	valid
8.0ms	50×	body	512	valid
2.0ms	39×	body	128	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify164.0ms (1.4%)

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: 39.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.8b	(tan.f64 (+.f64 x eps))

rewrite17.0ms (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:

10.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series344.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

219.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
125.0ms	(tan.f64 (+.f64 x eps))

simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4932	529
1	4932	529

prune39.0ms (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: 14.8b

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))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite44.0ms (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:

14.0ms	(-.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 (16.5%)

Counts

4 → 12

Calls

4 calls:

988.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
559.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
202.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
187.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5065	2549

prune137.0ms (1.2%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	83	14	97
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	87	18	105

Merged error: 14.6b

Counts

105 → 18

Compiler

Compiled 2881 to 989 computations (65.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.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)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
4.5b	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite91.0ms (0.8%)

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:

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))
13.0ms	(/.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))

series2.4s (20.3%)

Counts

4 → 12

Calls

4 calls:

1.0s	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
615.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (+.f64 (tan.f64 x) (tan.f64 eps)))
567.0ms	(/.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))

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5404	6503

prune238.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	192	15	207

Merged error: 14.6b

Counts

207 → 15

Compiler

Compiled 5898 to 2156 computations (63.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (tan.f64 eps))
0.6b	(cbrt.f64 (tan.f64 eps))
0.6b	(cbrt.f64 (tan.f64 eps))
2.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (*.f64 (cbrt.f64 (tan.f64 eps)) (cbrt.f64 (tan.f64 eps)))) (cbrt.f64 (tan.f64 eps))))) (tan.f64 x))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1783`
9×	`cbrt-prod_binary64_1790` `*-un-lft-identity_binary64_1762`
7×	`add-cube-cbrt_binary64_1794`
6×	`add-log-exp_binary64_1798`
4×	`tan-quot_binary64_1918` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
3×	`pow1/3_binary64_1841` `cbrt-div_binary64_1791`
2×	`difference-of-squares_binary64_1731`
1×	`flip3--_binary64_1766` `diff-log_binary64_1851` `times-frac_binary64_1768` `distribute-lft-out--_binary64_1716` `frac-sub_binary64_1771` `flip--_binary64_1737` `sub-neg_binary64_1755`

Counts

4 → 51

Calls

4 calls:

16.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (*.f64 (cbrt.f64 (tan.f64 eps)) (cbrt.f64 (tan.f64 eps)))) (cbrt.f64 (tan.f64 eps))))) (tan.f64 x))
2.0ms	(cbrt.f64 (tan.f64 eps))
2.0ms	(cbrt.f64 (tan.f64 eps))
2.0ms	(cbrt.f64 (tan.f64 eps))

series1.6s (14%)

Counts

4 → 12

Calls

4 calls:

995.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (*.f64 (cbrt.f64 (tan.f64 eps)) (cbrt.f64 (tan.f64 eps)))) (cbrt.f64 (tan.f64 eps))))) (tan.f64 x))
216.0ms	(cbrt.f64 (tan.f64 eps))
215.0ms	(cbrt.f64 (tan.f64 eps))
214.0ms	(cbrt.f64 (tan.f64 eps))

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4927	1221
1	4927	1221

prune68.0ms (0.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	63	15	78

Merged error: 14.6b

Counts

78 → 15

Compiler

Compiled 1884 to 524 computations (72.2% saved)

regimes105.0ms (0.9%)

Compiler: Compiled 762 to 442 computations (42% saved)

bsearch96.0ms (0.8%)

Steps

Iters	Range		Point
10	8.46549016947534e-20	7.754114732921885e-05	2.8352874239115425e-18
10	-1.764404644112276e-24	-6.239443958554844e-38	-8.82532240330736e-33

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	315	76
1	315	76

end0.0ms (0%)

sample3.1s (26.5%)

Algorithm

1×

intervals

Results

1.1s	3569×	body	1024	valid
854.0ms	1188×	body	2048	valid
231.0ms	1369×	body	512	valid
63.0ms	1310×	body	128	valid
63.0ms	562×	body	256	valid
3.0ms	2×	body	4096	valid

Compiler

Compiled 445 to 262 computations (41.1% saved)

Details

analyze784.0ms (6.7%)

sample82.0ms (0.7%)

simplify164.0ms (1.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite17.0ms (0.1%)

series344.0ms (2.9%)

simplify82.0ms (0.7%)

prune39.0ms (0.3%)

localize11.0ms (0.1%)

rewrite44.0ms (0.4%)

series1.9s (16.5%)

simplify73.0ms (0.6%)

prune137.0ms (1.2%)

localize13.0ms (0.1%)

rewrite91.0ms (0.8%)

series2.4s (20.3%)

simplify118.0ms (1%)

prune238.0ms (2%)

localize15.0ms (0.1%)

rewrite28.0ms (0.2%)

series1.6s (14%)

simplify70.0ms (0.6%)

prune68.0ms (0.6%)

regimes105.0ms (0.9%)

bsearch96.0ms (0.8%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.1s (26.5%)

Profiling