Details

analyze776.0ms (7.5%)

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)

sample87.0ms (0.8%)

Algorithm

1×

intervals

Results

41.0ms	119×	body	1024	valid
29.0ms	45×	body	2048	valid
6.0ms	32×	body	512	valid
2.0ms	45×	body	128	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify172.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune3.0ms (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: 40.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0b	(tan.f64 (+.f64 x eps))

rewrite15.0ms (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))
5.0ms	(tan.f64 (+.f64 x eps))

series348.0ms (3.4%)

Counts

2 → 6

Calls

2 calls:

219.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
128.0ms	(tan.f64 (+.f64 x eps))

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4932	529
1	4932	529

prune34.0ms (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: 16.8b

Counts

31 → 8

Compiler

Compiled 543 to 180 computations (66.9% saved)

localize14.0ms (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))))
0.3b	(*.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))

rewrite42.0ms (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))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.9s (18.1%)

Counts

4 → 12

Calls

4 calls:

959.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
535.0ms	(/.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))
187.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5065	2549

prune139.0ms (1.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 16.7b

Counts

105 → 16

Compiler

Compiled 2877 to 986 computations (65.7% 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 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))
2.6b	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))

rewrite49.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1783`
22×	`tan-quot_binary64_1918`
19×	`*-un-lft-identity_binary64_1762`
18×	`associate-r_binary64_1704`
15×	`add-exp-log_binary64_1797`
14×	`add-cube-cbrt_binary64_1794`
11×	`times-frac_binary64_1768` `add-cbrt-cube_binary64_1795`
8×	`add-log-exp_binary64_1798` `frac-sub_binary64_1771` `pow1_binary64_1820`
7×	`frac-times_binary64_1772` `associate-l/_binary64_1707` `associate-l*_binary64_1705`
5×	`prod-exp_binary64_1808` `flip3-+_binary64_1765` `flip-+_binary64_1736` `frac-add_binary64_1770`
4×	`unswap-sqr_binary64_1730`
3×	`associate-*r/_binary64_1706` `cbrt-unprod_binary64_1792`
2×	`associate-/r/_binary64_1710` `flip3--_binary64_1766` `pow-prod-down_binary64_1830` `div-exp_binary64_1810` `flip--_binary64_1737` `un-div-inv_binary64_1760` `*-commutative_binary64_1695` `distribute-lft-out_binary64_1715`
1×	`diff-log_binary64_1851` `div-inv_binary64_1759` `+-commutative_binary64_1694` `cbrt-undiv_binary64_1793` `sub-neg_binary64_1755` `1-exp_binary64_1803` `rec-exp_binary64_1809` `sum-log_binary64_1850`

Counts

4 → 98

Calls

4 calls:

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

series1.9s (18.6%)

Counts

4 → 12

Calls

4 calls:

967.0ms	(-.f64 (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))))) (tan.f64 x))
554.0ms	(.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 1 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
210.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
194.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify87.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5119	2957

prune149.0ms (1.4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	109	17	126

Merged error: 16.7b

Counts

126 → 17

Compiler

Compiled 3539 to 1290 computations (63.5% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 x) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 eps) (cos.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.6b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (cos.f64 eps) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
13×	`add-sqr-sqrt_binary64_1783`
12×	`associate-*r/_binary64_1706`
9×	`add-log-exp_binary64_1798` `-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794` `associate-l*_binary64_1705`
8×	`pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `associate-*l/_binary64_1707` `cbrt-unprod_binary64_1792` `tan-quot_binary64_1918`
7×	`associate-r_binary64_1704`
5×	`flip3--_binary64_1766` `flip--_binary64_1737`
4×	`frac-times_binary64_1772` `frac-sub_binary64_1771`
3×	`cos-mult_binary64_1913` `*-commutative_binary64_1695`
2×	`diff-log_binary64_1851` `flip3-+_binary64_1765` `flip-+_binary64_1736` `unswap-sqr_binary64_1730`
1×	`sub-neg_binary64_1755` `associate--l+_binary64_1701` `sum-log_binary64_1850`

Counts

4 → 85

Calls

4 calls:

13.0ms	(.f64 (cos.f64 x) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 eps) (cos.f64 x))))
12.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (cos.f64 eps) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series1.1s (10.5%)

Counts

4 → 12

Calls

4 calls:

367.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (cos.f64 eps) (.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))))
336.0ms	(.f64 (cos.f64 x) (.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 (cos.f64 eps) (cos.f64 x))))
200.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
182.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify75.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4988	2731
1	4988	2731

prune171.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	103	11	114

Merged error: 0.2b

Counts

114 → 11

Compiler

Compiled 5205 to 1480 computations (71.6% saved)

regimes78.0ms (0.8%)

Compiler: Compiled 940 to 510 computations (45.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	54
1	55	54

end0.0ms (0%)

sample2.9s (28.4%)

Algorithm

1×

intervals

Results

1.1s	3558×	body	1024	valid
888.0ms	1205×	body	2048	valid
236.0ms	1353×	body	512	valid
64.0ms	1347×	body	128	valid
56.0ms	536×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 519 to 289 computations (44.3% saved)

Details

analyze776.0ms (7.5%)

sample87.0ms (0.8%)

simplify172.0ms (1.7%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series348.0ms (3.4%)

simplify88.0ms (0.9%)

prune34.0ms (0.3%)

localize14.0ms (0.1%)

rewrite42.0ms (0.4%)

series1.9s (18.1%)

simplify77.0ms (0.7%)

prune139.0ms (1.3%)

localize12.0ms (0.1%)

rewrite49.0ms (0.5%)

series1.9s (18.6%)

simplify87.0ms (0.8%)

prune149.0ms (1.4%)

localize29.0ms (0.3%)

rewrite53.0ms (0.5%)

series1.1s (10.5%)

simplify75.0ms (0.7%)

prune171.0ms (1.7%)

regimes78.0ms (0.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.9s (28.4%)

Profiling