Details

analyze757.0ms (4.6%)

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 (0.5%)

Algorithm

1×

intervals

Results

35.0ms	114×	body	1024	valid
26.0ms	40×	body	2048	valid
7.0ms	40×	body	512	valid
2.0ms	48×	body	128	valid
2.0ms	1×	body	4096	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify172.0ms (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: 37.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

1.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.6b	(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))
5.0ms	(tan.f64 (+.f64 x eps))

series331.0ms (2%)

Counts

2 → 6

Calls

2 calls:

213.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
118.0ms	(tan.f64 (+.f64 x eps))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4932	529
1	4932	529

prune33.0ms (0.2%)

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: 15.5b

Counts

31 → 8

Compiler

Compiled 543 to 180 computations (66.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (*.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))
3.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 83

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))
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))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (11.9%)

Counts

4 → 12

Calls

4 calls:

990.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
534.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
235.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
199.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5027	2571

prune146.0ms (0.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	76	19	95
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	82	21	103

Merged error: 15.3b

Counts

103 → 21

Compiler

Compiled 3036 to 1092 computations (64% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.0b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1783`
11×	`*-un-lft-identity_binary64_1762`
9×	`add-log-exp_binary64_1798` `add-cube-cbrt_binary64_1794`
7×	`pow1_binary64_1820`
6×	`exp-prod_binary64_1811` `add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797`
5×	`tan-quot_binary64_1918`
4×	`log-prod_binary64_1845` `log-pow_binary64_1848`
3×	`sub-neg_binary64_1755` `associate-l_binary64_1705` `associate-r_binary64_1704`
2×	`diff-log_binary64_1851` `rem-exp-log_binary64_1799` `difference-of-squares_binary64_1731` `exp-diff_binary64_1807` `exp-sum_binary64_1805`
1×	`flip3--_binary64_1766` `frac-times_binary64_1772` `times-frac_binary64_1768` `pow-prod-down_binary64_1830` `prod-exp_binary64_1808` `unswap-sqr_binary64_1730` `associate-l/_binary64_1707` `distribute-lft-out--_binary64_1716` `associate-r/_binary64_1706` `frac-sub_binary64_1771` `cbrt-unprod_binary64_1792` `flip--_binary64_1737` `*-commutative_binary64_1695` `log-div_binary64_1846` `rem-log-exp_binary64_1800`

Counts

4 → 67

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
4.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))

series1.9s (11.7%)

Counts

4 → 12

Calls

4 calls:

1.1s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
360.0ms	(log.f64 (exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
274.0ms	(exp.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
183.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4925	1655
1	4925	1655

prune113.0ms (0.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	3	17	20
Picked	1	0	1
Done	0	0	0
Total	80	20	100

Merged error: 15.3b

Counts

100 → 20

Compiler

Compiled 2536 to 1007 computations (60.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
3.0b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`tan-quot_binary64_1918`
13×	`add-sqr-sqrt_binary64_1783`
11×	`add-cbrt-cube_binary64_1795` `add-exp-log_binary64_1797` `pow1_binary64_1820`
9×	`*-un-lft-identity_binary64_1762` `add-cube-cbrt_binary64_1794`
6×	`add-log-exp_binary64_1798` `associate-l_binary64_1705` `associate-r_binary64_1704`
5×	`frac-times_binary64_1772` `associate-*r/_binary64_1706` `frac-sub_binary64_1771`
4×	`associate-*l/_binary64_1707`
3×	`pow-prod-down_binary64_1830` `cube-div_binary64_1788` `prod-exp_binary64_1808` `cbrt-unprod_binary64_1792` `pow-unpow_binary64_1836`
2×	`rem-cube-cbrt_binary64_1784` `flip3-+_binary64_1765` `flip-+_binary64_1736` `unswap-sqr_binary64_1730` `pow-exp_binary64_1827` `pow-pow_binary64_1831` `*-commutative_binary64_1695` `associate--l+_binary64_1701`
1×	`cube-prod_binary64_1787` `flip3--_binary64_1766` `cube-mult_binary64_1789` `diff-log_binary64_1851` `sqr-pow_binary64_1734` `unpow3_binary64_1825` `distribute-rgt-in_binary64_1714` `flip--_binary64_1737` `sub-neg_binary64_1755` `distribute-lft-in_binary64_1713` `pow-to-exp_binary64_1828` `unpow-prod-down_binary64_1838`

Counts

4 → 85

Calls

4 calls:

27.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
7.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series7.1s (42.8%)

Counts

4 → 12

Calls

4 calls:

6.4s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
349.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
184.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
169.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5050	3220

prune184.0ms (1.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	4	15	19
Picked	1	0	1
Done	0	0	0
Total	97	20	117

Merged error: 15.2b

Counts

117 → 20

Compiler

Compiled 5150 to 1880 computations (63.5% saved)

regimes144.0ms (0.9%)

Compiler: Compiled 1662 to 896 computations (46.1% saved)

bsearch68.0ms (0.4%)

Steps

Iters	Range		Point
6	3.0876816840121187e-115	1.9489484085498834e-114	1.914951132073428e-114
6	-2.70031633841226e-53	-2.8742722130247817e-54	-2.5441009276949707e-53

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	583	149
1	583	149

end0.0ms (0%)

sample3.0s (18.2%)

Algorithm

1×

intervals

Results

1.0s	3537×	body	1024	valid
839.0ms	1220×	body	2048	valid
223.0ms	1400×	body	512	valid
61.0ms	1244×	body	128	valid
59.0ms	595×	body	256	valid
7.0ms	4×	body	4096	valid

Compiler

Compiled 940 to 506 computations (46.2% saved)

Details

analyze757.0ms (4.6%)

sample82.0ms (0.5%)

simplify172.0ms (1%)

prune2.0ms (0%)

localize8.0ms (0%)

rewrite14.0ms (0.1%)

series331.0ms (2%)

simplify83.0ms (0.5%)

prune33.0ms (0.2%)

localize13.0ms (0.1%)

rewrite39.0ms (0.2%)

series2.0s (11.9%)

simplify74.0ms (0.4%)

prune146.0ms (0.9%)

localize15.0ms (0.1%)

rewrite43.0ms (0.3%)

series1.9s (11.7%)

simplify48.0ms (0.3%)

prune113.0ms (0.7%)

localize20.0ms (0.1%)

rewrite58.0ms (0.3%)

series7.1s (42.8%)

simplify79.0ms (0.5%)

prune184.0ms (1.1%)

regimes144.0ms (0.9%)

bsearch68.0ms (0.4%)

simplify23.0ms (0.1%)

end0.0ms (0%)

sample3.0s (18.2%)

Profiling