Details

analyze942.0ms (5.8%)

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)

sample77.0ms (0.5%)

Algorithm

1×

intervals

Results

33.0ms	111×	body	1024	valid
24.0ms	37×	body	2048	valid
8.0ms	47×	body	512	valid
2.0ms	20×	body	256	valid
2.0ms	41×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify163.0ms (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: 38.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.8b	(tan.f64 (+.f64 x eps))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`tan-quot_binary64_1581` `add-sqr-sqrt_binary64_1446` `add-log-exp_binary64_1461` `*-un-lft-identity_binary64_1425`
2×	`add-cube-cbrt_binary64_1457` `tan-sum_binary64_1557` `add-cbrt-cube_binary64_1458` `frac-sub_binary64_1434` `pow1_binary64_1483` `add-exp-log_binary64_1460`
1×	`flip--_binary64_1400` `diff-log_binary64_1514` `distribute-lft-out--_binary64_1379` `sub-neg_binary64_1418` `difference-of-squares_binary64_1394` `flip3--_binary64_1429`

Counts

2 → 24

Calls

2 calls:

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

series318.0ms (2%)

Counts

2 → 6

Calls

2 calls:

207.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
111.0ms	(tan.f64 (+.f64 x eps))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4932	529
1	4932	529

prune34.0ms (0.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.7b

Counts

31 → 7

Compiler

Compiled 529 to 172 computations (67.5% saved)

localize11.0ms (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))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.2b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_1425`
22×	`add-sqr-sqrt_binary64_1446`
15×	`add-cube-cbrt_binary64_1457`
13×	`times-frac_binary64_1431`
9×	`tan-quot_binary64_1581`
8×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460` `add-log-exp_binary64_1461`
6×	`pow1_binary64_1483`
5×	`distribute-lft-out_binary64_1378`
4×	`associate-/l*_binary64_1372`
3×	`associate-/r_binary64_1371` `associate-l_binary64_1368` `associate-r*_binary64_1367` `associate-/l/_binary64_1374`
2×	`flip--_binary64_1400` `flip3-+_binary64_1428` `associate-/r/_binary64_1373` `difference-of-squares_binary64_1394` `flip-+_binary64_1399` `frac-add_binary64_1433` `flip3--_binary64_1429`
1×	`diff-log_binary64_1514` `frac-2neg_binary64_1436` `distribute-lft-out--_binary64_1379` `unswap-sqr_binary64_1393` `prod-exp_binary64_1471` `sub-neg_binary64_1418` `cbrt-unprod_binary64_1455` `clear-num_binary64_1424` `associate-r/_binary64_1369` `div-inv_binary64_1422` `sum-log_binary64_1513` `div-exp_binary64_1473` `frac-sub_binary64_1434` `+-commutative_binary64_1357` `associate-l/_binary64_1370` `cbrt-undiv_binary64_1456` `*-commutative_binary64_1358` `frac-times_binary64_1435` `pow-prod-down_binary64_1493`

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))
12.0ms	(/.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))

series1.8s (11.3%)

Counts

4 → 12

Calls

4 calls:

936.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
519.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
192.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
183.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5065	2549

prune138.0ms (0.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	83	14	97
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	88	16	104

Merged error: 14.5b

Counts

104 → 16

Compiler

Compiled 2916 to 990 computations (66% saved)

localize17.0ms (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	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
2.2b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.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))

rewrite52.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`pow1_binary64_1483`
45×	`tan-quot_binary64_1581`
21×	`frac-times_binary64_1435`
20×	`add-cbrt-cube_binary64_1458` `add-exp-log_binary64_1460`
19×	`pow-prod-down_binary64_1493`
15×	`associate-*r/_binary64_1369`
14×	`associate-*l/_binary64_1370`
12×	`add-sqr-sqrt_binary64_1446`
10×	`prod-exp_binary64_1471` `cbrt-unprod_binary64_1455`
8×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
7×	`associate-l_binary64_1368` `associate-r_binary64_1367`
6×	`add-log-exp_binary64_1461`
5×	`frac-sub_binary64_1434`
4×	`pow-sqr_binary64_1398` `pow-prod-up_binary64_1492`
3×	`*-commutative_binary64_1358`
2×	`unswap-sqr_binary64_1393` `pow-plus_binary64_1485` `flip3-+_binary64_1428` `associate--l+_binary64_1364` `flip-+_binary64_1399`
1×	`distribute-lft-in_binary64_1376` `flip--_binary64_1400` `diff-log_binary64_1514` `sub-neg_binary64_1418` `pow2_binary64_1503` `distribute-rgt-in_binary64_1377` `swap-sqr_binary64_1392` `flip3--_binary64_1429`

Counts

4 → 109

Calls

4 calls:

15.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.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))
11.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.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))

series4.3s (26.3%)

Counts

4 → 12

Calls

4 calls:

3.6s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.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))
288.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
191.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
184.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify55.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5092	3141

prune180.0ms (1.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	115	6	121
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	120	17	137

Merged error: 14.4b

Counts

137 → 17

Compiler

Compiled 5237 to 1772 computations (66.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.5b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 6)
2.2b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 6)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
13.0b	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 6))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1446`
9×	`tan-quot_binary64_1581` `pow1_binary64_1483` `add-exp-log_binary64_1460`
8×	`add-cube-cbrt_binary64_1457` `*-un-lft-identity_binary64_1425`
6×	`add-cbrt-cube_binary64_1458` `add-log-exp_binary64_1461`
5×	`cbrt-prod_binary64_1453` `frac-sub_binary64_1434`
3×	`pow-unpow_binary64_1499` `associate-l_binary64_1368` `associate-r/_binary64_1369` `associate-r*_binary64_1367` `frac-times_binary64_1435`
2×	`pow-pow_binary64_1494` `prod-exp_binary64_1471` `flip3-+_binary64_1428` `unpow-prod-down_binary64_1501` `pow-exp_binary64_1490` `associate--l+_binary64_1364` `flip-+_binary64_1399` `associate-*l/_binary64_1370` `sqr-pow_binary64_1397` `pow-prod-down_binary64_1493`
1×	`distribute-lft-in_binary64_1376` `flip--_binary64_1400` `diff-log_binary64_1514` `unswap-sqr_binary64_1393` `pow-to-exp_binary64_1491` `sub-neg_binary64_1418` `cbrt-unprod_binary64_1455` `distribute-rgt-in_binary64_1377` `pow1/3_binary64_1504` `flip3--_binary64_1429` `*-commutative_binary64_1358`

Counts

4 → 69

Calls

4 calls:

21.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 6)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
6.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 6)
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 6))

series4.4s (27.4%)

Counts

4 → 12

Calls

4 calls:

3.5s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (cbrt.f64 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 6)))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
424.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 6)
272.0ms	(cbrt.f64 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 6))
197.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5184	2651

prune126.0ms (0.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	14	16
Picked	1	0	1
Done	0	0	0
Total	82	16	98

Merged error: 14.4b

Counts

98 → 16

Compiler

Compiled 3152 to 1349 computations (57.2% saved)

regimes132.0ms (0.8%)

Compiler: Compiled 1284 to 678 computations (47.2% saved)

bsearch81.0ms (0.5%)

Steps

Iters	Range		Point
9	3.762858264550735e-32	1.2920571637587814e-22	4.907363205004435e-32
6	-9.983193871347345e-70	-2.0772157333420918e-70	-4.521195450558315e-70

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	545	164
1	545	164

end0.0ms (0%)

sample2.9s (18.2%)

Algorithm

1×

intervals

Results

1.1s	3519×	body	1024	valid
815.0ms	1170×	body	2048	valid
227.0ms	1382×	body	512	valid
63.0ms	1355×	body	128	valid
63.0ms	573×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 760 to 397 computations (47.8% saved)

Details

analyze942.0ms (5.8%)

sample77.0ms (0.5%)

simplify163.0ms (1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite14.0ms (0.1%)

series318.0ms (2%)

simplify83.0ms (0.5%)

prune34.0ms (0.2%)

localize11.0ms (0.1%)

rewrite44.0ms (0.3%)

series1.8s (11.3%)

simplify73.0ms (0.5%)

prune138.0ms (0.9%)

localize17.0ms (0.1%)

rewrite52.0ms (0.3%)

series4.3s (26.3%)

simplify55.0ms (0.3%)

prune180.0ms (1.1%)

localize16.0ms (0.1%)

rewrite44.0ms (0.3%)

series4.4s (27.4%)

simplify70.0ms (0.4%)

prune126.0ms (0.8%)

regimes132.0ms (0.8%)

bsearch81.0ms (0.5%)

simplify18.0ms (0.1%)

end0.0ms (0%)

sample2.9s (18.2%)

Profiling