Details

analyze857.0ms (10.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

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)

sample59.0ms (0.7%)

Algorithm

1×

intervals

Results

28.0ms	115×	body	1024	valid
13.0ms	33×	body	2048	valid
6.0ms	45×	body	512	valid
2.0ms	25×	body	256	valid
2.0ms	38×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune7.0ms (0.1%)

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: 34.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.9b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.9b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `tan-quot_binary64_1601`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `frac-sub_binary64_1451` `add-exp-log_binary64_1480` `pow1_binary64_1503` `tan-sum_binary64_1577`
1×	`sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

2 → 27

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

series174.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

113.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
60.0ms	(tan.f64 (+.f64 x eps))

simplify100.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4834	544
1	4834	544

prune35.0ms (0.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Merged error: 11.7b

Counts

34 → 7

Compiler

Compiled 555 to 172 computations (69% saved)

localize12.0ms (0.2%)

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))
0.2b	(*.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))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1442`
23×	`add-sqr-sqrt_binary64_1464`
16×	`add-cube-cbrt_binary64_1477`
13×	`times-frac_binary64_1448`
9×	`tan-quot_binary64_1601`
8×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480`
6×	`pow1_binary64_1503`
5×	`distribute-lft-out_binary64_1393`
4×	`associate-/l*_binary64_1387`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-/l/_binary64_1389` `associate-l*_binary64_1383`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `difference-of-squares_binary64_1411`
1×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `frac-times_binary64_1452` `prod-exp_binary64_1491` `distribute-lft-out--_binary64_1394` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`

Counts

4 → 88

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
8.0ms	(/.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))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.0s (12.4%)

Counts

4 → 12

Calls

4 calls:

516.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
284.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
101.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
99.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5619	2567

prune135.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	87	13	100
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Merged error: 11.6b

Counts

107 → 15

Compiler

Compiled 2970 to 1009 computations (66% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 eps) (sin.f64 x))
2.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1464`
13×	`*-un-lft-identity_binary64_1442`
11×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
9×	`add-cube-cbrt_binary64_1477`
8×	`add-log-exp_binary64_1481`
6×	`pow1_binary64_1503`
5×	`tan-quot_binary64_1601`
4×	`times-frac_binary64_1448`
3×	`associate-r_binary64_1382` `associate-/r_binary64_1386` `cancel-sign-sub-inv_binary64_1408` `associate-l*_binary64_1383`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `associate-*l/_binary64_1385` `div-exp_binary64_1493`
1×	`sum-log_binary64_1533` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `associate-/l_binary64_1387` `flip3--_binary64_1446` `+-commutative_binary64_1372` `frac-sub_binary64_1451` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `distribute-lft-out--_binary64_1394` `unswap-sqr_binary64_1410`

Counts

4 → 72

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
6.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series809.0ms (10%)

Counts

4 → 12

Calls

4 calls:

543.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x)))) (tan.f64 x))
107.0ms	(/.f64 (*.f64 (tan.f64 eps) (sin.f64 x)) (cos.f64 x))
94.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
63.0ms	(*.f64 (tan.f64 eps) (sin.f64 x))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5270	1805

prune106.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	85	14	99

Merged error: 11.6b

Counts

99 → 14

Compiler

Compiled 2642 to 856 computations (67.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464`
10×	`*-un-lft-identity_binary64_1442`
9×	`cbrt-prod_binary64_1473`
8×	`add-cube-cbrt_binary64_1477`
6×	`add-log-exp_binary64_1481`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
3×	`cancel-sign-sub-inv_binary64_1408` `pow1/3_binary64_1524`
2×	`difference-of-squares_binary64_1411`
1×	`times-frac_binary64_1448` `sub-neg_binary64_1435` `flip3--_binary64_1446` `frac-sub_binary64_1451` `flip--_binary64_1417` `diff-log_binary64_1534` `tan-quot_binary64_1601` `distribute-lft-out--_binary64_1394`

Counts

4 → 51

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (tan.f64 eps) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))) (cos.f64 x)))) (tan.f64 x))
2.0ms	(cbrt.f64 (sin.f64 x))
2.0ms	(cbrt.f64 (sin.f64 x))
2.0ms	(cbrt.f64 (sin.f64 x))

series757.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

547.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (.f64 (tan.f64 eps) (*.f64 (cbrt.f64 (sin.f64 x)) (cbrt.f64 (sin.f64 x)))) (cbrt.f64 (sin.f64 x))) (cos.f64 x)))) (tan.f64 x))
74.0ms	(cbrt.f64 (sin.f64 x))
69.0ms	(cbrt.f64 (sin.f64 x))
66.0ms	(cbrt.f64 (sin.f64 x))

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5078	1292

prune68.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	63	14	77

Merged error: 11.6b

Counts

77 → 14

Compiler

Compiled 2074 to 563 computations (72.9% saved)

regimes412.0ms (5.1%)

Compiler: Compiled 4688 to 2512 computations (46.4% saved)

bsearch65.0ms (0.8%)

Steps

Iters	Range		Point
9	1.8514063739790203e-41	2.0866336633208193e-33	2.046397525732066e-33
8	-6.257961986116703e-30	-5.803577273182133e-33	-6.5060705864494465e-31

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	108	102
1	108	102

end0.0ms (0%)

sample3.0s (37.9%)

Algorithm

1×

intervals

Results

851.0ms	3574×	body	1024	valid
525.0ms	1196×	body	2048	valid
193.0ms	1362×	body	512	valid
67.0ms	1272×	body	128	valid
60.0ms	594×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 1620 to 869 computations (46.4% saved)

Details

analyze857.0ms (10.6%)

sample59.0ms (0.7%)

simplify10.0ms (0.1%)

prune7.0ms (0.1%)

localize6.0ms (0.1%)

rewrite13.0ms (0.2%)

series174.0ms (2.2%)

simplify100.0ms (1.2%)

prune35.0ms (0.4%)

localize12.0ms (0.2%)

rewrite39.0ms (0.5%)

series1.0s (12.4%)

simplify84.0ms (1%)

prune135.0ms (1.7%)

localize14.0ms (0.2%)

rewrite41.0ms (0.5%)

series809.0ms (10%)

simplify79.0ms (1%)

prune106.0ms (1.3%)

localize21.0ms (0.3%)

rewrite31.0ms (0.4%)

series757.0ms (9.4%)

simplify64.0ms (0.8%)

prune68.0ms (0.9%)

regimes412.0ms (5.1%)

bsearch65.0ms (0.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.0s (37.9%)

Profiling