Details

analyze957.0ms (8.5%)

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
5.0ms	32×	body	512	valid
2.0ms	45×	body	128	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify167.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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: 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

5×	`add-sqr-sqrt_binary64_1477` `*-un-lft-identity_binary64_1455`
4×	`add-log-exp_binary64_1494` `tan-quot_binary64_1614`
3×	`add-cube-cbrt_binary64_1490` `cancel-sign-sub-inv_binary64_1421`
2×	`tan-sum_binary64_1590` `pow1_binary64_1516` `add-cbrt-cube_binary64_1491` `frac-sub_binary64_1464` `add-exp-log_binary64_1493`
1×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424` `flip--_binary64_1430` `diff-log_binary64_1547` `sub-neg_binary64_1448` `flip3--_binary64_1459`

Counts

2 → 27

Calls

2 calls:

8.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms	(tan.f64 (+.f64 x eps))

series327.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

212.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
116.0ms	(tan.f64 (+.f64 x eps))

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4851	544
1	4851	544

prune97.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Merged error: 16.8b

Counts

34 → 8

Compiler

Compiled 1475 to 787 computations (46.6% saved)

localize13.0ms (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))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1455`
23×	`add-sqr-sqrt_binary64_1477`
16×	`add-cube-cbrt_binary64_1490`
13×	`times-frac_binary64_1461`
9×	`tan-quot_binary64_1614`
8×	`add-log-exp_binary64_1494` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
6×	`pow1_binary64_1516`
5×	`distribute-lft-out_binary64_1406`
4×	`associate-/l*_binary64_1400`
3×	`associate-r_binary64_1395` `associate-/l/_binary64_1402` `associate-/r_binary64_1399` `cancel-sign-sub-inv_binary64_1421` `associate-l*_binary64_1396`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `difference-of-squares_binary64_1424` `flip--_binary64_1430` `flip3-+_binary64_1458` `frac-add_binary64_1463` `flip3--_binary64_1459`
1×	`prod-exp_binary64_1504` `associate-r/_binary64_1397` `distribute-lft-out--_binary64_1407` `div-exp_binary64_1506` `clear-num_binary64_1454` `frac-times_binary64_1465` `-commutative_binary64_1386` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `cbrt-unprod_binary64_1488` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 88

Calls

4 calls:

16.0ms	(-.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))

series1.8s (16.1%)

Counts

4 → 12

Calls

4 calls:

929.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
521.0ms	(/.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))
175.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify79.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4949	2567
1	4949	2567

prune811.0ms (7.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	86	14	100
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	90	18	108

Merged error: 16.7b

Counts

108 → 18

Compiler

Compiled 16367 to 8458 computations (48.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
2.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

rewrite69.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64_1455`
41×	`add-sqr-sqrt_binary64_1477`
26×	`times-frac_binary64_1461`
20×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
19×	`add-cube-cbrt_binary64_1490`
12×	`difference-of-squares_binary64_1424`
7×	`distribute-lft-out_binary64_1406` `associate-/r*_binary64_1399`
6×	`distribute-lft-out--_binary64_1407` `pow1_binary64_1516` `add-log-exp_binary64_1494`
5×	`prod-exp_binary64_1504` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400` `cbrt-unprod_binary64_1488`
4×	`associate-/l/_binary64_1402`
3×	`associate-r_binary64_1395` `associate-/r/_binary64_1401` `tan-quot_binary64_1614` `cancel-sign-sub-inv_binary64_1421` `associate-l_binary64_1396`
2×	`sin-mult_binary64_1610` `clear-num_binary64_1454` `flip--_binary64_1430` `frac-2neg_binary64_1466` `div-inv_binary64_1452` `flip3--_binary64_1459`
1×	`flip-+_binary64_1429` `cos-mult_binary64_1609` `*-commutative_binary64_1386` `diff-log_binary64_1547` `frac-sub_binary64_1464` `sub-neg_binary64_1448` `flip3-+_binary64_1458` `frac-add_binary64_1463` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 111

Calls

4 calls:

24.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
14.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
6.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

series1.8s (15.9%)

Counts

4 → 12

Calls

4 calls:

977.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
554.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
199.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
71.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5490	4271

prune238.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	6	10	16
Picked	1	0	1
Done	1	0	1
Total	129	12	141

Merged error: 14.3b

Counts

141 → 12

Compiler

Compiled 5868 to 2017 computations (65.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
3.3b	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
12×	`add-sqr-sqrt_binary64_1477`
10×	`*-un-lft-identity_binary64_1455`
9×	`prod-exp_binary64_1504` `cbrt-unprod_binary64_1488`
8×	`div-exp_binary64_1506` `cbrt-undiv_binary64_1489`
6×	`pow1_binary64_1516` `add-log-exp_binary64_1494` `add-cube-cbrt_binary64_1490`
4×	`times-frac_binary64_1461`
3×	`sin-mult_binary64_1610` `associate-r_binary64_1395` `difference-of-sqr--1_binary64_1426` `div-inv_binary64_1452` `associate-l_binary64_1396`
2×	`distribute-lft-out_binary64_1406` `associate-/r/_binary64_1401` `associate-/l/_binary64_1402` `cos-mult_binary64_1609` `clear-num_binary64_1454` `associate-/r_binary64_1399` `frac-2neg_binary64_1466` `associate-/l_binary64_1400`
1×	`flip-+_binary64_1429` `*-commutative_binary64_1386` `flip3-+_binary64_1458` `sum-log_binary64_1546` `+-commutative_binary64_1385` `pow-prod-down_binary64_1526` `unswap-sqr_binary64_1423`

Counts

4 → 81

Calls

4 calls:

18.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)
12.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
6.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

series798.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)
203.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
200.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
71.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

simplify89.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4975	1984
1	4975	1984

prune462.0ms (4.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	86	7	93
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	89	16	105

Merged error: 14.2b

Counts

105 → 16

Compiler

Compiled 11357 to 5136 computations (54.8% saved)

regimes99.0ms (0.9%)

Compiler: Compiled 1272 to 716 computations (43.7% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	88	70
1	88	70

end0.0ms (0%)

sample3.0s (26.8%)

Algorithm

1×

intervals

Results

1.1s	3558×	body	1024	valid
896.0ms	1205×	body	2048	valid
227.0ms	1353×	body	512	valid
64.0ms	1347×	body	128	valid
59.0ms	536×	body	256	valid
2.0ms	1×	body	4096	valid

Compiler

Compiled 695 to 395 computations (43.2% saved)

Details

analyze957.0ms (8.5%)

sample87.0ms (0.8%)

simplify167.0ms (1.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series327.0ms (2.9%)

simplify126.0ms (1.1%)

prune97.0ms (0.9%)

localize13.0ms (0.1%)

rewrite45.0ms (0.4%)

series1.8s (16.1%)

simplify79.0ms (0.7%)

prune811.0ms (7.2%)

localize22.0ms (0.2%)

rewrite69.0ms (0.6%)

series1.8s (15.9%)

simplify64.0ms (0.6%)

prune238.0ms (2.1%)

localize23.0ms (0.2%)

rewrite57.0ms (0.5%)

series798.0ms (7.1%)

simplify89.0ms (0.8%)

prune462.0ms (4.1%)

regimes99.0ms (0.9%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample3.0s (26.8%)

Profiling