Details

analyze755.0ms (7.3%)

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)

sample62.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	114×	body	1024	valid
15.0ms	39×	body	2048	valid
7.0ms	45×	body	512	valid
2.0ms	20×	body	256	valid
2.0ms	38×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify97.0ms (0.9%)

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

Error

36.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.9b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (0.1%)

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 (1.7%)

Counts

2 → 6

Calls

2 calls:

113.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
61.0ms	(tan.f64 (+.f64 x eps))

simplify97.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4834	544
1	4834	544

prune38.0ms (0.4%)

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

Error

12.8b

Counts

34 → 8

Compiler

Compiled 566 to 179 computations (68.4% saved)

localize11.0ms (0.1%)

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))
0.3b	(*.f64 (tan.f64 x) (tan.f64 eps))
4.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite40.0ms (0.4%)

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:

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

series1.0s (9.7%)

Counts

4 → 12

Calls

4 calls:

515.0ms	(-.f64 (/.f64 (+.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 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
103.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
97.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5619	2567

prune138.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	87	13	100
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	93	15	108

Error

12.7b

Counts

108 → 15

Compiler

Compiled 3002 to 1022 computations (66% 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)))
4.1b	(-.f64 (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (sin.f64 x) (cos.f64 x)))

rewrite65.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
20×	`add-sqr-sqrt_binary64_1464`
18×	`*-un-lft-identity_binary64_1442`
13×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
12×	`times-frac_binary64_1448`
9×	`cbrt-unprod_binary64_1475` `add-log-exp_binary64_1481` `prod-exp_binary64_1491`
8×	`cbrt-undiv_binary64_1476` `div-exp_binary64_1493`
6×	`pow1_binary64_1503`
3×	`associate-r_binary64_1382` `div-inv_binary64_1439` `associate-l_binary64_1383` `frac-sub_binary64_1451` `sin-mult_binary64_1597`
2×	`associate-/r_binary64_1386` `associate-/l/_binary64_1389` `associate-/r/_binary64_1388` `clear-num_binary64_1441` `associate-/l_binary64_1387` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `cos-mult_binary64_1596` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`
1×	`associate--l+_binary64_1379` `sum-log_binary64_1533` `sub-neg_binary64_1435` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `distribute-lft-out_binary64_1393` `flip--_binary64_1417` `flip3-+_binary64_1445` `flip-+_binary64_1416` `frac-add_binary64_1450` `unswap-sqr_binary64_1410`

Counts

4 → 98

Calls

4 calls:

29.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
8.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
8.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

series801.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

547.0ms	(-.f64 (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))) (/.f64 (sin.f64 x) (.f64 (cos.f64 x) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))))) (/.f64 (sin.f64 x) (cos.f64 x)))
113.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
101.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
39.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

simplify101.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4979	4006
1	4979	4006

prune215.0ms (2.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	99	11	110
Fresh	10	4	14
Picked	1	0	1
Done	0	0	0
Total	110	15	125

Error

11.1b

Counts

125 → 15

Compiler

Compiled 7157 to 2004 computations (72% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1))))
3.6b	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)
3.6b	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)
3.6b	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)

rewrite100.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64_1464`
35×	`*-un-lft-identity_binary64_1442`
18×	`times-frac_binary64_1448` `difference-of-squares_binary64_1411`
10×	`add-log-exp_binary64_1481`
9×	`cancel-sign-sub-inv_binary64_1408` `difference-of-sqr-1_binary64_1412`
8×	`add-cube-cbrt_binary64_1477`
7×	`cbrt-div_binary64_1474`
6×	`distribute-lft-out--_binary64_1394`
5×	`flip3--_binary64_1446` `flip--_binary64_1417` `frac-add_binary64_1450`
4×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
3×	`div-inv_binary64_1439` `sub-neg_binary64_1435` `cbrt-prod_binary64_1473` `diff-log_binary64_1534`
2×	`associate-*r/_binary64_1384` `frac-times_binary64_1452`
1×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524` `associate-*l/_binary64_1385`

Counts

4 → 93

Calls

4 calls:

17.0ms	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)
17.0ms	(cbrt.f64 (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1))))
16.0ms	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)
16.0ms	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)

series1.4s (13.5%)

Counts

4 → 12

Calls

4 calls:

874.0ms	(cbrt.f64 (+.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 eps) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))))) (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1))))
180.0ms	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)
176.0ms	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)
171.0ms	(-.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) 1)

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4946	5663
1	4946	5663

prune489.0ms (4.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	97	8	105
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	100	20	120

Error

11.1b

Counts

120 → 20

Compiler

Compiled 15744 to 5010 computations (68.2% saved)

regimes649.0ms (6.3%)

Accuracy

Total 0.4b remaining (3.1%)

Threshold costs 0.4b (3.1%)

Compiler

Compiled 12336 to 5443 computations (55.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	70
1	81	70

end0.0ms (0%)

sample3.9s (37.3%)

Algorithm

1×

intervals

Results

848.0ms	3565×	body	1024	valid
511.0ms	1164×	body	2048	valid
199.0ms	1348×	body	512	valid
60.0ms	1328×	body	128	valid
57.0ms	593×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 4157 to 1838 computations (55.8% saved)

Details

analyze755.0ms (7.3%)

sample62.0ms (0.6%)

simplify97.0ms (0.9%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite13.0ms (0.1%)

series174.0ms (1.7%)

simplify97.0ms (0.9%)

prune38.0ms (0.4%)

localize11.0ms (0.1%)

rewrite40.0ms (0.4%)

series1.0s (9.7%)

simplify84.0ms (0.8%)

prune138.0ms (1.3%)

localize23.0ms (0.2%)

rewrite65.0ms (0.6%)

series801.0ms (7.7%)

simplify101.0ms (1%)

prune215.0ms (2.1%)

localize34.0ms (0.3%)

rewrite100.0ms (1%)

series1.4s (13.5%)

simplify91.0ms (0.9%)

prune489.0ms (4.7%)

regimes649.0ms (6.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (37.3%)

Profiling