Details

analyze915.0ms (13.6%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample59.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms	193×	body	128	valid
13.0ms	32×	body	1024	valid
5.0ms	58×	body	128	invalid
5.0ms	20×	body	512	valid
4.0ms	15×	body	512	invalid
3.0ms	10×	body	1024	invalid
2.0ms	11×	body	256	valid
1.0ms	8×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify266.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	7278	24

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

28.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
4.3b	(.f64 (.f64 x (pow.f64 s 2)) x)
7.9b	(*.f64 x (pow.f64 s 2))
18.3b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64_457`
82×	`prod-exp_binary64_468`
34×	`add-cbrt-cube_binary64_455`
18×	`add-sqr-sqrt_binary64_441` `pow-exp_binary64_487` `pow-to-exp_binary64_488`
16×	`cbrt-unprod_binary64_452` `div-exp_binary64_470`
12×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `associate-l*_binary64_360`
7×	`unpow-prod-down_binary64_498`
6×	`pow1_binary64_480`
4×	`add-log-exp_binary64_458` `unswap-sqr_binary64_387` `cbrt-undiv_binary64_453`
3×	`times-frac_binary64_425` `sqr-pow_binary64_391` `-commutative_binary64_350` `unpow2_binary64_484` `associate-/l_binary64_364`
1×	`cos-2_binary64_561` `pow-prod-down_binary64_490` `clear-num_binary64_418` `div-inv_binary64_416` `frac-2neg_binary64_430` `associate-/r*_binary64_363` `div-sub_binary64_424`

Counts

4 → 119

Calls

4 calls:

11.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
11.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
10.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))

series180.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
57.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
26.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
23.0ms	(*.f64 x (pow.f64 s 2))

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5001	2228

prune138.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	10	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	10	132

Error

2.9b

Counts

132 → 10

Compiler

Compiled 2731 to 1259 computations (53.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
0.4b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
6.1b	(.f64 s (.f64 c x))
6.1b	(.f64 s (.f64 c x))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
14×	`add-sqr-sqrt_binary64_441`
12×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`associate-l_binary64_360`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
7×	`pow-prod-down_binary64_490`
5×	`associate-r_binary64_359`
4×	`add-log-exp_binary64_458`
3×	`times-frac_binary64_425` `-commutative_binary64_350` `swap-sqr_binary64_386` `associate-/l_binary64_364`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`cos-2_binary64_561` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `sqr-abs_binary64_434` `pow-plus_binary64_482` `frac-2neg_binary64_430` `pow-sqr_binary64_392` `associate-/r*_binary64_363` `pow-prod-up_binary64_489` `pow2_binary64_500` `div-sub_binary64_424`

Counts

4 → 84

Calls

4 calls:

5.0ms	(.f64 s (.f64 c x))
5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

series188.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
26.0ms	(.f64 s (.f64 c x))
25.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
25.0ms	(.f64 s (.f64 c x))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5021	1306

prune116.0ms (1.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	92	14	106

Error

2.7b

Counts

106 → 14

Compiler

Compiled 2201 to 958 computations (56.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
0.4b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
6.1b	(.f64 s (.f64 c x))
6.1b	(.f64 s (.f64 c x))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_425`
56×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
21×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
16×	`associate-/l*_binary64_364`
14×	`pow1_binary64_480`
6×	`pow-prod-down_binary64_490` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `associate-/r*_binary64_363`
4×	`add-log-exp_binary64_458` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `associate-r_binary64_359` `*-commutative_binary64_350` `frac-2neg_binary64_430`
1×	`associate-/l/_binary64_366`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))

series221.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
56.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
26.0ms	(.f64 s (.f64 c x))
25.0ms	(.f64 s (.f64 c x))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4971	4039
1	4971	4039

prune171.0ms (2.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	143	16	159

Error

2.7b

Counts

159 → 16

Compiler

Compiled 4194 to 1694 computations (59.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
6.1b	(.f64 s (.f64 c x))
6.1b	(.f64 s (.f64 c x))
13.5b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_441`
23×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
21×	`times-frac_binary64_425`
19×	`add-exp-log_binary64_457`
16×	`add-cbrt-cube_binary64_455`
15×	`pow1_binary64_480`
12×	`unpow-prod-down_binary64_498`
7×	`associate-/r*_binary64_363`
6×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sqr-pow_binary64_391`
3×	`sqrt-prod_binary64_435` `div-exp_binary64_470` `associate-/l*_binary64_364`
2×	`associate-r_binary64_359` `*-commutative_binary64_350`
1×	`clear-num_binary64_418` `pow1/2_binary64_499` `div-inv_binary64_416` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `cbrt-undiv_binary64_453`

Counts

4 → 94

Calls

4 calls:

5.0ms	(.f64 s (.f64 c x))
5.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
5.0ms	(.f64 s (.f64 c x))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series299.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
28.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
25.0ms	(.f64 s (.f64 c x))
25.0ms	(.f64 s (.f64 c x))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4928	2146
1	4928	2146

prune120.0ms (1.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Error

2.7b

Counts

122 → 15

Compiler

Compiled 2952 to 1188 computations (59.8% saved)

regimes813.0ms (12.1%)

Accuracy

Total 1.2b remaining (49.4%)

Threshold costs 0b (0%)

Compiler

Compiled 8613 to 6167 computations (28.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	33
1	18	33

end0.0ms (0%)

sample2.7s (40.8%)

Algorithm

1×

intervals

Results

483.0ms	6126×	body	128	valid
302.0ms	963×	body	1024	valid
156.0ms	1914×	body	128	invalid
142.0ms	612×	body	512	valid
65.0ms	210×	body	1024	invalid
58.0ms	239×	body	512	invalid
46.0ms	298×	body	256	valid
24.0ms	159×	body	256	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 1428 to 1019 computations (28.6% saved)

Details

analyze915.0ms (13.6%)

sample59.0ms (0.9%)

simplify266.0ms (4%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite48.0ms (0.7%)

series180.0ms (2.7%)

simplify62.0ms (0.9%)

prune138.0ms (2.1%)

localize12.0ms (0.2%)

rewrite25.0ms (0.4%)

series188.0ms (2.8%)

simplify64.0ms (0.9%)

prune116.0ms (1.7%)

localize10.0ms (0.1%)

rewrite36.0ms (0.5%)

series221.0ms (3.3%)

simplify89.0ms (1.3%)

prune171.0ms (2.6%)

localize14.0ms (0.2%)

rewrite25.0ms (0.4%)

series299.0ms (4.5%)

simplify81.0ms (1.2%)

prune120.0ms (1.8%)

regimes813.0ms (12.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (40.8%)

Profiling