Details

analyze1.0s (14.1%)

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)

sample60.0ms (0.8%)

Algorithm

1×

intervals

Results

20.0ms	195×	body	128	valid
12.0ms	31×	body	1024	valid
4.0ms	17×	body	512	valid
4.0ms	47×	body	128	invalid
3.0ms	7×	body	1024	invalid
2.0ms	10×	body	512	invalid
2.0ms	13×	body	256	valid
1.0ms	3×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify327.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (160.0ms)

Iter	Nodes	Cost
0	4892	24
1	4892	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

Merged error: 27.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
4.7b	(.f64 (.f64 x (pow.f64 s 2)) x)
9.2b	(*.f64 x (pow.f64 s 2))
15.9b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64_449`
82×	`prod-exp_binary64_460`
34×	`add-cbrt-cube_binary64_447`
18×	`pow-exp_binary64_479` `pow-to-exp_binary64_480` `add-sqr-sqrt_binary64_435`
16×	`cbrt-unprod_binary64_444` `div-exp_binary64_462`
12×	`add-cube-cbrt_binary64_446` `-un-lft-identity_binary64_414` `associate-l_binary64_357` `associate-r*_binary64_356`
7×	`unpow-prod-down_binary64_490`
6×	`pow1_binary64_472`
4×	`cbrt-undiv_binary64_445` `add-log-exp_binary64_450` `unswap-sqr_binary64_382`
3×	`times-frac_binary64_420` `-commutative_binary64_347` `sqr-pow_binary64_386` `unpow2_binary64_476` `associate-/l_binary64_361`
1×	`clear-num_binary64_413` `cos-2_binary64_553` `div-inv_binary64_411` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `div-sub_binary64_419` `associate-/r*_binary64_360`

Counts

4 → 119

Calls

4 calls:

12.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
10.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
6.0ms	(*.f64 x (pow.f64 s 2))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

series330.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
104.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
50.0ms	(*.f64 x (pow.f64 s 2))
45.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)

simplify88.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4944	2214
1	4944	2214

prune150.0ms (2.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	11	132

Merged error: 1.4b

Counts

132 → 11

Compiler

Compiled 2732 to 1362 computations (50.1% saved)

localize11.0ms (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))))
0.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
4.8b	(.f64 s (.f64 c x))
4.8b	(.f64 s (.f64 c x))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
14×	`add-sqr-sqrt_binary64_435`
12×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
9×	`associate-l_binary64_357`
8×	`prod-exp_binary64_460` `cbrt-unprod_binary64_444`
7×	`pow-prod-down_binary64_482`
5×	`associate-r_binary64_356`
4×	`add-log-exp_binary64_450`
3×	`times-frac_binary64_420` `-commutative_binary64_347` `swap-sqr_binary64_381` `associate-/l_binary64_361`
2×	`cbrt-undiv_binary64_445` `div-exp_binary64_462`
1×	`pow-plus_binary64_474` `clear-num_binary64_413` `cos-2_binary64_553` `div-inv_binary64_411` `pow-prod-up_binary64_481` `pow-sqr_binary64_387` `frac-2neg_binary64_425` `unswap-sqr_binary64_382` `div-sub_binary64_419` `pow2_binary64_492` `associate-/r*_binary64_360`

Counts

4 → 83

Calls

4 calls:

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

series350.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

196.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
59.0ms	(.f64 s (.f64 c x))
48.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
46.0ms	(.f64 s (.f64 c x))

simplify83.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4901	1303
1	4901	1303

prune122.0ms (1.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	88	18	106

Merged error: 1.2b

Counts

106 → 18

Compiler

Compiled 2206 to 995 computations (54.9% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
0.6b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
4.8b	(.f64 s (.f64 c x))
4.8b	(.f64 s (.f64 c x))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
20×	`add-exp-log_binary64_449`
18×	`times-frac_binary64_420` `add-cbrt-cube_binary64_447`
15×	`pow1_binary64_472`
6×	`prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-l_binary64_357` `associate-/l_binary64_361` `cbrt-unprod_binary64_444` `associate-/r_binary64_360`
4×	`add-log-exp_binary64_450`
3×	`div-exp_binary64_462`
2×	`clear-num_binary64_413` `div-inv_binary64_411` `-commutative_binary64_347` `cbrt-undiv_binary64_445` `frac-2neg_binary64_425` `associate-r*_binary64_356`
1×	`1-exp_binary64_455` `inv-pow_binary64_496` `pow-flip_binary64_485` `rec-exp_binary64_461`

Counts

4 → 94

Calls

4 calls:

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))))
3.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

series239.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
47.0ms	(.f64 s (.f64 c x))
45.0ms	(.f64 s (.f64 c x))
42.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4889	1714
1	4889	1714

prune136.0ms (1.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	101	5	106
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	106	18	124

Merged error: 1.2b

Counts

124 → 18

Compiler

Compiled 3083 to 1321 computations (57.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
0.6b	(/.f64 1 (/.f64 (fabs.f64 (.f64 s (.f64 c x))) (cos.f64 (*.f64 x 2))))
4.8b	(.f64 s (.f64 c x))
4.8b	(.f64 s (.f64 c x))

rewrite40.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_420`
56×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
29×	`add-exp-log_binary64_449`
21×	`add-cbrt-cube_binary64_447`
16×	`pow1_binary64_472` `associate-/r*_binary64_360`
9×	`div-exp_binary64_462`
6×	`div-inv_binary64_411` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-l_binary64_357` `associate-/l*_binary64_361` `cbrt-unprod_binary64_444`
4×	`cbrt-undiv_binary64_445` `add-log-exp_binary64_450`
3×	`1-exp_binary64_455` `rec-exp_binary64_461`
2×	`clear-num_binary64_413` `inv-pow_binary64_496` `pow-flip_binary64_485` `-commutative_binary64_347` `frac-2neg_binary64_425` `associate-r*_binary64_356`
1×	`associate-/r/_binary64_362`

Counts

4 → 143

Calls

4 calls:

7.0ms	(.f64 s (.f64 c x))
7.0ms	(/.f64 1 (/.f64 (fabs.f64 (.f64 s (.f64 c x))) (cos.f64 (*.f64 x 2))))
5.0ms	(.f64 s (.f64 c x))
3.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

series250.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(/.f64 1 (/.f64 (fabs.f64 (.f64 s (.f64 c x))) (cos.f64 (*.f64 x 2))))
49.0ms	(.f64 s (.f64 c x))
47.0ms	(.f64 s (.f64 c x))
43.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

simplify126.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5056	3409

prune176.0ms (2.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	155	18	173

Merged error: 1.2b

Counts

173 → 18

Compiler

Compiled 4545 to 1959 computations (56.9% saved)

regimes615.0ms (8.4%)

Compiler: Compiled 7438 to 5212 computations (29.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	28
1	15	28

end0.0ms (0%)

sample2.9s (40.1%)

Algorithm

1×

intervals

Results

695.0ms	6156×	body	128	valid
379.0ms	961×	body	1024	valid
157.0ms	1788×	body	128	invalid
142.0ms	547×	body	512	valid
77.0ms	198×	body	1024	invalid
67.0ms	245×	body	512	invalid
59.0ms	331×	body	256	valid
24.0ms	141×	body	256	invalid
3.0ms	5×	body	2048	valid
1.0ms	2×	body	2048	invalid

Compiler

Compiled 1238 to 862 computations (30.4% saved)

Details

analyze1.0s (14.1%)

sample60.0ms (0.8%)

simplify327.0ms (4.5%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite47.0ms (0.6%)

series330.0ms (4.5%)

simplify88.0ms (1.2%)

prune150.0ms (2.1%)

localize11.0ms (0.2%)

rewrite27.0ms (0.4%)

series350.0ms (4.8%)

simplify83.0ms (1.1%)

prune122.0ms (1.7%)

localize16.0ms (0.2%)

rewrite27.0ms (0.4%)

series239.0ms (3.3%)

simplify85.0ms (1.2%)

prune136.0ms (1.9%)

localize13.0ms (0.2%)

rewrite40.0ms (0.5%)

series250.0ms (3.4%)

simplify126.0ms (1.7%)

prune176.0ms (2.4%)

regimes615.0ms (8.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (40.1%)

Profiling