Details

analyze1.1s (16.8%)

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 (0.9%)

Algorithm

1×

intervals

Results

19.0ms	199×	body	128	valid
12.0ms	28×	body	1024	valid
5.0ms	18×	body	512	valid
5.0ms	48×	body	128	invalid
3.0ms	12×	body	512	invalid
2.0ms	11×	body	256	valid
2.0ms	6×	body	1024	invalid
0.0ms	2×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify329.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (157.0ms)

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: 27.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.5b	(.f64 (.f64 x (pow.f64 s 2)) x)
9.3b	(*.f64 x (pow.f64 s 2))
17.9b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite47.0ms (0.7%)

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 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))

series350.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
110.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
50.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
49.0ms	(*.f64 x (pow.f64 s 2))

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4944	2214
1	4944	2214

prune145.0ms (2.3%)

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: 1.5b

Counts

132 → 11

Compiler

Compiled 2739 to 1364 computations (50.2% 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))))
0.5b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
3.5b	(.f64 s (.f64 c x))
3.5b	(.f64 s (.f64 c x))

rewrite28.0ms (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:

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

series352.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
52.0ms	(.f64 s (.f64 c x))
50.0ms	(.f64 s (.f64 c x))
46.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4901	1303
1	4901	1303

prune121.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 1.0b

Counts

106 → 16

Compiler

Compiled 2199 to 966 computations (56.1% saved)

localize11.0ms (0.2%)

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))))
3.5b	(.f64 s (.f64 c x))
3.5b	(.f64 s (.f64 c x))

rewrite38.0ms (0.6%)

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`
21×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
16×	`associate-/l*_binary64_361`
14×	`pow1_binary64_472`
6×	`div-inv_binary64_411` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-l_binary64_357` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`
4×	`cbrt-undiv_binary64_445` `add-log-exp_binary64_450` `div-exp_binary64_462`
2×	`clear-num_binary64_413` `-commutative_binary64_347` `frac-2neg_binary64_425` `associate-r*_binary64_356`
1×	`associate-/l/_binary64_363`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/.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))))

series399.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
103.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
50.0ms	(.f64 s (.f64 c x))
48.0ms	(.f64 s (.f64 c x))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5045	3807

prune190.0ms (3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	145	16	161

Merged error: 1.0b

Counts

161 → 16

Compiler

Compiled 4071 to 1743 computations (57.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(.f64 s (.f64 c x))
3.5b	(.f64 s (.f64 c x))
12.0b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
12.0b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64_472`
14×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
10×	`add-sqr-sqrt_binary64_435`
8×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
6×	`prod-exp_binary64_460` `sqrt-prod_binary64_429` `pow-prod-down_binary64_482` `associate-l_binary64_357` `cbrt-unprod_binary64_444`
4×	`add-log-exp_binary64_450`
2×	`-commutative_binary64_347` `sqrt-pow1_binary64_431` `associate-r*_binary64_356` `pow1/2_binary64_491` `rem-sqrt-square_binary64_427`

Counts

4 → 62

Calls

4 calls:

5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series182.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

53.0ms	(.f64 s (.f64 c x))
47.0ms	(.f64 s (.f64 c x))
44.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
37.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4996	752
1	4996	752

prune84.0ms (1.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	74	16	90

Merged error: 1.0b

Counts

90 → 16

Compiler

Compiled 2390 to 741 computations (69% saved)

regimes138.0ms (2.2%)

Compiler: Compiled 1572 to 1112 computations (29.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	46
1	21	46

end0.0ms (0%)

sample2.4s (37.7%)

Algorithm

1×

intervals

Results

744.0ms	6144×	body	128	valid
404.0ms	958×	body	1024	valid
176.0ms	1880×	body	128	invalid
174.0ms	562×	body	512	valid
79.0ms	202×	body	1024	invalid
64.0ms	332×	body	256	valid
59.0ms	221×	body	512	invalid
26.0ms	145×	body	256	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 436 to 304 computations (30.3% saved)

Details

analyze1.1s (16.8%)

sample60.0ms (0.9%)

simplify329.0ms (5.2%)

prune3.0ms (0%)

localize14.0ms (0.2%)

rewrite47.0ms (0.7%)

series350.0ms (5.5%)

simplify83.0ms (1.3%)

prune145.0ms (2.3%)

localize11.0ms (0.2%)

rewrite28.0ms (0.4%)

series352.0ms (5.6%)

simplify84.0ms (1.3%)

prune121.0ms (1.9%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series399.0ms (6.3%)

simplify94.0ms (1.5%)

prune190.0ms (3%)

localize15.0ms (0.2%)

rewrite20.0ms (0.3%)

series182.0ms (2.9%)

simplify73.0ms (1.2%)

prune84.0ms (1.3%)

regimes138.0ms (2.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (37.7%)

Profiling