Details

analyze1.9s (16.5%)

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
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)

sample107.0ms (0.9%)

Algorithm

1×

intervals

Results

33.0ms	198×	body	128	valid
21.0ms	28×	body	1024	valid
12.0ms	70×	body	128	invalid
7.0ms	14×	body	512	valid
6.0ms	16×	body	256	valid
5.0ms	9×	body	512	invalid
2.0ms	5×	body	256	invalid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify603.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (289.0ms)

Iter	Nodes	Cost
0	4892	24
1	4892	24

prune5.0ms (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: 29.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
4.1b	(.f64 (.f64 x (pow.f64 s 2)) x)
8.4b	(*.f64 x (pow.f64 s 2))
19.8b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite95.0ms (0.8%)

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:

24.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
20.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
13.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
13.0ms	(*.f64 x (pow.f64 s 2))

series661.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
209.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
96.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
89.0ms	(*.f64 x (pow.f64 s 2))

simplify157.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4944	2214
1	4944	2214

prune284.0ms (2.4%)

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: 1.2b

Counts

132 → 11

Compiler

Compiled 2720 to 1364 computations (49.9% saved)

localize21.0ms (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))))
0.3b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
4.1b	(.f64 s (.f64 c x))
4.1b	(.f64 s (.f64 c x))

rewrite55.0ms (0.5%)

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:

11.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
11.0ms	(.f64 s (.f64 c x))
11.0ms	(.f64 s (.f64 c x))
7.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

series689.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
106.0ms	(.f64 s (.f64 c x))
104.0ms	(.f64 s (.f64 c x))
77.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4901	1303
1	4901	1303

prune238.0ms (2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	87	8	95
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 0.9b

Counts

106 → 16

Compiler

Compiled 2180 to 963 computations (55.8% saved)

localize22.0ms (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))))
1.2b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
4.1b	(.f64 s (.f64 c x))
4.1b	(.f64 s (.f64 c x))

rewrite76.0ms (0.7%)

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:

14.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
11.0ms	(.f64 s (.f64 c x))
10.0ms	(.f64 s (.f64 c x))
9.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))

series814.0ms (7%)

Counts

4 → 12

Calls

4 calls:

391.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
214.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
109.0ms	(.f64 s (.f64 c x))
99.0ms	(.f64 s (.f64 c x))

simplify181.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5045	3807

prune354.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	146	15	161

Merged error: 0.9b

Counts

161 → 15

Compiler

Compiled 4002 to 1702 computations (57.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
1.2b	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))
4.1b	(.f64 s (.f64 c x))
4.1b	(.f64 s (.f64 c x))

rewrite54.0ms (0.5%)

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:

11.0ms	(.f64 s (.f64 c x))
11.0ms	(.f64 s (.f64 c x))
8.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
6.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

series501.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
100.0ms	(.f64 s (.f64 c x))
98.0ms	(.f64 s (.f64 c x))
91.0ms	(/.f64 1 (fabs.f64 (.f64 s (.f64 c x))))

simplify163.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4889	1714
1	4889	1714

prune199.0ms (1.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	106	15	121

Merged error: 0.9b

Counts

121 → 15

Compiler

Compiled 2690 to 1038 computations (61.4% saved)

regimes267.0ms (2.3%)

Compiler: Compiled 1358 to 1001 computations (26.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	31
1	19	31

end0.0ms (0%)

sample4.0s (34.1%)

Algorithm

1×

intervals

Results

1.1s	6144×	body	128	valid
692.0ms	930×	body	1024	valid
327.0ms	1964×	body	128	invalid
319.0ms	614×	body	512	valid
165.0ms	218×	body	1024	invalid
110.0ms	307×	body	256	valid
104.0ms	217×	body	512	invalid
54.0ms	168×	body	256	invalid
6.0ms	5×	body	2048	valid

Compiler

Compiled 358 to 261 computations (27.1% saved)

Details

analyze1.9s (16.5%)

sample107.0ms (0.9%)

simplify603.0ms (5.2%)

prune5.0ms (0%)

localize27.0ms (0.2%)

rewrite95.0ms (0.8%)

series661.0ms (5.7%)

simplify157.0ms (1.3%)

prune284.0ms (2.4%)

localize21.0ms (0.2%)

rewrite55.0ms (0.5%)

series689.0ms (5.9%)

simplify156.0ms (1.3%)

prune238.0ms (2%)

localize22.0ms (0.2%)

rewrite76.0ms (0.7%)

series814.0ms (7%)

simplify181.0ms (1.6%)

prune354.0ms (3%)

localize24.0ms (0.2%)

rewrite54.0ms (0.5%)

series501.0ms (4.3%)

simplify163.0ms (1.4%)

prune199.0ms (1.7%)

regimes267.0ms (2.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (34.1%)

Profiling