Details

analyze1.0s (14.4%)

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)

sample57.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	199×	body	128	valid
11.0ms	28×	body	1024	valid
5.0ms	18×	body	512	valid
4.0ms	48×	body	128	invalid
3.0ms	12×	body	512	invalid
2.0ms	6×	body	1024	invalid
2.0ms	11×	body	256	valid
0.0ms	2×	body	256	invalid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify341.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (168.0ms)

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)

localize13.0ms (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))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`add-exp-log_binary64_461`
82×	`prod-exp_binary64_472`
34×	`add-cbrt-cube_binary64_459`
18×	`pow-to-exp_binary64_492` `pow-exp_binary64_491` `add-sqr-sqrt_binary64_445`
16×	`div-exp_binary64_474` `cbrt-unprod_binary64_456`
12×	`-un-lft-identity_binary64_423` `associate-l_binary64_364` `add-cube-cbrt_binary64_458` `associate-r*_binary64_363`
7×	`unpow-prod-down_binary64_502`
6×	`pow1_binary64_484`
4×	`add-log-exp_binary64_462` `unswap-sqr_binary64_391` `cbrt-undiv_binary64_457`
3×	`times-frac_binary64_429` `-commutative_binary64_354` `unpow2_binary64_488` `associate-/l_binary64_368` `sqr-pow_binary64_395`
1×	`cos-2_binary64_565` `pow-prod-down_binary64_494` `div-sub_binary64_428` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `associate-/r*_binary64_367`

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)))
11.0ms	(.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))

series325.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
105.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
47.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
45.0ms	(*.f64 x (pow.f64 s 2))

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	2214
1	4946	2214

prune326.0ms (4.7%)

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 6147 to 3688 computations (40% 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_484` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
14×	`add-sqr-sqrt_binary64_445`
12×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
9×	`associate-l_binary64_364`
8×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
7×	`pow-prod-down_binary64_494`
5×	`associate-r_binary64_363`
4×	`add-log-exp_binary64_462`
3×	`times-frac_binary64_429` `swap-sqr_binary64_390` `-commutative_binary64_354` `associate-/l_binary64_368`
2×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
1×	`cos-2_binary64_565` `pow-sqr_binary64_396` `sqr-abs_binary64_438` `pow-prod-up_binary64_493` `div-sub_binary64_428` `pow-plus_binary64_486` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `unswap-sqr_binary64_391` `associate-/r*_binary64_367` `pow2_binary64_504`

Counts

4 → 84

Calls

4 calls:

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

series347.0ms (5%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
53.0ms	(.f64 s (.f64 c x))
49.0ms	(.f64 s (.f64 c x))
44.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4976	1306
1	4976	1306

prune523.0ms (7.5%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	85	11	96
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	91	16	107

Merged error: 1.0b

Counts

107 → 16

Compiler

Compiled 9979 to 6227 computations (37.6% 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))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_429`
56×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-sqr-sqrt_binary64_445`
21×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
16×	`associate-/l*_binary64_368`
14×	`pow1_binary64_484`
6×	`pow-prod-down_binary64_494` `associate-l_binary64_364` `prod-exp_binary64_472` `div-inv_binary64_420` `associate-/r*_binary64_367` `cbrt-unprod_binary64_456`
4×	`add-log-exp_binary64_462` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`-commutative_binary64_354` `clear-num_binary64_422` `associate-r*_binary64_363` `frac-2neg_binary64_434`
1×	`associate-/l/_binary64_370`

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))))

series411.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
113.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
53.0ms	(.f64 s (.f64 c x))
52.0ms	(.f64 s (.f64 c x))

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4977	4039
1	4977	4039

prune429.0ms (6.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	7	8	15
Picked	0	1	1
Done	0	0	0
Total	144	17	161

Merged error: 1.0b

Counts

161 → 17

Compiler

Compiled 8946 to 4911 computations (45.1% 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_484`
14×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
10×	`add-sqr-sqrt_binary64_445`
8×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
6×	`pow-prod-down_binary64_494` `associate-l_binary64_364` `sqrt-prod_binary64_439` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
4×	`add-log-exp_binary64_462`
2×	`rem-sqrt-square_binary64_436` `-commutative_binary64_354` `associate-r*_binary64_363` `pow1/2_binary64_503` `sqrt-pow1_binary64_441`

Counts

4 → 62

Calls

4 calls:

6.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
2.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series176.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 s (.f64 c x))
45.0ms	(.f64 s (.f64 c x))
43.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))
41.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4996	752
1	4996	752

prune81.0ms (1.2%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	74	17	91

Merged error: 1.0b

Counts

91 → 17

Compiler

Compiled 2390 to 741 computations (69% saved)

regimes148.0ms (2.1%)

Compiler: Compiled 1688 to 1144 computations (32.2% 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%)

sample2.3s (33.1%)

Algorithm

1×

intervals

Results

580.0ms	6144×	body	128	valid
371.0ms	958×	body	1024	valid
311.0ms	1880×	body	128	invalid
152.0ms	562×	body	512	valid
79.0ms	202×	body	1024	invalid
65.0ms	332×	body	256	valid
56.0ms	221×	body	512	invalid
25.0ms	145×	body	256	invalid
3.0ms	4×	body	2048	valid

Compiler

Compiled 454 to 308 computations (32.2% saved)

Details

analyze1.0s (14.4%)

sample57.0ms (0.8%)

simplify341.0ms (4.9%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite48.0ms (0.7%)

series325.0ms (4.6%)

simplify87.0ms (1.2%)

prune326.0ms (4.7%)

localize11.0ms (0.2%)

rewrite28.0ms (0.4%)

series347.0ms (5%)

simplify65.0ms (0.9%)

prune523.0ms (7.5%)

localize11.0ms (0.2%)

rewrite37.0ms (0.5%)

series411.0ms (5.9%)

simplify90.0ms (1.3%)

prune429.0ms (6.1%)

localize15.0ms (0.2%)

rewrite20.0ms (0.3%)

series176.0ms (2.5%)

simplify76.0ms (1.1%)

prune81.0ms (1.2%)

regimes148.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (33.1%)

Profiling