Details

analyze987.0ms (12.7%)

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)

sample56.0ms (0.7%)

Algorithm

1×

intervals

Results

18.0ms	208×	body	128	valid
11.0ms	27×	body	1024	valid
5.0ms	60×	body	128	invalid
4.0ms	17×	body	512	valid
2.0ms	5×	body	1024	invalid
2.0ms	8×	body	512	invalid
1.0ms	5×	body	256	invalid
1.0ms	4×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify338.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (163.0ms)

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: 25.9b

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)))
4.3b	(.f64 (.f64 x (pow.f64 s 2)) x)
8.5b	(*.f64 x (pow.f64 s 2))
16.3b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite51.0ms (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))
7.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))

series327.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
103.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))
46.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
45.0ms	(*.f64 x (pow.f64 s 2))

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	2214
1	4946	2214

prune378.0ms (4.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	119	12	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Merged error: 1.0b

Counts

132 → 12

Compiler

Compiled 7225 to 4425 computations (38.8% saved)

localize10.0ms (0.1%)

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)))))
4.7b	(.f64 s (.f64 c x))
4.7b	(.f64 s (.f64 c x))

rewrite29.0ms (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:

7.0ms	(/.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))))

series340.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
49.0ms	(.f64 s (.f64 c x))
47.0ms	(.f64 s (.f64 c x))
41.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))

simplify63.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4976	1306
1	4976	1306

prune533.0ms (6.8%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	86	10	96
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	90	18	108

Merged error: 0.6b

Counts

108 → 18

Compiler

Compiled 10284 to 6563 computations (36.2% saved)

localize12.0ms (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))))
0.5b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
4.7b	(.f64 s (.f64 c x))
4.7b	(.f64 s (.f64 c x))

rewrite36.0ms (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))))

series420.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
116.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
52.0ms	(.f64 s (.f64 c x))
45.0ms	(.f64 s (.f64 c x))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4977	4039
1	4977	4039

prune604.0ms (7.7%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	136	9	145
Fresh	8	9	17
Picked	1	0	1
Done	0	0	0
Total	145	18	163

Merged error: 0.6b

Counts

163 → 18

Compiler

Compiled 12232 to 7308 computations (40.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
4.7b	(.f64 s (.f64 c x))
4.7b	(.f64 s (.f64 c x))
12.5b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_445`
23×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
21×	`times-frac_binary64_429`
19×	`add-exp-log_binary64_461`
16×	`add-cbrt-cube_binary64_459`
15×	`pow1_binary64_484`
12×	`unpow-prod-down_binary64_502`
7×	`associate-/r*_binary64_367`
6×	`pow-prod-down_binary64_494` `associate-l_binary64_364` `prod-exp_binary64_472` `cbrt-unprod_binary64_456`
4×	`add-log-exp_binary64_462` `sqr-pow_binary64_395`
3×	`sqrt-prod_binary64_439` `associate-/l*_binary64_368` `div-exp_binary64_474`
2×	`-commutative_binary64_354` `associate-r*_binary64_363`
1×	`pow-to-exp_binary64_492` `pow-exp_binary64_491` `rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457`

Counts

4 → 94

Calls

4 calls:

6.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series557.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

412.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
59.0ms	(.f64 s (.f64 c x))
44.0ms	(.f64 s (.f64 c x))
42.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5148	2146

prune399.0ms (5.1%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	4	13	17
Picked	0	1	1
Done	0	0	0
Total	106	18	124

Merged error: 0.5b

Counts

124 → 18

Compiler

Compiled 5489 to 2942 computations (46.4% saved)

regimes158.0ms (2%)

Compiler: Compiled 1651 to 1181 computations (28.5% 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%)

sample2.2s (28%)

Algorithm

1×

intervals

Results

559.0ms	6094×	body	128	valid
368.0ms	942×	body	1024	valid
188.0ms	673×	body	512	valid
169.0ms	1914×	body	128	invalid
91.0ms	236×	body	1024	invalid
52.0ms	288×	body	256	valid
52.0ms	210×	body	512	invalid
30.0ms	162×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 438 to 311 computations (29% saved)

Details

analyze987.0ms (12.7%)

sample56.0ms (0.7%)

simplify338.0ms (4.3%)

prune3.0ms (0%)

localize13.0ms (0.2%)

rewrite51.0ms (0.7%)

series327.0ms (4.2%)

simplify86.0ms (1.1%)

prune378.0ms (4.9%)

localize10.0ms (0.1%)

rewrite29.0ms (0.4%)

series340.0ms (4.4%)

simplify63.0ms (0.8%)

prune533.0ms (6.8%)

localize12.0ms (0.2%)

rewrite36.0ms (0.5%)

series420.0ms (5.4%)

simplify87.0ms (1.1%)

prune604.0ms (7.7%)

localize17.0ms (0.2%)

rewrite27.0ms (0.4%)

series557.0ms (7.1%)

simplify81.0ms (1%)

prune399.0ms (5.1%)

regimes158.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (28%)

Profiling