Details

analyze948.0ms (10%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample80.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	45×	body	1024	valid
14.0ms	41×	body	1024	invalid
11.0ms	153×	body	128	valid
9.0ms	38×	body	512	valid
8.0ms	33×	body	512	invalid
3.0ms	20×	body	256	valid
3.0ms	34×	body	128	invalid
1.0ms	8×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify183.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 2

Compiler

Compiled 77 to 63 computations (18.2% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite30.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_445`
38×	`times-frac_binary64_429`
31×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
22×	`sqrt-prod_binary64_439` `associate-r_binary64_363`
9×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`associate-/r*_binary64_367`
4×	`pow1_binary64_484`
3×	`associate-l_binary64_364` `unswap-sqr_binary64_391` `associate-/l*_binary64_368`
2×	`prod-exp_binary64_472` `associate-/l/_binary64_370` `add-log-exp_binary64_462` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `flip-+_binary64_397` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434`

Counts

2 → 83

Calls

2 calls:

14.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series449.0ms (4.7%)

Counts

2 → 6

Calls

2 calls:

345.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
104.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify55.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5678	2187

prune435.0ms (4.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 0.0b

Counts

91 → 10

Compiler

Compiled 8002 to 4831 computations (39.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.7b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite89.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_429`
102×	`sqrt-prod_binary64_439`
86×	`add-sqr-sqrt_binary64_445`
84×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
78×	`cbrt-prod_binary64_454`
58×	`associate-r_binary64_363`
38×	`add-exp-log_binary64_461`
29×	`add-cbrt-cube_binary64_459`
16×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
11×	`pow1_binary64_484`
9×	`associate-/r*_binary64_367` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
6×	`sqrt-div_binary64_440` `associate-/l*_binary64_368`
4×	`add-log-exp_binary64_462`
3×	`pow-prod-down_binary64_494` `flip-+_binary64_397` `associate-*l/_binary64_366` `flip3-+_binary64_426`
2×	`rem-sqrt-square_binary64_436` `associate-/l/_binary64_370` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420`
1×	`frac-times_binary64_433` `associate-l_binary64_364` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434`

Counts

4 → 201

Calls

4 calls:

33.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
13.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
5.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series593.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

264.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cos.f64 th)) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
227.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
51.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
50.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

simplify141.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4949	6988
1	4949	6988

prune451.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	214	9	223

Merged error: 0b

Counts

223 → 9

Compiler

Compiled 9887 to 4716 computations (52.3% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)))

0.2b

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

0.2b

(/.f64 (*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))) (cbrt.f64 (sqrt.f64 2)))

rewrite80.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`times-frac_binary64_429`
86×	`add-sqr-sqrt_binary64_445`
68×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
66×	`unpow-prod-down_binary64_502`
56×	`cbrt-prod_binary64_454`
46×	`associate-r_binary64_363`
34×	`add-exp-log_binary64_461`
28×	`sqrt-prod_binary64_439`
23×	`associate-/r*_binary64_367`
16×	`add-cbrt-cube_binary64_459`
14×	`div-exp_binary64_474`
8×	`prod-exp_binary64_472` `unpow2_binary64_488` `sqr-pow_binary64_395`
7×	`unswap-sqr_binary64_391`
6×	`cbrt-undiv_binary64_457`
5×	`pow1_binary64_484`
4×	`associate-/l*_binary64_368` `cbrt-unprod_binary64_456`
3×	`pow-to-exp_binary64_492` `associate-l_binary64_364` `pow-exp_binary64_491` `associate-/l/_binary64_370` `add-log-exp_binary64_462` `div-inv_binary64_420`
2×	`associate-*r/_binary64_365` `clear-num_binary64_422` `frac-2neg_binary64_434`
1×	`pow-prod-down_binary64_494` `flip-+_binary64_397` `*-commutative_binary64_354` `flip3-+_binary64_426`

Counts

3 → 185

Calls

3 calls:

25.0ms

(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)))

17.0ms

(/.f64 (*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))) (cbrt.f64 (sqrt.f64 2)))

12.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

series1.4s (14.4%)

Counts

3 → 9

Calls

3 calls:

673.0ms

(*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2)))

349.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))

343.0ms

(/.f64 (*.f64 (cos.f64 th) (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (pow.f64 (cbrt.f64 (sqrt.f64 2)) 2))) (cbrt.f64 (sqrt.f64 2)))

simplify96.0ms (1%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4950	5765
1	4950	5765

prune431.0ms (4.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	197	6	203

Merged error: 0b

Counts

203 → 6

Compiler

Compiled 8013 to 4720 computations (41.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b

(*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)))

0.2b

(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))

0.5b

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_461`
17×	`add-sqr-sqrt_binary64_445`
16×	`cbrt-prod_binary64_454`
13×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-cbrt-cube_binary64_459`
10×	`pow1_binary64_484`
9×	`times-frac_binary64_429` `associate-/r*_binary64_367`
7×	`prod-exp_binary64_472` `associate-r_binary64_363` `cbrt-unprod_binary64_456`
6×	`associate-l_binary64_364` `sqrt-prod_binary64_439` `associate-*l/_binary64_366`
4×	`pow-prod-down_binary64_494` `associate-*r/_binary64_365`
3×	`flip-+_binary64_397` `flip3-+_binary64_426` `add-log-exp_binary64_462` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`associate-/l/_binary64_370` `*-commutative_binary64_354` `unswap-sqr_binary64_391`
1×	`clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `associate-/l*_binary64_368`

Counts

3 → 81

Calls

3 calls:

13.0ms

(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))

10.0ms

(*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)))

9.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

series989.0ms (10.4%)

Counts

3 → 9

Calls

3 calls:

644.0ms

(/.f64 (*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 2)))

267.0ms

(*.f64 (cos.f64 th) (*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)))

77.0ms

(*.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4963	2177
1	4963	2177

prune147.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	90	6	96

Merged error: 0b

Counts

96 → 6

Compiler

Compiled 2686 to 1585 computations (41% saved)

regimes103.0ms (1.1%)

Compiler: Compiled 862 to 714 computations (17.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	27
1	19	27

end0.0ms (0%)

sample2.6s (27.8%)

Algorithm

1×

intervals

Results

617.0ms	1798×	body	1024	valid
548.0ms	1565×	body	1024	invalid
374.0ms	4884×	body	128	valid
202.0ms	869×	body	512	valid
191.0ms	819×	body	512	invalid
68.0ms	443×	body	256	valid
59.0ms	369×	body	256	invalid
52.0ms	629×	body	128	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 177 to 146 computations (17.5% saved)

Details

analyze948.0ms (10%)

sample80.0ms (0.8%)

simplify183.0ms (1.9%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite30.0ms (0.3%)

series449.0ms (4.7%)

simplify55.0ms (0.6%)

prune435.0ms (4.6%)

localize16.0ms (0.2%)

rewrite89.0ms (0.9%)

series593.0ms (6.3%)

simplify141.0ms (1.5%)

prune451.0ms (4.8%)

localize16.0ms (0.2%)

rewrite80.0ms (0.8%)

series1.4s (14.4%)

simplify96.0ms (1%)

prune431.0ms (4.5%)

localize14.0ms (0.1%)

rewrite40.0ms (0.4%)

series989.0ms (10.4%)

simplify76.0ms (0.8%)

prune147.0ms (1.6%)

regimes103.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (27.8%)

Profiling