Details

analyze755.0ms (8.5%)

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
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)

sample84.0ms (1%)

Algorithm

1×

intervals

Results

22.0ms	56×	body	1024	valid
18.0ms	52×	body	1024	invalid
13.0ms	165×	body	128	valid
7.0ms	28×	body	512	invalid
6.0ms	26×	body	512	valid
2.0ms	13×	body	256	invalid
1.0ms	18×	body	128	invalid
1.0ms	9×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify178.0ms (2%)

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: 0.4b

Counts

2 → 2

Compiler

Compiled 77 to 63 computations (18.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
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))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_445`
38×	`times-frac_binary64_429`
32×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
22×	`sqrt-prod_binary64_439` `associate-r_binary64_363`
10×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
6×	`associate-/r*_binary64_367`
5×	`pow1_binary64_484` `add-log-exp_binary64_462`
3×	`associate-l_binary64_364` `unswap-sqr_binary64_391` `associate-/l*_binary64_368`
2×	`flip-+_binary64_397` `prod-exp_binary64_472` `associate-/l/_binary64_370` `flip3-+_binary64_426` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `+-commutative_binary64_353` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `sum-log_binary64_514`

Counts

3 → 94

Calls

3 calls:

13.0ms	(.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))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series469.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

324.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
105.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
39.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4965	2380
1	4965	2380

prune483.0ms (5.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0b

Counts

105 → 10

Compiler

Compiled 9187 to 5687 computations (38.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))

rewrite102.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64_429`
111×	`add-sqr-sqrt_binary64_445`
94×	`cbrt-prod_binary64_454`
91×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
67×	`associate-r_binary64_363`
47×	`sqrt-prod_binary64_439`
32×	`add-exp-log_binary64_461`
22×	`div-inv_binary64_420`
20×	`add-cbrt-cube_binary64_459`
12×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
10×	`associate-/l_binary64_368` `associate-/r_binary64_367`
7×	`prod-exp_binary64_472` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
6×	`pow1_binary64_484` `add-log-exp_binary64_462`
3×	`associate-l_binary64_364` `associate-/l/_binary64_370`
2×	`flip-+_binary64_397` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434`
1×	`pow-prod-down_binary64_494` `+-commutative_binary64_353` `associate-r/_binary64_365` `-commutative_binary64_354` `sum-log_binary64_514`

Counts

4 → 225

Calls

4 calls:

32.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
16.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
11.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series826.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
337.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
108.0ms	(/.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2)))
39.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify128.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4923	8061
1	4923	8061

prune447.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	239	8	247

Merged error: 0b

Counts

247 → 8

Compiler

Compiled 8346 to 4849 computations (41.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (cos.f64 th) (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))
0.3b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_445`
22×	`cbrt-prod_binary64_454`
20×	`add-exp-log_binary64_461`
19×	`associate-r_binary64_363`
18×	`*-un-lft-identity_binary64_423` `times-frac_binary64_429` `add-cube-cbrt_binary64_458`
13×	`add-cbrt-cube_binary64_459`
9×	`sqrt-prod_binary64_439` `associate-/r*_binary64_367`
8×	`pow1_binary64_484`
6×	`associate-l_binary64_364` `prod-exp_binary64_472` `add-log-exp_binary64_462` `cbrt-unprod_binary64_456`
4×	`associate-*l/_binary64_366` `cbrt-undiv_binary64_457` `div-exp_binary64_474`
3×	`flip-+_binary64_397` `flip3-+_binary64_426` `unswap-sqr_binary64_391`
2×	`pow-prod-down_binary64_494` `associate-/l/_binary64_370` `*-commutative_binary64_354` `div-inv_binary64_420`
1×	`+-commutative_binary64_353` `associate-r/_binary64_365` `clear-num_binary64_422` `frac-2neg_binary64_434` `associate-/l_binary64_368` `sum-log_binary64_514`

Counts

4 → 103

Calls

4 calls:

14.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))
10.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))
9.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.0s (11.6%)

Counts

4 → 12

Calls

4 calls:

623.0ms	(.f64 (cos.f64 th) (/.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2))))
298.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2)) (cbrt.f64 (sqrt.f64 2)))
68.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))
39.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5007	2633

prune208.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	115	8	123

Merged error: 0b

Counts

123 → 8

Compiler

Compiled 3920 to 2415 computations (38.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th))
0.3b	(/.f64 (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
0.4b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))

rewrite45.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_461`
18×	`add-sqr-sqrt_binary64_445`
16×	`cbrt-prod_binary64_454`
14×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458` `add-cbrt-cube_binary64_459`
11×	`pow1_binary64_484`
10×	`associate-*l/_binary64_366`
9×	`times-frac_binary64_429` `associate-r_binary64_363` `associate-/r*_binary64_367`
7×	`prod-exp_binary64_472` `cbrt-unprod_binary64_456`
6×	`sqrt-prod_binary64_439` `add-log-exp_binary64_462`
4×	`pow-prod-down_binary64_494` `associate-l_binary64_364` `flip-+_binary64_397` `flip3-+_binary64_426`
3×	`cbrt-undiv_binary64_457` `div-exp_binary64_474`
2×	`associate-/l/_binary64_370` `*-commutative_binary64_354` `unswap-sqr_binary64_391`
1×	`+-commutative_binary64_353` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `associate-/l*_binary64_368` `sum-log_binary64_514`

Counts

4 → 92

Calls

4 calls:

13.0ms	(/.f64 (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
10.0ms	(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th))
9.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series765.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

468.0ms	(/.f64 (.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th)) (cbrt.f64 (sqrt.f64 2)))
189.0ms	(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 1/2)) (cos.f64 th))
71.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cbrt.f64 1/2))
37.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4970	2353
1	4970	2353

prune127.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	104	8	112

Merged error: 0b

Counts

112 → 8

Compiler

Compiled 2542 to 1365 computations (46.3% saved)

regimes158.0ms (1.8%)

Compiler: Compiled 1430 to 1166 computations (18.5% 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%)

sample2.7s (30.3%)

Algorithm

1×

intervals

Results

642.0ms	1759×	body	1024	valid
542.0ms	1517×	body	1024	invalid
374.0ms	4891×	body	128	valid
214.0ms	889×	body	512	valid
184.0ms	774×	body	512	invalid
75.0ms	455×	body	256	valid
64.0ms	409×	body	256	invalid
57.0ms	632×	body	128	invalid
4.0ms	6×	body	2048	valid

Compiler

Compiled 207 to 169 computations (18.4% saved)

Details

analyze755.0ms (8.5%)

sample84.0ms (1%)

simplify178.0ms (2%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite35.0ms (0.4%)

series469.0ms (5.3%)

simplify71.0ms (0.8%)

prune483.0ms (5.5%)

localize17.0ms (0.2%)

rewrite102.0ms (1.1%)

series826.0ms (9.3%)

simplify128.0ms (1.4%)

prune447.0ms (5%)

localize15.0ms (0.2%)

rewrite51.0ms (0.6%)

series1.0s (11.6%)

simplify85.0ms (1%)

prune208.0ms (2.3%)

localize15.0ms (0.2%)

rewrite45.0ms (0.5%)

series765.0ms (8.6%)

simplify65.0ms (0.7%)

prune127.0ms (1.4%)

regimes158.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (30.3%)

Profiling