Details

analyze835.0ms (10.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	279	80
1	279	80
0	3	3
1	3	3

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)

sample76.0ms (1%)

Algorithm

1×

intervals

Results

16.0ms	54×	body	1024	valid
13.0ms	143×	body	128	valid
13.0ms	43×	body	1024	invalid
8.0ms	39×	body	512	valid
5.0ms	24×	body	512	invalid
3.0ms	20×	body	256	valid
2.0ms	14×	body	256	invalid
2.0ms	21×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune5.0ms (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 45 to 37 computations (17.8% saved)

localize10.0ms (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))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
22×	`associate-r_binary64_359` `sqrt-prod_binary64_435`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`associate-/r*_binary64_363`
5×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `+-commutative_binary64_349`

Counts

3 → 94

Calls

3 calls:

15.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series245.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

171.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
54.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
20.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify75.0ms (1%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4977	2380
1	4977	2380

prune125.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	96	9	105

Merged error: 0b

Counts

105 → 9

Compiler

Compiled 2469 to 981 computations (60.3% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_419` `add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
13×	`add-cube-cbrt_binary64_454`
12×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`associate-r_binary64_359` `pow1_binary64_480`
4×	`div-inv_binary64_416` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
3×	`add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `associate-l*_binary64_360`
2×	`clear-num_binary64_418` `frac-2neg_binary64_430` `associate-/l*_binary64_364`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `frac-add_binary64_427` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `distribute-lft-out_binary64_370` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `flip-+_binary64_393` `distribute-rgt-out_binary64_372`

Counts

3 → 79

Calls

3 calls:

15.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
6.0ms	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
5.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

series255.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

179.0ms	(.f64 (cos.f64 th) (+.f64 (/.f64 (.f64 a1 a1) (sqrt.f64 2)) (/.f64 (*.f64 a2 a2) (sqrt.f64 2))))
38.0ms	(/.f64 (*.f64 a1 a1) (sqrt.f64 2))
37.0ms	(/.f64 (*.f64 a2 a2) (sqrt.f64 2))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4967	1406
1	4967	1406

prune101.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Merged error: 0b

Counts

97 → 9

Compiler

Compiled 2029 to 1197 computations (41% 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)) (.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)))

rewrite90.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64_425`
111×	`add-sqr-sqrt_binary64_441`
94×	`cbrt-prod_binary64_450`
91×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
67×	`associate-r_binary64_359`
47×	`sqrt-prod_binary64_435`
32×	`add-exp-log_binary64_457`
22×	`div-inv_binary64_416`
20×	`add-cbrt-cube_binary64_455`
12×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
10×	`associate-/r_binary64_363` `associate-/l_binary64_364`
7×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`associate-l_binary64_360` `associate-/l/_binary64_366`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `frac-2neg_binary64_430` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `+-commutative_binary64_349`

Counts

4 → 225

Calls

4 calls:

28.0ms	(.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))))
14.0ms	(/.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)))
10.0ms	(/.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))

series394.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
155.0ms	(.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))))
54.0ms	(/.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)))
23.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify116.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5249	8061

prune388.0ms (5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	237	9	246

Merged error: 0b

Counts

246 → 9

Compiler

Compiled 7684 to 4315 computations (43.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
0.6b	(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

rewrite61.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64_441`
70×	`times-frac_binary64_425`
49×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
46×	`cbrt-prod_binary64_450`
32×	`add-exp-log_binary64_457`
31×	`associate-r_binary64_359`
23×	`sqrt-prod_binary64_435`
22×	`add-cbrt-cube_binary64_455`
10×	`associate-/r*_binary64_363` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
9×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`unswap-sqr_binary64_387`
7×	`associate-l_binary64_360`
6×	`add-log-exp_binary64_458` `pow1_binary64_480` `associate-/l*_binary64_364`
4×	`div-inv_binary64_416`
2×	`flip3-+_binary64_422` `clear-num_binary64_418` `frac-2neg_binary64_430` `flip-+_binary64_393` `associate-/l/_binary64_366`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `frac-times_binary64_429` `sum-log_binary64_510` `associate-r/_binary64_361` `*-commutative_binary64_350` `+-commutative_binary64_349`

Counts

4 → 155

Calls

4 calls:

21.0ms	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
8.0ms	(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
8.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series465.0ms (6%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
164.0ms	(/.f64 (cos.f64 th) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
113.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2)))
22.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

simplify118.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4933	4690
1	4933	4690

prune231.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	2	4	6
Picked	1	0	1
Done	1	1	2
Total	169	7	176

Merged error: 0b

Counts

176 → 7

Compiler

Compiled 4893 to 2633 computations (46.2% saved)

regimes675.0ms (8.7%)

Compiler: Compiled 8557 to 6234 computations (27.1% 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%)

sample3.3s (42.4%)

Algorithm

1×

intervals

Results

536.0ms	1768×	body	1024	valid
487.0ms	1585×	body	1024	invalid
368.0ms	4862×	body	128	valid
212.0ms	958×	body	512	valid
171.0ms	791×	body	512	invalid
66.0ms	412×	body	256	valid
59.0ms	706×	body	128	invalid
57.0ms	368×	body	256	invalid

Compiler

Compiled 1091 to 796 computations (27% saved)

Details

analyze835.0ms (10.8%)

sample76.0ms (1%)

simplify9.0ms (0.1%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

rewrite34.0ms (0.4%)

series245.0ms (3.2%)

simplify75.0ms (1%)

prune125.0ms (1.6%)

localize11.0ms (0.1%)

rewrite32.0ms (0.4%)

series255.0ms (3.3%)

simplify87.0ms (1.1%)

prune101.0ms (1.3%)

localize15.0ms (0.2%)

rewrite90.0ms (1.2%)

series394.0ms (5.1%)

simplify116.0ms (1.5%)

prune388.0ms (5%)

localize13.0ms (0.2%)

rewrite61.0ms (0.8%)

series465.0ms (6%)

simplify118.0ms (1.5%)

prune231.0ms (3%)

regimes675.0ms (8.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (42.4%)

Profiling