Details

analyze1.3s (7.5%)

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

Symmetry

(sort a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample115.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	64×	body	1024	valid
17.0ms	45×	body	1024	invalid
14.0ms	31×	body	512	valid
13.0ms	143×	body	128	valid
8.0ms	22×	body	512	invalid
3.0ms	18×	body	256	valid
3.0ms	27×	body	128	invalid
2.0ms	9×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune8.0ms (0%)

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

Error

0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.1b	(.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))

rewrite179.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `flip3-+_binary64_422` `associate-/l/_binary64_366` `flip-+_binary64_393` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 94

Calls

3 calls:

12.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series912.0ms (5.4%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

528.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
221.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
119.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1676 to 1476 computations (11.9% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5044	2993

prune180.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	130	8	138

Error

0.0b

Counts

138 → 8

Compiler

Compiled 2928 to 1188 computations (59.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
9.2b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite708.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

149×	`add-sqr-sqrt_binary64_441`
146×	`times-frac_binary64_425`
127×	`sqrt-prod_binary64_435`
90×	`cbrt-prod_binary64_450`
87×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
58×	`associate-r_binary64_359`
27×	`add-exp-log_binary64_457`
21×	`unswap-sqr_binary64_387`
19×	`add-cbrt-cube_binary64_455`
10×	`associate-l_binary64_360`
9×	`associate-/r*_binary64_363`
8×	`pow1_binary64_480` `div-exp_binary64_470` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cbrt-undiv_binary64_453`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `div-inv_binary64_416`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `frac-times_binary64_429` `associate-l/_binary64_362` `associate-r/_binary64_361` `*-commutative_binary64_350` `frac-2neg_binary64_430` `clear-num_binary64_418`

Counts

4 → 226

Calls

4 calls:

41.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 11015 to 4717 computations (57.2% saved)

series853.0ms (5%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

322.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2)))
232.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (cbrt.f64 (sqrt.f64 2))))
126.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
102.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3771 to 3005 computations (20.3% saved)

simplify192.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4954	9022
1	4954	9022

prune579.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	273	9	282

Error

0.0b

Counts

282 → 9

Compiler

Compiled 10834 to 5131 computations (52.6% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite96.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

11×	`add-sqr-sqrt_binary64_441`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
6×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
5×	`pow1_binary64_480` `add-log-exp_binary64_458`
4×	`associate-*l/_binary64_362`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-l_binary64_360` `associate-r_binary64_359`
2×	`prod-exp_binary64_468` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452` `associate-/l/_binary64_366`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

3 → 60

Calls

3 calls:

9.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
5.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1347 to 424 computations (68.5% saved)

series966.0ms (5.7%)

Error

0.0b

Counts

3 → 48

Calls

3 calls:

501.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
305.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
110.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2074 to 1778 computations (14.3% saved)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4967	2050
1	4967	2050

prune113.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	108	9	117

Error

Counts

117 → 9

Compiler

Compiled 2055 to 832 computations (59.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite410.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 155

Calls

4 calls:

35.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
13.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
5.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 5230 to 3057 computations (41.5% saved)

series1.6s (9.2%)

Error

Counts

4 → 48

Calls

4 calls:

727.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
480.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2))))
180.0ms	(/.f64 (cos.f64 th) (cbrt.f64 (sqrt.f64 2)))
104.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2836 to 2569 computations (9.4% saved)

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4984	5234
1	4984	5234

prune356.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	3	3	6
Picked	1	0	1
Done	1	1	2
Total	205	7	212

Error

Counts

212 → 7

Compiler

Compiled 5460 to 3141 computations (42.5% saved)

regimes2.1s (12.1%)

Accuracy

Total 0.4b remaining (93.2%)

Threshold costs 0.4b (93.2%)

Compiler

Compiled 21379 to 15925 computations (25.5% saved)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	52
1	19	52

Remove

(sort a1 a2)

Compiler

Compiled 64 to 44 computations (31.3% saved)

end0.0ms (0%)

sample6.0s (35.4%)

Algorithm

1×

intervals

Results

716.0ms	1838×	body	1024	valid
615.0ms	4815×	body	128	valid
589.0ms	1517×	body	1024	invalid
242.0ms	887×	body	512	valid
207.0ms	761×	body	512	invalid
83.0ms	456×	body	256	valid
71.0ms	672×	body	128	invalid
62.0ms	341×	body	256	invalid
2.0ms	4×	body	2048	valid

Compiler

Compiled 2704 to 2010 computations (25.7% saved)

Details

analyze1.3s (7.5%)

sample115.0ms (0.7%)

simplify17.0ms (0.1%)

prune8.0ms (0%)

localize18.0ms (0.1%)

rewrite179.0ms (1.1%)

series912.0ms (5.4%)

simplify83.0ms (0.5%)

prune180.0ms (1.1%)

localize16.0ms (0.1%)

rewrite708.0ms (4.2%)

series853.0ms (5%)

simplify192.0ms (1.1%)

prune579.0ms (3.4%)

localize17.0ms (0.1%)

rewrite96.0ms (0.6%)

series966.0ms (5.7%)

simplify103.0ms (0.6%)

prune113.0ms (0.7%)

localize13.0ms (0.1%)

rewrite410.0ms (2.4%)

series1.6s (9.2%)

simplify122.0ms (0.7%)

prune356.0ms (2.1%)

regimes2.1s (12.1%)

bsearch0.0ms (0%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample6.0s (35.4%)

Profiling