Details

analyze963.0ms (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

Symmetry

sort(a1 a2)

Compiler

Compiled 20 to 16 computations (20% saved)

sample87.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	55×	body	1024	valid
16.0ms	44×	body	1024	invalid
10.0ms	146×	body	128	valid
8.0ms	36×	body	512	valid
6.0ms	26×	body	512	invalid
3.0ms	19×	body	256	valid
2.0ms	26×	body	128	invalid
2.0ms	12×	body	256	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

prune4.0ms (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

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize9.0ms (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))

rewrite155.0ms (1.3%)

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)))
7.0ms	(/.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)

series701.0ms (5.8%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

392.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
173.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
92.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1676 to 1476 computations (11.9% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5044	2993

prune146.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	126	10	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

0.0b

Counts

138 → 10

Compiler

Compiled 2978 to 1218 computations (59.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
5.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite263.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

100×	`sqrt-prod_binary64_435`
91×	`add-sqr-sqrt_binary64_441`
80×	`times-frac_binary64_425`
61×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
40×	`associate-r_binary64_359`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`sqrt-div_binary64_436` `unswap-sqr_binary64_387`
8×	`pow1_binary64_480`
6×	`associate-/l_binary64_364` `associate-/r_binary64_363` `associate-l_binary64_360`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`add-log-exp_binary64_458`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `sqrt-undiv_binary64_440` `div-inv_binary64_416` `associate-/l/_binary64_366` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `associate-*l/_binary64_362`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `sqrt-unprod_binary64_439` `associate-r/_binary64_361` `-commutative_binary64_350`

Counts

4 → 168

Calls

4 calls:

24.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
8.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (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 6288 to 1682 computations (73.3% saved)

series531.0ms (4.4%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

174.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
146.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
84.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
83.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2751 to 1985 computations (27.8% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5073	5137

prune236.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	216	10	226

Error

Counts

226 → 10

Compiler

Compiled 6527 to 2161 computations (66.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
5.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.5b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite174.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64_441`
39×	`sqrt-prod_binary64_435`
23×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
17×	`sqrt-div_binary64_436` `associate-r_binary64_359`
15×	`pow1_binary64_480`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`associate-l_binary64_360`
7×	`associate-*r/_binary64_361`
6×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`pow1/2_binary64_499` `add-log-exp_binary64_458` `sqrt-pow1_binary64_437` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-times_binary64_429` `associate-*l/_binary64_362`
3×	`rem-sqrt-square_binary64_432`
2×	`div-inv_binary64_416` `*-commutative_binary64_350`
1×	`sqrt-unprod_binary64_439`

Counts

4 → 110

Calls

4 calls:

17.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3866 to 1050 computations (72.8% saved)

series786.0ms (6.5%)

Error

Counts

4 → 54

Calls

4 calls:

356.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
152.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
124.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
85.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 2904 to 2265 computations (22% saved)

simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4969	4128
1	4969	4128

prune167.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	3	164
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	167	7	174

Error

Counts

174 → 7

Compiler

Compiled 4481 to 1479 computations (67% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
0.3b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)))
5.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.5b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite142.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

33×	`sqrt-prod_binary64_435`
31×	`add-sqr-sqrt_binary64_441`
23×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
13×	`pow1_binary64_480`
12×	`sqrt-div_binary64_436`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
7×	`associate-*r/_binary64_361`
4×	`add-log-exp_binary64_458` `flip3-+_binary64_422` `flip-+_binary64_393` `pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
3×	`rem-sqrt-square_binary64_432`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `div-inv_binary64_416` `frac-times_binary64_429` `associate-l/_binary64_362` `-commutative_binary64_350` `unswap-sqr_binary64_387`

Counts

4 → 100

Calls

4 calls:

18.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)))
8.0ms	(.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
5.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 3424 to 836 computations (75.6% saved)

series815.0ms (6.8%)

Error

Counts

4 → 60

Calls

4 calls:

354.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)))
201.0ms	(.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
117.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
79.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 3787 to 2744 computations (27.5% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4968	3743
1	4968	3743

prune150.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	160	7	167

Error

Counts

167 → 7

Compiler

Compiled 4312 to 1272 computations (70.5% saved)

regimes1.7s (13.9%)

Accuracy

Total 0.3b remaining (99.9%)

Threshold costs 0.3b (99.9%)

Compiler

Compiled 21643 to 15483 computations (28.5% saved)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

Removed

((sort a1 a2))

Compiler

Compiled 44 to 26 computations (40.9% saved)

end0.0ms (0%)

sample4.6s (38.5%)

Algorithm

1×

intervals

Results

537.0ms	1771×	body	1024	valid
494.0ms	1583×	body	1024	invalid
356.0ms	4816×	body	128	valid
203.0ms	923×	body	512	valid
166.0ms	763×	body	512	invalid
71.0ms	485×	body	256	valid
61.0ms	404×	body	256	invalid
50.0ms	657×	body	128	invalid
5.0ms	5×	body	2048	valid

Compiler

Compiled 2730 to 1948 computations (28.6% saved)

Details

analyze963.0ms (8%)

sample87.0ms (0.7%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite155.0ms (1.3%)

series701.0ms (5.8%)

simplify68.0ms (0.6%)

prune146.0ms (1.2%)

localize12.0ms (0.1%)

rewrite263.0ms (2.2%)

series531.0ms (4.4%)

simplify85.0ms (0.7%)

prune236.0ms (2%)

localize13.0ms (0.1%)

rewrite174.0ms (1.4%)

series786.0ms (6.5%)

simplify91.0ms (0.8%)

prune167.0ms (1.4%)

localize11.0ms (0.1%)

rewrite142.0ms (1.2%)

series815.0ms (6.8%)

simplify94.0ms (0.8%)

prune150.0ms (1.2%)

regimes1.7s (13.9%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample4.6s (38.5%)

Profiling