Details

analyze1.1s (5.9%)

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)

sample93.0ms (0.5%)

Algorithm

1×

intervals

Results

20.0ms	63×	body	1024	valid
16.0ms	51×	body	1024	invalid
11.0ms	147×	body	128	valid
8.0ms	35×	body	512	valid
5.0ms	24×	body	512	invalid
2.0ms	11×	body	256	valid
2.0ms	11×	body	256	invalid
2.0ms	21×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune10.0ms (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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 th)
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))

rewrite173.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

41×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
33×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`pow1_binary64_480` `add-log-exp_binary64_458` `associate-/r*_binary64_363`
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

4 → 101

Calls

4 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))
1.0ms	(cos.f64 th)

Compiler

Compiled 2216 to 800 computations (63.9% saved)

series1.1s (6%)

Error

0.4b

Counts

4 → 48

Calls

4 calls:

650.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
297.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
139.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
20.0ms	(cos.f64 th)

Compiler

Compiled 1530 to 1388 computations (9.3% saved)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4967	3100
1	4967	3100

prune153.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	10	149
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Error

Counts

151 → 12

Compiler

Compiled 2273 to 969 computations (57.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.6s (8.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1137×	`sqrt-prod_binary64_435`
1119×	`times-frac_binary64_425`
625×	`add-sqr-sqrt_binary64_441`
578×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
283×	`associate-r_binary64_359`
34×	`associate-/l*_binary64_364`
22×	`div-inv_binary64_416`
20×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
18×	`associate-/r*_binary64_363`
13×	`unswap-sqr_binary64_387`
7×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
3×	`associate-/l/_binary64_366` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393`
1×	`pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 713

Calls

4 calls:

84.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
25.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 18034 to 10006 computations (44.5% saved)

series1.5s (8%)

Error

Counts

4 → 54

Calls

4 calls:

660.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
386.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
294.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
136.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1912 to 1814 computations (5.1% saved)

simplify302.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

767 → 767

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4970	26923
1	4970	26923

prune539.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	765	2	767
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	772	7	779

Error

Counts

779 → 7

Compiler

Compiled 8819 to 4568 computations (48.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.4b	(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
1.0b	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))
1.0b	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite2.1s (11.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1116×	`sqrt-prod_binary64_435`
1098×	`times-frac_binary64_425`
581×	`add-sqr-sqrt_binary64_441`
579×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
286×	`associate-r_binary64_359`
54×	`add-exp-log_binary64_457`
34×	`add-cbrt-cube_binary64_455` `associate-/l*_binary64_364`
25×	`pow1_binary64_480`
22×	`div-inv_binary64_416`
20×	`sqrt-pow1_binary64_437` `div-exp_binary64_470`
18×	`associate-/r*_binary64_363`
16×	`prod-exp_binary64_468`
14×	`pow-flip_binary64_493`
10×	`pow-div_binary64_494` `pow1/2_binary64_499` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452`
8×	`associate-*l/_binary64_362`
4×	`1-exp_binary64_463` `rec-exp_binary64_469` `add-log-exp_binary64_458` `pow-prod-down_binary64_490` `associate-l_binary64_360`
3×	`flip3-+_binary64_422` `flip-+_binary64_393`
2×	`inv-pow_binary64_504` `frac-2neg_binary64_430` `clear-num_binary64_418` `frac-times_binary64_429` `*-commutative_binary64_350`
1×	`associate-/l/_binary64_366` `associate-*r/_binary64_361` `unswap-sqr_binary64_387`

Counts

4 → 740

Calls

4 calls:

72.0ms	(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
18.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
5.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 17083 to 11746 computations (31.2% saved)

series1.8s (9.3%)

Error

Counts

4 → 36

Calls

4 calls:

1.1s	(.f64 (.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (cos.f64 th)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
648.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 1720 to 1546 computations (10.1% saved)

simplify448.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

776 → 776

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5141	20639

prune821.0ms (4.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	776	0	776
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	776	7	783

Error

Counts

783 → 7

Compiler

Compiled 7352 to 4752 computations (35.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 th)
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))

rewrite95.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`add-sqr-sqrt_binary64_441`
11×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
10×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
6×	`pow1_binary64_480` `add-log-exp_binary64_458` `times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
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

4 → 67

Calls

4 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))
4.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
1.0ms	(cos.f64 th)

Compiler

Compiled 1401 to 435 computations (69% saved)

series1.5s (7.8%)

Error

Counts

4 → 54

Calls

4 calls:

647.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
548.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
202.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))
29.0ms	(cos.f64 th)

Compiler

Compiled 1877 to 1663 computations (11.4% saved)

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5034	2157

prune137.0ms (0.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	121	7	128

Error

Counts

128 → 7

Compiler

Compiled 1475 to 584 computations (60.4% saved)

regimes2.5s (12.9%)

Accuracy

Total 0.4b remaining (91.3%)

Threshold costs 0.4b (91.3%)

Compiler

Compiled 21077 to 16233 computations (23% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	43
1	24	43

end11.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 78 to 72 computations (7.7% saved)

sample2.7s (14.5%)

Algorithm

1×

intervals

Results

603.0ms	1791×	body	1024	valid
504.0ms	1577×	body	1024	invalid
373.0ms	4821×	body	128	valid
222.0ms	949×	body	512	valid
189.0ms	792×	body	512	invalid
71.0ms	437×	body	256	valid
57.0ms	364×	body	256	invalid
56.0ms	652×	body	128	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 188 to 164 computations (12.8% saved)

Details

analyze1.1s (5.9%)

sample93.0ms (0.5%)

simplify9.0ms (0%)

prune10.0ms (0.1%)

localize11.0ms (0.1%)

rewrite173.0ms (0.9%)

series1.1s (6%)

simplify91.0ms (0.5%)

prune153.0ms (0.8%)

localize13.0ms (0.1%)

rewrite1.6s (8.2%)

series1.5s (8%)

simplify302.0ms (1.6%)

prune539.0ms (2.8%)

localize14.0ms (0.1%)

rewrite2.1s (11.3%)

series1.8s (9.3%)

simplify448.0ms (2.4%)

prune821.0ms (4.3%)

localize10.0ms (0.1%)

rewrite95.0ms (0.5%)

series1.5s (7.8%)

simplify84.0ms (0.4%)

prune137.0ms (0.7%)

regimes2.5s (12.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end11.0ms (0.1%)

sample2.7s (14.5%)

Profiling