Details

analyze981.0ms (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)

sample107.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	52×	body	1024	valid
20.0ms	48×	body	1024	invalid
15.0ms	149×	body	128	valid
12.0ms	41×	body	512	valid
5.0ms	19×	body	512	invalid
3.0ms	13×	body	256	valid
2.0ms	23×	body	128	invalid
2.0ms	11×	body	256	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify143.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune9.0ms (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)

localize19.0ms (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))

rewrite169.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

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)))
10.0ms	(/.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)

series888.0ms (4.6%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

487.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
219.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
126.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1676 to 1476 computations (11.9% saved)

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5044	2993

prune192.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	131	7	138

Error

Counts

138 → 7

Compiler

Compiled 2871 to 1157 computations (59.7% saved)

localize20.0ms (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)))
0.5b	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
5.9b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
5.9b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite333.0ms (1.7%)

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:

31.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
9.0ms	(/.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)

series896.0ms (4.6%)

Error

Counts

4 → 66

Calls

4 calls:

292.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (sqrt.f64 2))
210.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1))) (sqrt.f64 2)))
156.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
152.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 4050 to 2888 computations (28.7% saved)

simplify122.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5034	5581

prune288.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	234	7	241

Error

Counts

241 → 7

Compiler

Compiled 6939 to 2325 computations (66.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
0.3b	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))
0.7b	(/.f64 (cos.f64 th) (sqrt.f64 2))

rewrite294.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

76×	`times-frac_binary64_425`
70×	`add-sqr-sqrt_binary64_441`
60×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
44×	`sqrt-prod_binary64_435` `associate-l_binary64_360`
32×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
14×	`pow1_binary64_480`
12×	`associate-/r*_binary64_363` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l*_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387`
4×	`add-log-exp_binary64_458` `div-inv_binary64_416`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `associate-l/_binary64_362` `associate-r_binary64_359` `-commutative_binary64_350`

Counts

4 → 168

Calls

4 calls:

11.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
10.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
5.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 4634 to 2439 computations (47.4% saved)

series572.0ms (2.9%)

Error

Counts

4 → 30

Calls

4 calls:

192.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1))
177.0ms	(.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2))
82.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))
76.0ms	(/.f64 (cos.f64 th) (sqrt.f64 2))

Compiler

Compiled 1870 to 1456 computations (22.1% saved)

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5087	3432

prune332.0ms (1.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	198	7	205

Error

Counts

205 → 7

Compiler

Compiled 5223 to 2838 computations (45.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite2.5s (12.9%)

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:

108.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
23.0ms	(/.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)))
8.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 27448 to 15232 computations (44.5% saved)

series1.2s (6.1%)

Error

Counts

4 → 54

Calls

4 calls:

436.0ms	(.f64 (cos.f64 th) (/.f64 (/.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
327.0ms	(/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2)))
222.0ms	(/.f64 (/.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
112.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2486 to 2250 computations (9.5% saved)

simplify376.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

767 → 767

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4970	26923
1	4970	26923

prune2.0s (10.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	766	1	767
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	767	7	774

Error

Counts

774 → 7

Compiler

Compiled 24529 to 12118 computations (50.6% saved)

regimes2.1s (10.8%)

Accuracy

Total 0.3b remaining (99.7%)

Threshold costs 0.3b (99.7%)

Compiler

Compiled 19671 to 14367 computations (27% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample5.7s (29.5%)

Algorithm

1×

intervals

Results

715.0ms	1878×	body	1024	valid
624.0ms	1590×	body	1024	invalid
419.0ms	4751×	body	128	valid
261.0ms	886×	body	512	valid
232.0ms	817×	body	512	invalid
90.0ms	478×	body	256	valid
72.0ms	396×	body	256	invalid
65.0ms	665×	body	128	invalid
4.0ms	7×	body	2048	valid

Compiler

Compiled 2471 to 1798 computations (27.2% saved)

Details

analyze981.0ms (5%)

sample107.0ms (0.5%)

simplify143.0ms (0.7%)

prune9.0ms (0%)

localize19.0ms (0.1%)

rewrite169.0ms (0.9%)

series888.0ms (4.6%)

simplify90.0ms (0.5%)

prune192.0ms (1%)

localize20.0ms (0.1%)

rewrite333.0ms (1.7%)

series896.0ms (4.6%)

simplify122.0ms (0.6%)

prune288.0ms (1.5%)

localize12.0ms (0.1%)

rewrite294.0ms (1.5%)

series572.0ms (2.9%)

simplify83.0ms (0.4%)

prune332.0ms (1.7%)

localize19.0ms (0.1%)

rewrite2.5s (12.9%)

series1.2s (6.1%)

simplify376.0ms (1.9%)

prune2.0s (10.1%)

regimes2.1s (10.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.7s (29.5%)

Profiling