Details

analyze738.0ms (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)

sample84.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	57×	body	1024	valid
17.0ms	51×	body	1024	invalid
15.0ms	156×	body	128	valid
7.0ms	31×	body	512	invalid
6.0ms	27×	body	512	valid
2.0ms	16×	body	256	valid
2.0ms	13×	body	256	invalid
2.0ms	22×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify176.0ms (1.2%)

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

Merged error: 0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 83

Calls

2 calls:

17.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
9.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series435.0ms (3%)

Counts

2 → 6

Calls

2 calls:

330.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
104.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5678	2187

prune113.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	8	91

Merged error: 0.0b

Counts

91 → 8

Compiler

Compiled 2181 to 855 computations (60.8% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(.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)) (sqrt.f64 2))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_441`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
4×	`associate-*l/_binary64_362` `pow1_binary64_480`
3×	`associate-r_binary64_359` `associate-l_binary64_360`
2×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `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` `div-inv_binary64_416` `unswap-sqr_binary64_387` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

2 → 49

Calls

2 calls:

10.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
8.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))

series400.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

245.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
154.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5265	1100

prune62.0ms (0.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 0.0b

Counts

63 → 8

Compiler

Compiled 1207 to 477 computations (60.5% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b

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

0.2b

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))

0.3b

(/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite267.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 702

Calls

3 calls:

92.0ms

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

22.0ms

(/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

10.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))

series614.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

328.0ms

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

172.0ms

(/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))

113.0ms

(/.f64 (/.f64 (+.f64 (*.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

simplify290.0ms (2%)

Algorithm

1×	egg-herbie

Counts

711 → 711

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4956	25973
1	4956	25973

prune1.4s (9.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	708	3	711
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	712	7	719

Merged error: 0b

Counts

719 → 7

Compiler

Compiled 23689 to 11678 computations (50.7% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2))))
0.4b	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.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 (cbrt.f64 (sqrt.f64 2))))

rewrite424.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

1597×	`times-frac_binary64_425`
1571×	`sqrt-prod_binary64_435`
994×	`add-sqr-sqrt_binary64_441`
793×	`*-un-lft-identity_binary64_419`
769×	`add-cube-cbrt_binary64_454`
406×	`cbrt-prod_binary64_450`
376×	`associate-r_binary64_359`
58×	`unswap-sqr_binary64_387`
54×	`add-exp-log_binary64_457`
37×	`associate-/l*_binary64_364`
34×	`add-cbrt-cube_binary64_455`
30×	`div-inv_binary64_416`
26×	`div-exp_binary64_470`
24×	`associate-/r*_binary64_363`
14×	`cbrt-undiv_binary64_453`
13×	`associate-l_binary64_360`
10×	`prod-exp_binary64_468` `pow1_binary64_480`
7×	`pow-flip_binary64_493` `sqrt-pow1_binary64_437`
6×	`cbrt-unprod_binary64_452`
4×	`1-exp_binary64_463` `add-log-exp_binary64_458` `rec-exp_binary64_469`
3×	`clear-num_binary64_418` `pow1/2_binary64_499` `frac-2neg_binary64_430` `associate-/l/_binary64_366`
2×	`pow1/3_binary64_501` `pow-div_binary64_494`
1×	`flip3-+_binary64_422` `associate-l/_binary64_362` `pow-prod-down_binary64_490` `inv-pow_binary64_504` `frac-times_binary64_429` `associate-r/_binary64_361` `*-commutative_binary64_350` `flip-+_binary64_393`

Counts

4 → 997

Calls

4 calls:

165.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
24.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2))))
6.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

series558.0ms (3.8%)

Counts

4 → 8

Calls

4 calls:

452.0ms	(.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2)))) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2)))))
106.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (fabs.f64 (cbrt.f64 (sqrt.f64 2))))
0.0ms	(/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (sqrt.f64 2))))
0.0ms	(/.f64 1 (sqrt.f64 (sqrt.f64 2)))

simplify366.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1005 → 1005

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4965	38537
1	4965	38537

prune4.2s (28.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	1005	0	1005
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	1005	7	1012

Merged error: 0b

Counts

1012 → 7

Compiler

Compiled 38938 to 29177 computations (25.1% saved)

regimes808.0ms (5.5%)

Compiler: Compiled 10162 to 7583 computations (25.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	43
1	24	43

end0.0ms (0%)

sample3.5s (23.6%)

Algorithm

1×

intervals

Results

603.0ms	1790×	body	1024	valid
510.0ms	1499×	body	1024	invalid
356.0ms	4859×	body	128	valid
215.0ms	919×	body	512	valid
159.0ms	720×	body	512	invalid
69.0ms	428×	body	256	valid
63.0ms	420×	body	256	invalid
52.0ms	651×	body	128	invalid
2.0ms	4×	body	2048	valid

Compiler

Compiled 1301 to 974 computations (25.1% saved)

Details

analyze738.0ms (5%)

sample84.0ms (0.6%)

simplify176.0ms (1.2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite34.0ms (0.2%)

series435.0ms (3%)

simplify55.0ms (0.4%)

prune113.0ms (0.8%)

localize10.0ms (0.1%)

rewrite22.0ms (0.1%)

series400.0ms (2.7%)

simplify68.0ms (0.5%)

prune62.0ms (0.4%)

localize13.0ms (0.1%)

rewrite267.0ms (1.8%)

series614.0ms (4.2%)

simplify290.0ms (2%)

prune1.4s (9.6%)

localize21.0ms (0.1%)

rewrite424.0ms (2.9%)

series558.0ms (3.8%)

simplify366.0ms (2.5%)

prune4.2s (28.8%)

regimes808.0ms (5.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.5s (23.6%)

Profiling