Details

analyze1.5s (6.2%)

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)

sample149.0ms (0.6%)

Algorithm

1×

intervals

Results

41.0ms	69×	body	1024	valid
27.0ms	39×	body	1024	invalid
20.0ms	143×	body	128	valid
12.0ms	28×	body	512	valid
8.0ms	19×	body	512	invalid
5.0ms	16×	body	256	valid
4.0ms	14×	body	256	invalid
3.0ms	20×	body	128	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify173.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune15.0ms (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)

localize21.0ms (0.1%)

Local error

Found 3 expressions with local error:

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))

rewrite290.0ms (1.2%)

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:

24.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
15.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
8.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 2362 to 862 computations (63.5% saved)

series1.3s (5.5%)

Error

0.3b

Counts

3 → 42

Calls

3 calls:

737.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
343.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
155.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 1676 to 1476 computations (11.9% saved)

simplify141.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5044	2993

prune280.0ms (1.2%)

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

Counts

138 → 8

Compiler

Compiled 2900 to 1180 computations (59.3% saved)

localize20.0ms (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))

rewrite152.0ms (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:

17.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
14.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
8.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 1347 to 424 computations (68.5% saved)

series1.5s (6.1%)

Error

Counts

3 → 48

Calls

3 calls:

744.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
452.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))
171.0ms	(+.f64 (.f64 a2 a2) (.f64 a1 a1))

Compiler

Compiled 2074 to 1778 computations (14.3% saved)

simplify170.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4967	2050
1	4967	2050

prune175.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Error

Counts

116 → 7

Compiler

Compiled 1993 to 798 computations (60% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
6.8b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.8b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite409.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 157

Calls

4 calls:

37.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
15.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
7.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 5839 to 1470 computations (74.8% saved)

series1.7s (7%)

Error

Counts

4 → 72

Calls

4 calls:

692.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
386.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
238.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
222.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 4592 to 3299 computations (28.2% saved)

simplify195.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4999	5857
1	4999	5857

prune419.0ms (1.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	229	7	236

Error

Counts

236 → 7

Compiler

Compiled 6784 to 2111 computations (68.9% saved)

localize22.0ms (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) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
0.2b	(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
0.4b	(/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))

rewrite339.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`times-frac_binary64_425`
37×	`add-sqr-sqrt_binary64_441`
35×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
32×	`add-exp-log_binary64_457`
20×	`add-cbrt-cube_binary64_455`
18×	`sqrt-prod_binary64_435`
14×	`div-exp_binary64_470`
13×	`associate-/r*_binary64_363`
12×	`associate-*r/_binary64_361`
11×	`associate-/r/_binary64_365`
9×	`associate-/l*_binary64_364`
7×	`pow1_binary64_480` `cbrt-undiv_binary64_453` `flip3-+_binary64_422` `flip-+_binary64_393`
6×	`add-log-exp_binary64_458` `div-inv_binary64_416`
5×	`prod-exp_binary64_468`
3×	`cbrt-unprod_binary64_452` `1-exp_binary64_463` `rec-exp_binary64_469` `associate-l_binary64_360` `associate-r_binary64_359`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418`
1×	`inv-pow_binary64_504` `pow-flip_binary64_493` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `sum-log_binary64_510` `+-commutative_binary64_349`

Counts

4 → 138

Calls

4 calls:

21.0ms	(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
15.0ms	(/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
13.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
8.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 3547 to 1481 computations (58.2% saved)

series2.4s (9.9%)

Error

Counts

4 → 66

Calls

4 calls:

834.0ms	(/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2))))
750.0ms	(/.f64 1 (/.f64 (sqrt.f64 2) (.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))))
458.0ms	(.f64 (cos.f64 th) (+.f64 (.f64 a1 a1) (*.f64 a2 a2)))
165.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 4264 to 3632 computations (14.8% saved)

simplify173.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5242	5629

prune417.0ms (1.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	202	2	204
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	204	7	211

Error

Counts

211 → 7

Compiler

Compiled 4698 to 2118 computations (54.9% saved)

regimes3.3s (13.9%)

Accuracy

Total 0.4b remaining (90.2%)

Threshold costs 0.4b (90.2%)

Compiler

Compiled 20211 to 14709 computations (27.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	36
1	16	36

end0.0ms (0%)

sample8.7s (36.4%)

Algorithm

1×

intervals

Results

1.1s	1808×	body	1024	valid
915.0ms	1519×	body	1024	invalid
661.0ms	4853×	body	128	valid
378.0ms	891×	body	512	valid
350.0ms	813×	body	512	invalid
121.0ms	442×	body	256	valid
115.0ms	657×	body	128	invalid
110.0ms	375×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 2546 to 1846 computations (27.5% saved)

Details

analyze1.5s (6.2%)

sample149.0ms (0.6%)

simplify173.0ms (0.7%)

prune15.0ms (0.1%)

localize21.0ms (0.1%)

rewrite290.0ms (1.2%)

series1.3s (5.5%)

simplify141.0ms (0.6%)

prune280.0ms (1.2%)

localize20.0ms (0.1%)

rewrite152.0ms (0.6%)

series1.5s (6.1%)

simplify170.0ms (0.7%)

prune175.0ms (0.7%)

localize30.0ms (0.1%)

rewrite409.0ms (1.7%)

series1.7s (7%)

simplify195.0ms (0.8%)

prune419.0ms (1.8%)

localize22.0ms (0.1%)

rewrite339.0ms (1.4%)

series2.4s (9.9%)

simplify173.0ms (0.7%)

prune417.0ms (1.7%)

regimes3.3s (13.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.7s (36.4%)

Profiling