Details

analyze988.0ms (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)

sample96.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	52×	body	1024	valid
17.0ms	48×	body	1024	invalid
17.0ms	149×	body	128	valid
10.0ms	41×	body	512	valid
5.0ms	19×	body	512	invalid
2.0ms	23×	body	128	invalid
2.0ms	13×	body	256	valid
2.0ms	11×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune6.0ms (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)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
0.1b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
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))

rewrite66.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_782`
38×	`times-frac_binary64_766`
32×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
22×	`sqrt-prod_binary64_776` `associate-r_binary64_700`
10×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
6×	`associate-/r*_binary64_704`
5×	`add-log-exp_binary64_799` `pow1_binary64_821`
3×	`unswap-sqr_binary64_728` `associate-/l_binary64_705` `associate-l*_binary64_701`
2×	`cbrt-undiv_binary64_794` `prod-exp_binary64_809` `flip3-+_binary64_763` `associate-/l/_binary64_707` `div-inv_binary64_757` `flip-+_binary64_734` `cbrt-unprod_binary64_793` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

3 → 94

Calls

6 calls:

27.0ms	(.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))
7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))

series858.0ms (5.4%)

Counts

3 → 42

Calls

3 calls:

507.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
235.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
115.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 995 to 969 computations (2.6% saved)

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5044	2993

prune240.0ms (1.5%)

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 1154 computations (59.8% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
0.5b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite71.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`sqrt-prod_binary64_776`
91×	`add-sqr-sqrt_binary64_782`
80×	`times-frac_binary64_766`
61×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
40×	`associate-r_binary64_700`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`unswap-sqr_binary64_728` `sqrt-div_binary64_777`
8×	`pow1_binary64_821`
6×	`associate-/r_binary64_704` `associate-/l_binary64_705` `associate-l_binary64_701`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
4×	`add-log-exp_binary64_799`
2×	`rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `associate-*l/_binary64_703` `prod-exp_binary64_809` `associate-/l/_binary64_707` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `sqrt-undiv_binary64_781` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `div-exp_binary64_811`
1×	`frac-2neg_binary64_771` `sqrt-unprod_binary64_780` `associate-r/_binary64_702` `clear-num_binary64_759` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 168

Calls

8 calls:

32.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
7.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series793.0ms (5%)

Counts

4 → 66

Calls

4 calls:

269.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
208.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
177.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
137.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2496 to 2070 computations (17.1% saved)

simplify134.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5034	5581

prune294.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	234	7	241

Error

Counts

241 → 7

Compiler

Compiled 6946 to 2291 computations (67% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)
0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.0b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite50.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_782`
39×	`sqrt-prod_binary64_776`
23×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
21×	`times-frac_binary64_766`
17×	`sqrt-div_binary64_777` `associate-r_binary64_700`
15×	`pow1_binary64_821`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
9×	`associate-l_binary64_701`
7×	`associate-*r/_binary64_702`
6×	`unswap-sqr_binary64_728` `pow-prod-down_binary64_831`
5×	`flip3-+_binary64_763` `flip-+_binary64_734`
4×	`associate-*l/_binary64_703` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `add-log-exp_binary64_799` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `pow1/2_binary64_840`
3×	`rem-sqrt-square_binary64_773`
2×	`div-inv_binary64_757` `*-commutative_binary64_691`
1×	`sqrt-unprod_binary64_780`

Counts

4 → 110

Calls

8 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
14.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (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 a1 a1) (.f64 a2 a2)))
0.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)

series1.1s (6.7%)

Counts

4 → 66

Calls

4 calls:

426.0ms	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))))
266.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
198.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
171.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2297 to 1977 computations (13.9% saved)

simplify100.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4971	4449
1	4971	4449

prune205.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	177	6	183

Error

Counts

183 → 6

Compiler

Compiled 4839 to 1649 computations (65.9% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 1/2)))
0.1b	(.f64 (cos.f64 th) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.0b	(+.f64 (.f64 a1 a1) (.f64 a2 a2))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 1/2)))
0.4b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
5.9b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_782`
19×	`sqrt-prod_binary64_776`
18×	`sqrt-div_binary64_777` `pow1_binary64_821`
12×	`-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `associate-l*_binary64_701`
11×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
10×	`associate-*l/_binary64_703` `pow-prod-down_binary64_831`
9×	`flip3-+_binary64_763` `flip-+_binary64_734`
7×	`sqrt-pow1_binary64_778` `associate-r_binary64_700` `pow1/2_binary64_840`
4×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `add-log-exp_binary64_799` `frac-times_binary64_770` `cbrt-unprod_binary64_793`
3×	`sqrt-unprod_binary64_780`
2×	`rem-sqrt-square_binary64_773` `associate-r/_binary64_702` `-commutative_binary64_691`

Counts

4 → 94

Calls

8 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 1/2)))
12.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series702.0ms (4.4%)

Counts

4 → 66

Calls

4 calls:

245.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 1/2))
183.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 1/2)))
138.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
136.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2496 to 2070 computations (17.1% saved)

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5302	3040

prune171.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	160	6	166

Error

Counts

166 → 6

Compiler

Compiled 4226 to 1418 computations (66.4% saved)

simplify30.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	497	2063
1	497	2063

regimes988.0ms (6.2%)

Accuracy

Total 0.3b remaining (95.3%)

Threshold costs 0.3b (95.3%)

Compiler

Compiled 9191 to 6653 computations (27.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample8.6s (54.2%)

Algorithm

1×

intervals

Results

723.0ms	1878×	body	1024	valid
604.0ms	1590×	body	1024	invalid
428.0ms	4751×	body	128	valid
245.0ms	886×	body	512	valid
224.0ms	817×	body	512	invalid
92.0ms	478×	body	256	valid
73.0ms	396×	body	256	invalid
64.0ms	665×	body	128	invalid
3.0ms	7×	body	2048	valid

Compiler

Compiled 3923 to 2821 computations (28.1% saved)

Pareto

0.49157701333512493

Details

analyze988.0ms (6.2%)

sample96.0ms (0.6%)

simplify109.0ms (0.7%)

prune6.0ms (0%)

localize10.0ms (0.1%)

rewrite66.0ms (0.4%)

series858.0ms (5.4%)

simplify95.0ms (0.6%)

prune240.0ms (1.5%)

localize24.0ms (0.2%)

rewrite71.0ms (0.4%)

series793.0ms (5%)

simplify134.0ms (0.8%)

prune294.0ms (1.9%)

localize21.0ms (0.1%)

rewrite50.0ms (0.3%)

series1.1s (6.7%)

simplify100.0ms (0.6%)

prune205.0ms (1.3%)

localize14.0ms (0.1%)

rewrite48.0ms (0.3%)

series702.0ms (4.4%)

simplify71.0ms (0.5%)

prune171.0ms (1.1%)

simplify30.0ms (0.2%)

regimes988.0ms (6.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.6s (54.2%)

Profiling