Details

analyze1.6s (8.7%)

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

Compiler

Compiled 20 to 16 computations (20% saved)

sample159.0ms (0.9%)

Algorithm

1×

intervals

Results

42.0ms	68×	body	1024	valid
27.0ms	51×	body	1024	invalid
18.0ms	140×	body	128	valid
11.0ms	29×	body	512	invalid
11.0ms	28×	body	512	valid
6.0ms	20×	body	256	valid
4.0ms	29×	body	128	invalid
3.0ms	11×	body	256	invalid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune9.0ms (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

0.3b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize20.0ms (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)))
0.3b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite64.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
32×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
22×	`associate-r_binary64_359` `sqrt-prod_binary64_435`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`associate-/r*_binary64_363`
5×	`add-log-exp_binary64_458` `pow1_binary64_480`
3×	`unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
2×	`flip3-+_binary64_422` `div-inv_binary64_416` `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` `sum-log_binary64_510` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `+-commutative_binary64_349`

Counts

3 → 94

Calls

3 calls:

22.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
7.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

series1.2s (6.7%)

Counts

3 → 40

Calls

3 calls:

726.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
331.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
162.0ms	(+.f64 (.f64 a1 a1) (.f64 a2 a2))

Compiler

Compiled 904 to 889 computations (1.7% saved)

simplify145.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5013	2823

prune248.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	7	134
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Error

Counts

136 → 8

Compiler

Compiled 2792 to 1113 computations (60.1% saved)

localize24.0ms (0.1%)

Local error

Found 4 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)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
7.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite121.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`sqrt-prod_binary64_435`
91×	`add-sqr-sqrt_binary64_441`
80×	`times-frac_binary64_425`
61×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
40×	`associate-r_binary64_359`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`sqrt-div_binary64_436` `unswap-sqr_binary64_387`
8×	`pow1_binary64_480`
6×	`associate-l_binary64_360` `associate-/r_binary64_363` `associate-/l_binary64_364`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`add-log-exp_binary64_458`
2×	`associate-*l/_binary64_362` `sqrt-undiv_binary64_440` `pow1/2_binary64_499` `div-inv_binary64_416` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `sqrt-unprod_binary64_439` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

4 → 168

Calls

4 calls:

50.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
16.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
8.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series1.2s (6.4%)

Counts

4 → 60

Calls

4 calls:

385.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
331.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (sqrt.f64 2)))
220.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
216.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2247 to 1869 computations (16.8% saved)

simplify179.0ms (1%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5260	5433

prune474.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	229	7	236

Error

Counts

236 → 7

Compiler

Compiled 6794 to 2227 computations (67.2% saved)

localize24.0ms (0.1%)

Local error

Found 4 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))))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
7.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.3b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite103.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_441`
39×	`sqrt-prod_binary64_435`
23×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
21×	`times-frac_binary64_425`
17×	`sqrt-div_binary64_436` `associate-r_binary64_359`
15×	`pow1_binary64_480`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
9×	`associate-l_binary64_360`
7×	`associate-*r/_binary64_361`
6×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387`
5×	`flip3-+_binary64_422` `flip-+_binary64_393`
4×	`associate-*l/_binary64_362` `add-log-exp_binary64_458` `pow1/2_binary64_499` `frac-times_binary64_429` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sqrt-pow1_binary64_437`
3×	`rem-sqrt-square_binary64_432`
2×	`div-inv_binary64_416` `*-commutative_binary64_350`
1×	`sqrt-unprod_binary64_439`

Counts

4 → 110

Calls

4 calls:

35.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
27.0ms	(.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))))
10.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
7.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series1.3s (7.4%)

Counts

4 → 60

Calls

4 calls:

568.0ms	(.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))))
299.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
271.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) 2)))
203.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2037 to 1760 computations (13.6% saved)

simplify189.0ms (1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4971	4199
1	4971	4199

prune332.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	170	7	177

Error

Counts

177 → 7

Compiler

Compiled 4654 to 1562 computations (66.4% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cos.f64 th))
0.2b	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)))
7.2b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
7.3b	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))

rewrite89.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`sqrt-prod_binary64_435`
31×	`add-sqr-sqrt_binary64_441`
23×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
19×	`times-frac_binary64_425` `associate-r_binary64_359`
13×	`pow1_binary64_480`
12×	`sqrt-div_binary64_436`
11×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`associate-*l/_binary64_362`
7×	`associate-l_binary64_360`
4×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip-+_binary64_393`
3×	`rem-sqrt-square_binary64_432`
2×	`pow1/2_binary64_499` `div-inv_binary64_416` `unswap-sqr_binary64_387` `frac-times_binary64_429` `*-commutative_binary64_350` `sqrt-pow1_binary64_437`
1×	`associate-*r/_binary64_361`

Counts

4 → 100

Calls

4 calls:

30.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)))
16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cos.f64 th))
10.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
8.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

series1.6s (8.8%)

Counts

4 → 68

Calls

4 calls:

625.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cos.f64 th)) (sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2)))
441.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cos.f64 th))
314.0ms	(sqrt.f64 (/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) 2))
204.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 2688 to 2181 computations (18.9% saved)

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5283	3865

prune293.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	167	1	168
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	168	7	175

Error

Counts

175 → 7

Compiler

Compiled 4527 to 1365 computations (69.8% saved)

regimes2.0s (11%)

Accuracy

Total 0.3b remaining (91.8%)

Threshold costs 0.3b (91.8%)

Compiler

Compiled 10279 to 7325 computations (28.7% saved)

bsearch0.0ms (0%)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

Compiler

Compiled 44 to 26 computations (40.9% saved)

end0.0ms (0%)

sample6.6s (36.3%)

Algorithm

1×

intervals

Results

1.0s	1806×	body	1024	valid
857.0ms	1515×	body	1024	invalid
633.0ms	4845×	body	128	valid
362.0ms	898×	body	512	valid
305.0ms	767×	body	512	invalid
123.0ms	448×	body	256	valid
99.0ms	371×	body	256	invalid
90.0ms	663×	body	128	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 1312 to 931 computations (29% saved)

Details

analyze1.6s (8.7%)

sample159.0ms (0.9%)

simplify16.0ms (0.1%)

prune9.0ms (0.1%)

localize20.0ms (0.1%)

rewrite64.0ms (0.4%)

series1.2s (6.7%)

simplify145.0ms (0.8%)

prune248.0ms (1.4%)

localize24.0ms (0.1%)

rewrite121.0ms (0.7%)

series1.2s (6.4%)

simplify179.0ms (1%)

prune474.0ms (2.6%)

localize24.0ms (0.1%)

rewrite103.0ms (0.6%)

series1.3s (7.4%)

simplify189.0ms (1%)

prune332.0ms (1.8%)

localize25.0ms (0.1%)

rewrite89.0ms (0.5%)

series1.6s (8.8%)

simplify117.0ms (0.6%)

prune293.0ms (1.6%)

regimes2.0s (11%)

bsearch0.0ms (0%)

simplify17.0ms (0.1%)

end0.0ms (0%)

sample6.6s (36.3%)

Profiling