Details

analyze1.4s (8.4%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample160.0ms (0.9%)

Algorithm

1×

intervals

Results

116.0ms	160×	body	1024	valid
21.0ms	43×	body	512	valid
5.0ms	37×	body	128	valid
4.0ms	16×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify175.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5170	26

prune3.0ms (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

4.7b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite206.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`unswap-sqr_binary64_46` `associate-r_binary64_18`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-l/_binary64_21` `div-inv_binary64_75` `-commutative_binary64_9`

Counts

4 → 103

Calls

4 calls:

17.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2766 to 1522 computations (45% saved)

series907.0ms (5.4%)

Error

2.5b

Counts

4 → 35

Calls

4 calls:

633.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
180.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 ky) 2)
18.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2280 to 1608 computations (29.5% saved)

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4947	3115
1	4947	3115

prune201.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	126	12	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	12	139

Error

2.4b

Counts

139 → 12

Compiler

Compiled 3591 to 1994 computations (44.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b	(pow.f64 (sin.f64 kx) 2)
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite238.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

72×	`*-un-lft-identity_binary64_78`
50×	`times-frac_binary64_84`
49×	`add-sqr-sqrt_binary64_100`
41×	`sqrt-prod_binary64_94`
40×	`add-cube-cbrt_binary64_113`
30×	`associate-r_binary64_18`
19×	`unpow-prod-down_binary64_157`
16×	`distribute-lft-out_binary64_29`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
8×	`pow1_binary64_139` `associate-/r*_binary64_22`
6×	`sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `pow-unpow_binary64_155` `unswap-sqr_binary64_46` `associate-l_binary64_19` `associate-/l*_binary64_23`
2×	`div-exp_binary64_129` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `div-inv_binary64_75`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 134

Calls

4 calls:

19.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
12.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3846 to 2113 computations (45.1% saved)

series1.4s (8.4%)

Error

2.4b

Counts

4 → 44

Calls

4 calls:

631.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
520.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
180.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
22.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3060 to 2138 computations (30.1% saved)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5036	4801

prune228.0ms (1.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	177	13	190

Error

2.4b

Counts

190 → 13

Compiler

Compiled 4697 to 2534 computations (46.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite270.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

62×	`sqrt-prod_binary64_94`
56×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
33×	`times-frac_binary64_84`
32×	`add-cube-cbrt_binary64_113`
15×	`unpow-prod-down_binary64_157`
12×	`distribute-lft-out_binary64_29`
11×	`associate-/r*_binary64_22`
8×	`sqrt-div_binary64_95`
7×	`pow1_binary64_139` `add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-/r/_binary64_24`
1×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 113

Calls

4 calls:

13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 4658 to 2833 computations (39.2% saved)

series1.0s (6.1%)

Error

2.4b

Counts

4 → 34

Calls

4 calls:

576.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
194.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
182.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3294 to 2372 computations (28% saved)

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4982	3940
1	4982	3940

prune283.0ms (1.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	147	13	160

Error

2.4b

Counts

160 → 13

Compiler

Compiled 5728 to 3456 computations (39.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite362.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

2.4b

Rules

104×	`sqrt-prod_binary64_94`
60×	`add-sqr-sqrt_binary64_100`
50×	`*-un-lft-identity_binary64_78`
34×	`sqrt-pow1_binary64_96`
30×	`pow1_binary64_139`
28×	`sqrt-div_binary64_95`
20×	`add-cube-cbrt_binary64_113`
19×	`swap-sqr_binary64_45`
18×	`pow1/2_binary64_158`
15×	`unpow-prod-down_binary64_157`
14×	`distribute-lft-out_binary64_29`
11×	`associate-l_binary64_19` `associate-r_binary64_18`
10×	`rem-sqrt-square_binary64_91`
9×	`pow-prod-up_binary64_148` `unswap-sqr_binary64_46`
8×	`flip3-+_binary64_81` `flip-+_binary64_52`
7×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114`
5×	`pow-prod-down_binary64_149` `pow-sqr_binary64_51`
4×	`add-log-exp_binary64_117` `sqr-abs_binary64_93` `frac-times_binary64_88`
3×	`pow-unpow_binary64_155`
2×	`associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `pow-plus_binary64_141` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `sqrt-unprod_binary64_98` `rem-square-sqrt_binary64_90` `*-commutative_binary64_9` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 147

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 6119 to 3861 computations (36.9% saved)

series645.0ms (3.8%)

Error

2.4b

Counts

4 → 36

Calls

4 calls:

191.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
191.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
183.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
25.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2898 to 2036 computations (29.7% saved)

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4971	3757
1	4971	3757

prune277.0ms (1.6%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	183	13	196

Error

2.4b

Counts

196 → 13

Compiler

Compiled 5509 to 3239 computations (41.2% saved)

regimes1.8s (10.6%)

Accuracy

Total 1.8b remaining (49%)

Threshold costs 0b (0%)

Compiler

Compiled 19710 to 15321 computations (22.3% saved)

bsearch5.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	70
1	23	70

end0.0ms (0%)

sample6.8s (40.6%)

Algorithm

1×

intervals

Results

3.4s	4612×	body	1024	valid
668.0ms	1444×	body	512	valid
176.0ms	1386×	body	128	valid
159.0ms	545×	body	256	valid
17.0ms	13×	body	2048	valid

Compiler

Compiled 2167 to 1680 computations (22.5% saved)

Details

analyze1.4s (8.4%)

sample160.0ms (0.9%)

simplify175.0ms (1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite206.0ms (1.2%)

series907.0ms (5.4%)

simplify73.0ms (0.4%)

prune201.0ms (1.2%)

localize16.0ms (0.1%)

rewrite238.0ms (1.4%)

series1.4s (8.4%)

simplify89.0ms (0.5%)

prune228.0ms (1.4%)

localize17.0ms (0.1%)

rewrite270.0ms (1.6%)

series1.0s (6.1%)

simplify84.0ms (0.5%)

prune283.0ms (1.7%)

localize17.0ms (0.1%)

rewrite362.0ms (2.2%)

series645.0ms (3.8%)

simplify83.0ms (0.5%)

prune277.0ms (1.6%)

regimes1.8s (10.6%)

bsearch5.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.8s (40.6%)

Profiling