Details

analyze1.3s (8.8%)

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)

sample312.0ms (2.2%)

Algorithm

1×

intervals

Results

268.0ms	154×	body	1024	valid
20.0ms	40×	body	512	valid
7.0ms	48×	body	128	valid
4.0ms	13×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify251.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

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

Merged error: 4.2b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (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)
0.2b	(pow.f64 (sin.f64 kx) 2)
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_79`
34×	`add-sqr-sqrt_binary64_101`
30×	`associate-l_binary64_20`
26×	`times-frac_binary64_85`
25×	`add-cube-cbrt_binary64_114`
21×	`sqrt-prod_binary64_95`
14×	`unpow-prod-down_binary64_158`
11×	`add-exp-log_binary64_117`
9×	`add-cbrt-cube_binary64_115` `pow1_binary64_140`
8×	`distribute-lft-out_binary64_30`
6×	`pow-unpow_binary64_156`
4×	`sqrt-div_binary64_96` `add-log-exp_binary64_118`
3×	`unswap-sqr_binary64_47` `associate-r_binary64_19`
2×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `flip-+_binary64_53` `unpow2_binary64_144` `sqr-pow_binary64_51` `pow-pow_binary64_151` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-/r/_binary64_25` `flip3-+_binary64_82`
1×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `associate-l/_binary64_22` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`

Counts

4 → 103

Calls

4 calls:

21.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
10.0ms	(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)

series611.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

399.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
160.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
27.0ms	(pow.f64 (sin.f64 ky) 2)
24.0ms	(pow.f64 (sin.f64 kx) 2)

simplify78.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5013	2288

prune832.0ms (5.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	104	11	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	104	12	116

Merged error: 3.1b

Counts

116 → 12

Compiler

Compiled 13545 to 10006 computations (26.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
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)))))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_79`
50×	`times-frac_binary64_85`
49×	`add-sqr-sqrt_binary64_101`
41×	`sqrt-prod_binary64_95`
40×	`add-cube-cbrt_binary64_114`
30×	`associate-r_binary64_19`
19×	`unpow-prod-down_binary64_158`
16×	`distribute-lft-out_binary64_30`
12×	`add-exp-log_binary64_117`
11×	`add-cbrt-cube_binary64_115`
8×	`associate-/r*_binary64_23` `pow1_binary64_140`
6×	`sqrt-div_binary64_96`
4×	`associate-/r/_binary64_25` `add-log-exp_binary64_118`
3×	`associate-l_binary64_20` `pow-unpow_binary64_156` `flip-+_binary64_53` `associate-/l*_binary64_24` `unswap-sqr_binary64_47` `flip3-+_binary64_82`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `cbrt-unprod_binary64_112` `prod-exp_binary64_128`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `unpow2_binary64_144` `sqr-pow_binary64_51` `pow-pow_binary64_151` `associate-r/_binary64_21` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `frac-2neg_binary64_90`

Counts

4 → 134

Calls

4 calls:

23.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
14.0ms	(/.f64 (sin.f64 th) (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)))
3.0ms	(pow.f64 (sin.f64 kx) 2)

series913.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

387.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
344.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
154.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
28.0ms	(pow.f64 (sin.f64 kx) 2)

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5228	3544

prune451.0ms (3.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	4	6	10
Picked	1	0	1
Done	0	1	1
Total	147	11	158

Merged error: 3.1b

Counts

158 → 11

Compiler

Compiled 7792 to 5304 computations (31.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite121.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

346×	`times-frac_binary64_85`
262×	`*-un-lft-identity_binary64_79`
193×	`add-sqr-sqrt_binary64_101`
171×	`add-cube-cbrt_binary64_114`
112×	`sqrt-prod_binary64_95`
89×	`associate-r_binary64_19`
47×	`unpow-prod-down_binary64_158`
44×	`distribute-lft-out_binary64_30`
35×	`add-exp-log_binary64_117`
28×	`associate-/r*_binary64_23`
18×	`add-cbrt-cube_binary64_115`
14×	`div-exp_binary64_130`
9×	`div-inv_binary64_76` `pow1_binary64_140`
7×	`unswap-sqr_binary64_47` `prod-exp_binary64_128`
6×	`cbrt-undiv_binary64_113`
4×	`1-exp_binary64_123` `rec-exp_binary64_129` `add-log-exp_binary64_118`
3×	`associate-l_binary64_20` `pow-unpow_binary64_156` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112`
2×	`associate-/r/_binary64_25` `sqrt-div_binary64_96`
1×	`pow-exp_binary64_147` `pow-to-exp_binary64_148` `flip-+_binary64_53` `unpow2_binary64_144` `un-div-inv_binary64_77` `sqr-pow_binary64_51` `pow-pow_binary64_151` `associate-r/_binary64_21` `inv-pow_binary64_164` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `flip3-+_binary64_82` `frac-2neg_binary64_90` `pow-flip_binary64_153`

Counts

4 → 291

Calls

4 calls:

41.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))))
21.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)

series964.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))))
374.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
159.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 kx) 2)

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

303 → 303

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5105	9038

prune529.0ms (3.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	303	11	314

Merged error: 3.1b

Counts

314 → 11

Compiler

Compiled 9948 to 5897 computations (40.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite77.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`sqrt-prod_binary64_95`
94×	`*-un-lft-identity_binary64_79`
66×	`times-frac_binary64_85`
56×	`add-sqr-sqrt_binary64_101`
54×	`add-cube-cbrt_binary64_114`
22×	`associate-/r*_binary64_23`
20×	`unpow-prod-down_binary64_158` `distribute-lft-out_binary64_30`
12×	`sqrt-div_binary64_96`
8×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
6×	`associate-/l*_binary64_24` `pow1_binary64_140`
4×	`flip-+_binary64_53` `associate-/r/_binary64_25` `add-log-exp_binary64_118` `flip3-+_binary64_82`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `div-inv_binary64_76` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `frac-2neg_binary64_90`

Counts

4 → 156

Calls

4 calls:

18.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
15.0ms	(/.f64 (sin.f64 th) (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)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.1s (7.8%)

Counts

4 → 12

Calls

4 calls:

398.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
367.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
173.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
164.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4944	5213
1	4944	5213

prune328.0ms (2.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	168	11	179

Merged error: 3.1b

Counts

179 → 11

Compiler

Compiled 6515 to 3866 computations (40.7% saved)

regimes252.0ms (1.8%)

Compiler: Compiled 2226 to 1870 computations (16% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	26
1	16	26

end0.0ms (0%)

sample5.6s (39.3%)

Algorithm

1×

intervals

Results

3.9s	4595×	body	1024	valid
740.0ms	1431×	body	512	valid
194.0ms	1432×	body	128	valid
162.0ms	528×	body	256	valid
27.0ms	14×	body	2048	valid

Compiler

Compiled 271 to 228 computations (15.9% saved)

Details

analyze1.3s (8.8%)

sample312.0ms (2.2%)

simplify251.0ms (1.8%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite48.0ms (0.3%)

series611.0ms (4.3%)

simplify78.0ms (0.6%)

prune832.0ms (5.9%)

localize15.0ms (0.1%)

rewrite68.0ms (0.5%)

series913.0ms (6.5%)

simplify90.0ms (0.6%)

prune451.0ms (3.2%)

localize17.0ms (0.1%)

rewrite121.0ms (0.9%)

series964.0ms (6.8%)

simplify125.0ms (0.9%)

prune529.0ms (3.7%)

localize18.0ms (0.1%)

rewrite77.0ms (0.5%)

series1.1s (7.8%)

simplify109.0ms (0.8%)

prune328.0ms (2.3%)

regimes252.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.6s (39.3%)

Profiling