Details

analyze2.6s (8.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5547	104
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
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)

sample285.0ms (0.9%)

Algorithm

1×

intervals

Results

205.0ms	147×	body	1024	valid
36.0ms	44×	body	512	valid
12.0ms	49×	body	128	valid
8.0ms	16×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify199.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (187.0ms)

Iter	Nodes	Cost
0	5170	26

prune7.0ms (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

3.7b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize38.0ms (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 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite80.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

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×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

33.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
17.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
5.0ms	(pow.f64 (sin.f64 kx) 2)
5.0ms	(pow.f64 (sin.f64 ky) 2)

series1.6s (5%)

Counts

4 → 41

Calls

4 calls:

1.2s	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
332.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
56.0ms	(pow.f64 (sin.f64 ky) 2)
53.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1512 to 1199 computations (20.7% saved)

simplify225.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (158.0ms)

Iter	Nodes	Cost
0	4979	3464
1	4979	3464

prune432.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	132	12	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	12	145

Error

1.9b

Counts

145 → 12

Compiler

Compiled 3872 to 2158 computations (44.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(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	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite109.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

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×	`associate-/r*_binary64_22` `pow1_binary64_139`
6×	`sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`associate-l_binary64_19` `flip-+_binary64_52` `associate-/l*_binary64_23` `unswap-sqr_binary64_46` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75`
1×	`-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 134

Calls

4 calls:

37.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
23.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (sin.f64 ky) 2)

series2.8s (8.7%)

Counts

4 → 54

Calls

4 calls:

1.2s	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
951.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
584.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
58.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2094 to 1637 computations (21.8% saved)

simplify176.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	5074	5672

prune539.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	188	12	200

Error

1.9b

Counts

200 → 12

Compiler

Compiled 5317 to 2898 computations (45.5% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.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)))))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite222.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`sqrt-prod_binary64_94`
130×	`add-sqr-sqrt_binary64_100`
123×	`times-frac_binary64_84`
120×	`*-un-lft-identity_binary64_78`
72×	`add-cube-cbrt_binary64_113`
39×	`associate-l_binary64_19` `associate-r_binary64_18`
24×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
18×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
16×	`unswap-sqr_binary64_46` `sqrt-div_binary64_95`
11×	`associate-/r*_binary64_22`
8×	`pow1_binary64_139`
6×	`associate-/r/_binary64_24`
5×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
3×	`div-inv_binary64_75` `associate-/l*_binary64_23`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 209

Calls

4 calls:

103.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
27.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series3.2s (10%)

Counts

4 → 54

Calls

4 calls:

1.3s	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.3s	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
348.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
345.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 2756 to 2137 computations (22.5% saved)

simplify264.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5329	11179

prune1.3s (4.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	263	12	275

Error

1.9b

Counts

275 → 12

Compiler

Compiled 11073 to 6554 computations (40.8% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.8b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite177.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`sqrt-prod_binary64_94`
87×	`*-un-lft-identity_binary64_78`
66×	`times-frac_binary64_84`
53×	`add-sqr-sqrt_binary64_100`
51×	`add-cube-cbrt_binary64_113`
45×	`add-exp-log_binary64_116`
39×	`associate-l_binary64_19`
27×	`add-cbrt-cube_binary64_114`
20×	`prod-exp_binary64_127`
18×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
12×	`sqrt-div_binary64_95`
11×	`div-exp_binary64_129` `associate-/r*_binary64_22` `pow1_binary64_139`
10×	`cbrt-unprod_binary64_111`
6×	`cbrt-undiv_binary64_112`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `associate-/r/_binary64_24` `flip3-+_binary64_81`
3×	`1-exp_binary64_122` `associate-/l_binary64_23` `rec-exp_binary64_128` `pow-prod-down_binary64_149` `associate-r/_binary64_20`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-r_binary64_18` `associate-l/_binary64_21` `clear-num_binary64_77`

Counts

4 → 166

Calls

4 calls:

72.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
27.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
16.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series3.2s (9.7%)

Counts

4 → 54

Calls

4 calls:

1.3s	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
1.2s	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
346.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
346.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 2852 to 2233 computations (21.7% saved)

simplify220.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5409	7924

prune1.1s (3.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	220	12	232

Error

1.9b

Counts

232 → 12

Compiler

Compiled 8519 to 5243 computations (38.5% saved)

regimes2.5s (7.6%)

Accuracy

Total 1.4b remaining (45.7%)

Threshold costs 0b (0%)

Compiler

Compiled 13898 to 11082 computations (20.3% saved)

bsearch8.0ms (0%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	65
1	23	65

end0.0ms (0%)

sample11.1s (34.1%)

Algorithm

1×

intervals

Results

5.8s	4561×	body	1024	valid
1.2s	1438×	body	512	valid
328.0ms	1450×	body	128	valid
284.0ms	532×	body	256	valid
43.0ms	19×	body	2048	valid

Compiler

Compiled 1536 to 1220 computations (20.6% saved)

Details

analyze2.6s (8.1%)

sample285.0ms (0.9%)

simplify199.0ms (0.6%)

prune7.0ms (0%)

localize38.0ms (0.1%)

rewrite80.0ms (0.2%)

series1.6s (5%)

simplify225.0ms (0.7%)

prune432.0ms (1.3%)

localize27.0ms (0.1%)

rewrite109.0ms (0.3%)

series2.8s (8.7%)

simplify176.0ms (0.5%)

prune539.0ms (1.7%)

localize32.0ms (0.1%)

rewrite222.0ms (0.7%)

series3.2s (10%)

simplify264.0ms (0.8%)

prune1.3s (4.1%)

localize36.0ms (0.1%)

rewrite177.0ms (0.5%)

series3.2s (9.7%)

simplify220.0ms (0.7%)

prune1.1s (3.3%)

regimes2.5s (7.6%)

bsearch8.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample11.1s (34.1%)

Profiling