Details

analyze1.3s (6.1%)

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)

sample153.0ms (0.7%)

Algorithm

1×

intervals

Results

108.0ms	151×	body	1024	valid
18.0ms	38×	body	512	valid
6.0ms	20×	body	256	valid
6.0ms	47×	body	128	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify177.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

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

3.2b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.1b	(*.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)
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_71`
34×	`add-sqr-sqrt_binary64_93`
30×	`associate-l_binary64_12`
26×	`times-frac_binary64_77`
25×	`add-cube-cbrt_binary64_106`
21×	`sqrt-prod_binary64_87`
14×	`unpow-prod-down_binary64_150`
11×	`add-exp-log_binary64_109`
9×	`add-cbrt-cube_binary64_107` `pow1_binary64_132`
8×	`distribute-lft-out_binary64_22`
6×	`pow-unpow_binary64_148`
4×	`sqrt-div_binary64_88` `add-log-exp_binary64_110`
3×	`unswap-sqr_binary64_39` `associate-r_binary64_11`
2×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `associate-/r/_binary64_17` `sqr-pow_binary64_43` `unpow2_binary64_136` `pow-pow_binary64_143` `prod-exp_binary64_120` `flip-+_binary64_45` `cbrt-unprod_binary64_104` `flip3-+_binary64_74`
1×	`div-exp_binary64_122` `div-inv_binary64_68` `associate-l/_binary64_14` `-commutative_binary64_2` `cbrt-undiv_binary64_105` `sqrt-pow1_binary64_89` `pow-prod-down_binary64_142` `rem-sqrt-square_binary64_84` `pow1/2_binary64_151`

Counts

4 → 103

Calls

8 calls:

19.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
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)
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series883.0ms (4.3%)

Counts

4 → 39

Calls

4 calls:

642.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
186.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
28.0ms	(pow.f64 (sin.f64 ky) 2)
27.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1385 to 1117 computations (19.4% saved)

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4993	3140
1	4993	3140

prune299.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	129	13	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	13	143

Error

1.1b

Counts

143 → 13

Compiler

Compiled 3720 to 2079 computations (44.1% saved)

localize14.0ms (0.1%)

Local error

Found 8 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)))))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(+.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 ky) 2)
0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite60.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_71`
50×	`times-frac_binary64_77`
49×	`add-sqr-sqrt_binary64_93`
41×	`sqrt-prod_binary64_87`
40×	`add-cube-cbrt_binary64_106`
30×	`associate-r_binary64_11`
19×	`unpow-prod-down_binary64_150`
16×	`distribute-lft-out_binary64_22`
12×	`add-exp-log_binary64_109`
11×	`add-cbrt-cube_binary64_107`
8×	`associate-/r*_binary64_15` `pow1_binary64_132`
6×	`sqrt-div_binary64_88`
4×	`associate-/r/_binary64_17` `add-log-exp_binary64_110`
3×	`unswap-sqr_binary64_39` `associate-l_binary64_12` `associate-/l*_binary64_16` `pow-unpow_binary64_148` `flip-+_binary64_45` `flip3-+_binary64_74`
2×	`div-exp_binary64_122` `div-inv_binary64_68` `cbrt-undiv_binary64_105` `prod-exp_binary64_120` `cbrt-unprod_binary64_104`
1×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `sqr-pow_binary64_43` `unpow2_binary64_136` `clear-num_binary64_70` `pow-pow_binary64_143` `-commutative_binary64_2` `sqrt-pow1_binary64_89` `pow-prod-down_binary64_142` `rem-sqrt-square_binary64_84` `frac-2neg_binary64_82` `associate-r/_binary64_13` `pow1/2_binary64_151`

Counts

4 → 134

Calls

8 calls:

20.0ms	(*.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))))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series1.4s (6.8%)

Counts

4 → 49

Calls

4 calls:

665.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
536.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
184.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1875 to 1493 computations (20.4% saved)

simplify92.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4978	4875
1	4978	4875

prune263.0ms (1.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	183	13	196

Error

1.1b

Counts

196 → 13

Compiler

Compiled 4854 to 2640 computations (45.6% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

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))))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
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))))
0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite115.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

346×	`times-frac_binary64_77`
262×	`*-un-lft-identity_binary64_71`
193×	`add-sqr-sqrt_binary64_93`
171×	`add-cube-cbrt_binary64_106`
112×	`sqrt-prod_binary64_87`
89×	`associate-r_binary64_11`
47×	`unpow-prod-down_binary64_150`
44×	`distribute-lft-out_binary64_22`
35×	`add-exp-log_binary64_109`
28×	`associate-/r*_binary64_15`
18×	`add-cbrt-cube_binary64_107`
14×	`div-exp_binary64_122`
9×	`div-inv_binary64_68` `pow1_binary64_132`
7×	`unswap-sqr_binary64_39` `prod-exp_binary64_120`
6×	`cbrt-undiv_binary64_105`
4×	`add-log-exp_binary64_110` `rec-exp_binary64_121` `1-exp_binary64_115`
3×	`associate-l_binary64_12` `associate-/l*_binary64_16` `pow-unpow_binary64_148` `cbrt-unprod_binary64_104`
2×	`sqrt-div_binary64_88` `associate-/r/_binary64_17`
1×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `inv-pow_binary64_156` `sqr-pow_binary64_43` `unpow2_binary64_136` `clear-num_binary64_70` `pow-pow_binary64_143` `-commutative_binary64_2` `sqrt-pow1_binary64_89` `flip-+_binary64_45` `pow-prod-down_binary64_142` `rem-sqrt-square_binary64_84` `un-div-inv_binary64_69` `frac-2neg_binary64_82` `associate-r/_binary64_13` `flip3-+_binary64_74` `pow1/2_binary64_151` `pow-flip_binary64_145`

Counts

4 → 291

Calls

8 calls:

36.0ms	(*.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))))
16.0ms	(/.f64 1 (/.f64 (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 ky) 2)
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series1.4s (6.9%)

Counts

4 → 49

Calls

4 calls:

665.0ms	(*.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))))
549.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
183.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1923 to 1541 computations (19.9% saved)

simplify148.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4965	10541
1	4965	10541

prune606.0ms (2.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	337	3	340
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	340	13	353

Error

1.1b

Counts

353 → 13

Compiler

Compiled 10077 to 5696 computations (43.5% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
0.2b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.2b	(/.f64 (sin.f64 ky) (/.f64 (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)
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite58.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64_77`
150×	`*-un-lft-identity_binary64_71`
99×	`add-sqr-sqrt_binary64_93`
98×	`add-cube-cbrt_binary64_106`
65×	`sqrt-prod_binary64_87`
32×	`unpow-prod-down_binary64_150`
28×	`associate-/r*_binary64_15`
26×	`distribute-lft-out_binary64_22`
11×	`add-exp-log_binary64_109`
9×	`add-cbrt-cube_binary64_107`
7×	`pow1_binary64_132`
6×	`pow-unpow_binary64_148`
5×	`div-inv_binary64_68`
4×	`add-log-exp_binary64_110`
3×	`div-exp_binary64_122` `associate-/l*_binary64_16` `cbrt-undiv_binary64_105`
2×	`pow-exp_binary64_139` `sqrt-div_binary64_88` `pow-to-exp_binary64_140` `sqr-pow_binary64_43` `unpow2_binary64_136` `pow-pow_binary64_143`
1×	`associate-/r/_binary64_17` `clear-num_binary64_70` `sqrt-pow1_binary64_89` `flip-+_binary64_45` `rem-sqrt-square_binary64_84` `frac-2neg_binary64_82` `flip3-+_binary64_74` `pow1/2_binary64_151`

Counts

4 → 183

Calls

8 calls:

20.0ms	(/.f64 (sin.f64 ky) (/.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 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series897.0ms (4.3%)

Counts

4 → 39

Calls

4 calls:

649.0ms	(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
190.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
29.0ms	(pow.f64 (sin.f64 kx) 2)
28.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1385 to 1117 computations (19.4% saved)

simplify127.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4953	7265
1	4953	7265

prune302.0ms (1.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	223	12	235

Error

1.1b

Counts

235 → 12

Compiler

Compiled 5885 to 2983 computations (49.3% saved)

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	416	2678
1	416	2678

regimes1.2s (5.8%)

Accuracy

Total 1.3b remaining (44.7%)

Threshold costs 0b (0%)

Compiler

Compiled 12994 to 10528 computations (19% saved)

bsearch4.0ms (0%)

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

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	79
1	30	79

end0.0ms (0%)

sample11.0s (53.1%)

Algorithm

1×

intervals

Results

3.3s	4581×	body	1024	valid
689.0ms	1470×	body	512	valid
183.0ms	1416×	body	128	valid
146.0ms	524×	body	256	valid
17.0ms	9×	body	2048	valid

Compiler

Compiled 4870 to 3917 computations (19.6% saved)

Pareto

0.26956481384885506

Details

analyze1.3s (6.1%)

sample153.0ms (0.7%)

simplify177.0ms (0.9%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite43.0ms (0.2%)

series883.0ms (4.3%)

simplify75.0ms (0.4%)

prune299.0ms (1.4%)

localize14.0ms (0.1%)

rewrite60.0ms (0.3%)

series1.4s (6.8%)

simplify92.0ms (0.4%)

prune263.0ms (1.3%)

localize16.0ms (0.1%)

rewrite115.0ms (0.6%)

series1.4s (6.9%)

simplify148.0ms (0.7%)

prune606.0ms (2.9%)

localize14.0ms (0.1%)

rewrite58.0ms (0.3%)

series897.0ms (4.3%)

simplify127.0ms (0.6%)

prune302.0ms (1.5%)

simplify37.0ms (0.2%)

regimes1.2s (5.8%)

bsearch4.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample11.0s (53.1%)

Profiling