Details

analyze1.3s (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)

sample162.0ms (0.1%)

Algorithm

1×

intervals

Results

103.0ms	138×	body	1024	valid
29.0ms	54×	body	512	valid
7.0ms	21×	body	256	valid
5.0ms	41×	body	128	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 36 to 38 computations (-5.6% saved)

simplify179.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5171	29

prune3.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

3.5b

Counts

8 → 4

Compiler

Compiled 19 to 17 computations (10.5% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
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))
0.1b	(/.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))
0.2b	(*.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)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite49.0ms (0%)

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

8 calls:

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

series917.0ms (0.7%)

Counts

4 → 39

Calls

4 calls:

675.0ms	(*.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)
28.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1385 to 1117 computations (19.4% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4993	3140
1	4993	3140

prune792.0ms (0.6%)

Pruning

85 alts after pruning (84 fresh and 1 done)

	Pruned	Kept	Total
New	61	81	142
Fresh	0	3	3
Picked	0	0	0
Done	0	1	1
Total	61	85	146

Error

1.1b

Counts

146 → 85

Compiler

Compiled 4719 to 3092 computations (34.5% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
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))
0.1b	(/.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))
0.2b	(*.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)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite49.0ms (0%)

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

8 calls:

23.0ms	(*.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))

series904.0ms (0.7%)

Counts

4 → 39

Calls

4 calls:

654.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
188.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 kx) 2)
31.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1605 to 1337 computations (16.7% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4993	3140
1	4993	3140

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.0b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2))))
0.0b	(*.f64 (pow.f64 kx 6) 2/45)
0.0b	(+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2))
0.2b	(pow.f64 (sin.f64 ky) 2)
6.9b	(sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))
17.1b	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
21.0b	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_117`
9×	`*-un-lft-identity_binary64_78`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
5×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94`
3×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
2×	`flip-+_binary64_52` `diff-log_binary64_170` `associate-+l+_binary64_11` `sqrt-div_binary64_95` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `associate-+l-_binary64_13` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `flip--_binary64_53` `distribute-lft-out_binary64_29` `pow1/2_binary64_158`

Counts

4 → 61

Calls

8 calls:

11.0ms	(sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))
4.0ms	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2))

series462.0ms (0.3%)

Counts

4 → 29

Calls

4 calls:

300.0ms	(sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))
74.0ms	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
59.0ms	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))
28.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1309 to 1122 computations (14.3% saved)

simplify44.0ms (0%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5011	2021

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2))))
0.0b	(+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.9b	(pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2))
1.3b	(pow.f64 (sin.f64 kx) (sqrt.f64 2))
2.4b	(sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`unpow-prod-down_binary64_157` `*-un-lft-identity_binary64_78`
15×	`add-sqr-sqrt_binary64_100` `pow-unpow_binary64_155`
14×	`add-cube-cbrt_binary64_113`
10×	`sqrt-prod_binary64_94`
8×	`add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`pow-exp_binary64_146`
4×	`add-cbrt-cube_binary64_114` `pow-to-exp_binary64_147` `add-log-exp_binary64_117` `sqr-pow_binary64_50`
3×	`pow-pow_binary64_150`
2×	`sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `distribute-lft-out_binary64_29` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 80

Calls

8 calls:

11.0ms	(sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2))
3.0ms	(pow.f64 (sin.f64 kx) (sqrt.f64 2))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2))

series1.2s (0.9%)

Counts

4 → 22

Calls

4 calls:

787.0ms	(sqrt.f64 (+.f64 (pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2)) (pow.f64 (sin.f64 ky) 2)))
249.0ms	(pow.f64 (pow.f64 (sin.f64 kx) (sqrt.f64 2)) (sqrt.f64 2))
127.0ms	(pow.f64 (sin.f64 kx) (sqrt.f64 2))
24.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1932 to 1688 computations (12.6% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4919	1506
1	4919	1506

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.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	(sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.1b	(sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_78`
12×	`add-sqr-sqrt_binary64_100`
10×	`sqrt-prod_binary64_94` `unpow-prod-down_binary64_157` `add-cube-cbrt_binary64_113`
8×	`pow1_binary64_139`
6×	`add-exp-log_binary64_116` `pow-unpow_binary64_155`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-div_binary64_95` `distribute-lft-out_binary64_29`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 70

Calls

8 calls:

9.0ms	(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)
3.0ms	(pow.f64 (sin.f64 kx) 2)
0.0ms	(sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series462.0ms (0.3%)

Counts

4 → 32

Calls

4 calls:

203.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
190.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
36.0ms	(pow.f64 (sin.f64 kx) 2)
33.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1864 to 1388 computations (25.5% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4945	1616
1	4945	1616

prune8.7s (6.4%)

Pruning

272 alts after pruning (266 fresh and 6 done)

	Pruned	Kept	Total
New	245	191	436
Fresh	4	75	79
Picked	0	0	0
Done	0	6	6
Total	249	272	521

Error

0.9b

Counts

521 → 272

Compiler

Compiled 17718 to 12202 computations (31.1% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
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))
0.1b	(/.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))
0.2b	(*.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)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite48.0ms (0%)

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

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))
11.0ms	(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))

series917.0ms (0.7%)

Counts

4 → 39

Calls

4 calls:

661.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
194.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
33.0ms	(pow.f64 (sin.f64 kx) 2)
28.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1825 to 1557 computations (14.7% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4993	3140
1	4993	3140

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (sin.f64 ky) (fabs.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))))
0.0b	(.f64 (/.f64 (sin.f64 ky) (fabs.f64 (sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2))))) (sin.f64 th))
0.0b	(*.f64 (pow.f64 kx 6) 2/45)
0.0b	(+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2))
0.2b	(pow.f64 (sin.f64 ky) 2)
6.9b	(sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))
17.1b	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
21.0b	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-log-exp_binary64_117`
9×	`*-un-lft-identity_binary64_78`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
5×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94`
3×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
2×	`flip-+_binary64_52` `diff-log_binary64_170` `associate-+l+_binary64_11` `sqrt-div_binary64_95` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `associate-+l-_binary64_13` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `flip--_binary64_53` `distribute-lft-out_binary64_29` `pow1/2_binary64_158`

Counts

4 → 61

Calls

8 calls:

11.0ms	(sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))
4.0ms	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2))

series458.0ms (0.3%)

Counts

4 → 29

Calls

4 calls:

301.0ms	(sqrt.f64 (+.f64 (+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45)) (pow.f64 (sin.f64 ky) 2)))
77.0ms	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
53.0ms	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))
27.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1352 to 1165 computations (13.8% saved)

simplify46.0ms (0%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5011	2021

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (sin.f64 th) (/.f64 (sqrt.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	(sqrt.f64 (sin.f64 ky))
0.1b	(sqrt.f64 (sin.f64 ky))
0.2b	(/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_78`
67×	`sqrt-prod_binary64_94`
48×	`times-frac_binary64_84`
42×	`add-sqr-sqrt_binary64_100`
41×	`add-cube-cbrt_binary64_113`
22×	`unpow-prod-down_binary64_157`
16×	`distribute-lft-out_binary64_29`
8×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `sqrt-undiv_binary64_99` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 130

Calls

8 calls:

13.0ms	(/.f64 (sqrt.f64 (sin.f64 ky)) (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)
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(sqrt.f64 (sin.f64 ky))

series587.0ms (0.4%)

Counts

4 → 31

Calls

4 calls:

318.0ms	(/.f64 (sqrt.f64 (sin.f64 ky)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
202.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
34.0ms	(pow.f64 (sin.f64 kx) 2)
33.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1581 to 1293 computations (18.2% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5024	4141

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
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 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.6b	(sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)))
4.6b	(sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)))

rewrite53.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_78`
12×	`sqrt-prod_binary64_94` `pow1_binary64_139`
8×	`add-sqr-sqrt_binary64_100`
6×	`sqrt-pow1_binary64_96` `add-cube-cbrt_binary64_113` `sqrt-div_binary64_95`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `unpow-prod-down_binary64_157` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29` `pow1/2_binary64_158`
2×	`flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-*l/_binary64_21` `pow-prod-down_binary64_149` `flip3-+_binary64_81`

Counts

4 → 58

Calls

8 calls:

13.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)))
13.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)))
11.0ms	(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)))
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))

series2.3s (1.7%)

Counts

4 → 46

Calls

4 calls:

944.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)))
927.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th)))
199.0ms	(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)))

Compiler

Compiled 3128 to 2236 computations (28.5% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5120	2784

prune18.9s (14%)

Pruning

480 alts after pruning (469 fresh and 11 done)

	Pruned	Kept	Total
New	278	219	497
Fresh	11	250	261
Picked	0	0	0
Done	0	11	11
Total	289	480	769

Error

0.0b

Counts

769 → 480

Compiler

Compiled 28265 to 20017 computations (29.2% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2))))
0.1b	(+.f64 (*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2))
0.2b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx)))
3.7b	(sqrt.f64 (+.f64 (*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))

rewrite37.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_100`
27×	`associate-l_binary64_19`
25×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`times-frac_binary64_84`
15×	`pow1_binary64_139`
13×	`sqrt-prod_binary64_94`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
6×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unpow-prod-down_binary64_157` `swap-sqr_binary64_45` `pow-unpow_binary64_155`
2×	`*-commutative_binary64_9` `flip-+_binary64_52` `pow-prod-down_binary64_149` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`pow2_binary64_159` `sqr-abs_binary64_93` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `pow-sqr_binary64_51` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `pow-pow_binary64_150` `pow-prod-up_binary64_148` `associate-*l/_binary64_21` `pow-plus_binary64_141` `pow1/2_binary64_158`

Counts

4 → 103

Calls

8 calls:

14.0ms	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
6.0ms	(sqrt.f64 (+.f64 (*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx)))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2))

series970.0ms (0.7%)

Counts

4 → 33

Calls

4 calls:

739.0ms	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
172.0ms	(sqrt.f64 (+.f64 (*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx))) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)
27.0ms	(*.f64 (fabs.f64 (sin.f64 kx)) (fabs.f64 (sin.f64 kx)))

Compiler

Compiled 1336 to 1042 computations (22% saved)

simplify113.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4940	3211
1	4940	3211

localize6.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize36.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))) (pow.f64 (sin.f64 ky) 2))))
0.0b	(+.f64 (-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))) (pow.f64 (sin.f64 ky) 2))
0.0b	(+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45))
0.0b	(+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))
0.1b	(*.f64 (pow.f64 kx 4) 1/3)
0.2b	(pow.f64 (sin.f64 ky) 2)
3.6b	(sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))) (pow.f64 (sin.f64 ky) 2)))
27.9b	(-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8))))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_100`
18×	`*-un-lft-identity_binary64_78`
16×	`add-log-exp_binary64_117`
11×	`add-cube-cbrt_binary64_113`
10×	`add-exp-log_binary64_116`
7×	`associate-l_binary64_19` `unpow-prod-down_binary64_157`
6×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
5×	`sqrt-prod_binary64_94` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`frac-sub_binary64_87` `diff-log_binary64_170` `sum-log_binary64_169`
3×	`prod-exp_binary64_127` `sqr-pow_binary64_50` `associate-r_binary64_18` `unswap-sqr_binary64_46` `pow-unpow_binary64_155` `cancel-sign-sub-inv_binary64_44`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `distribute-lft-out--_binary64_30` `sqrt-div_binary64_95` `distribute-lft-out_binary64_29`
1×	`*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `unpow2_binary64_143` `associate--l+_binary64_15` `associate--r+_binary64_14` `pow-pow_binary64_150` `flip--_binary64_53` `difference-of-squares_binary64_47` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 85

Calls

8 calls:

16.0ms	(sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8))))
5.0ms	(*.f64 (pow.f64 kx 4) 1/3)
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))

series407.0ms (0.3%)

Counts

4 → 26

Calls

4 calls:

272.0ms	(sqrt.f64 (+.f64 (-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8)))) (pow.f64 (sin.f64 ky) 2)))
63.0ms	(-.f64 (+.f64 (.f64 kx kx) (.f64 (pow.f64 kx 6) 2/45)) (+.f64 (.f64 (pow.f64 kx 4) 1/3) (.f64 1/315 (pow.f64 kx 8))))
36.0ms	(*.f64 (pow.f64 kx 4) 1/3)
36.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1578 to 1375 computations (12.9% saved)

simplify65.0ms (0%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4997	3168
1	4997	3168

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)))))) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.1b	(sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.0b	(+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky))))
0.0b	(.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)))
0.4b	(/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)))))
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.8b	(/.f64 (*.f64 kx kx) (sin.f64 ky))
13.6b	(sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky))))))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
22×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84`
20×	`sqrt-prod_binary64_94`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-/r*_binary64_22` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `associate-/l*_binary64_23` `associate-/r/_binary64_24`
3×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `sqrt-div_binary64_95` `flip3-+_binary64_81`
2×	`sqrt-pow1_binary64_96` `unpow-prod-down_binary64_157` `frac-2neg_binary64_89` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `pow1/2_binary64_158`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`

Counts

4 → 94

Calls

8 calls:

8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)))))
6.0ms	(sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky))))))
5.0ms	(/.f64 (*.f64 kx kx) (sin.f64 ky))
0.0ms	(.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)))

series887.0ms (0.7%)

Counts

4 → 38

Calls

4 calls:

401.0ms	(sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky))))))
190.0ms	(/.f64 (sin.f64 ky) (+.f64 (sin.f64 ky) (.f64 1/2 (/.f64 (.f64 kx kx) (sin.f64 ky)))))
187.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
108.0ms	(/.f64 (*.f64 kx kx) (sin.f64 ky))

Compiler

Compiled 2640 to 2020 computations (23.5% saved)

simplify82.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4959	3668
1	4959	3668

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.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	(sqrt.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))))
0.1b	(sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.5b	(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.9b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_78`
30×	`sqrt-prod_binary64_94`
28×	`unpow-prod-down_binary64_157`
22×	`cbrt-prod_binary64_109`
18×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `cube-prod_binary64_106`
12×	`distribute-lft-out_binary64_29`
8×	`sqrt-div_binary64_95` `pow1_binary64_139`
5×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `cube-div_binary64_107` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`sqrt-pow1_binary64_96` `pow-pow_binary64_150` `pow-unpow_binary64_155` `pow1/2_binary64_158`
2×	`cube-mult_binary64_108` `cbrt-div_binary64_110` `rem-sqrt-square_binary64_91` `sqr-pow_binary64_50` `unpow3_binary64_144`
1×	`rem-cube-cbrt_binary64_101` `sqrt-pow2_binary64_97` `rem-cbrt-cube_binary64_102` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow1/3_binary64_160`

Counts

4 → 105

Calls

8 calls:

12.0ms	(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3)
11.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))
9.0ms	(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)))
0.0ms	(sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series906.0ms (0.7%)

Counts

4 → 45

Calls

4 calls:

322.0ms	(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3)
199.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) 3))
193.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
190.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 2708 to 2020 computations (25.4% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5115	3555

prune28.3s (21%)

Pruning

699 alts after pruning (684 fresh and 15 done)

	Pruned	Kept	Total
New	294	235	529
Fresh	15	449	464
Picked	0	0	0
Done	1	15	16
Total	310	699	1009

Error

0.0b

Counts

1009 → 699

Compiler

Compiled 14537 to 8178 computations (43.7% saved)

simplify797.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4994	55067
1	4994	55067

regimes24.5s (18.1%)

Compiler: Compiled 196123 to 145920 computations (25.6% saved)

bsearch42.0ms (0%)

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

regimes1.7s (1.3%)

Compiler: Compiled 6784 to 5966 computations (12.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 4 to 6 computations (-50% saved)

regimes1.4s (1.1%)

Compiler: Compiled 5021 to 4519 computations (10% saved)

bsearch2.0ms (0%)

Compiler: Compiled 4 to 6 computations (-50% saved)

regimes919.0ms (0.7%)

Compiler: Compiled 3251 to 2971 computations (8.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 4 computations (-100% saved)

regimes702.0ms (0.5%)

Compiler: Compiled 2070 to 1996 computations (3.6% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 4 computations (-100% saved)

regimes608.0ms (0.5%)

Compiler: Compiled 1600 to 1600 computations (0% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 4 computations (-100% saved)

regimes425.0ms (0.3%)

Compiler: Compiled 1098 to 1098 computations (0% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 4 computations (-100% saved)

regimes283.0ms (0.2%)

Compiler: Compiled 322 to 413 computations (-28.3% saved)

bsearch124.0ms (0.1%)

Steps

Iters	Range		Point
10	8.022534705912205e-52	2.5515969501100053e-37	2.5073726237800466e-37
4	-0.05398046381745485	-0.03281088659107353	-0.033472435879397945

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes252.0ms (0.2%)

Compiler: Compiled 259 to 357 computations (-37.8% saved)

bsearch240.0ms (0.2%)

Steps

Iters	Range		Point
9	4.2510925688866986e-107	2.8178005652473096e-100	5.425391492838313e-104
8	4.094281001631858e-154	2.5060731010565417e-151	1.0818695835402839e-152
9	4.564380189661613e-208	1.9318991468802383e-202	1.9132400570361906e-202
4	-1.6010392203265926e-75	-1.038324017640297e-75	-1.3451745365367447e-75

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes188.0ms (0.1%)

Compiler: Compiled 186 to 270 computations (-45.2% saved)

bsearch245.0ms (0.2%)

Steps

Iters	Range		Point
9	4.2510925688866986e-107	2.8178005652473096e-100	2.3151185714216374e-106
8	4.094281001631858e-154	2.5060731010565417e-151	1.80769309951527e-152
9	4.564380189661613e-208	1.9318991468802383e-202	1.6146946195314308e-202
4	-0.05398046381745485	-0.03281088659107353	-0.04538032306923744

Compiler

Compiled 2 to 4 computations (-100% saved)

regimes148.0ms (0.1%)

Compiler: Compiled 74 to 149 computations (-101.4% saved)

bsearch155.0ms (0.1%)

Steps

Iters	Range		Point
7	1.001026926498438e-131	1.7981766008968552e-130	4.0640731494757617e-131
9	-249170.4714371465	-0.001858490622145534	-9.303156171150226

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes94.0ms (0.1%)

Compiler: Compiled 30 to 90 computations (-200% saved)

bsearch161.0ms (0.1%)

Steps

Iters	Range		Point
8	1.5842080873298614e-134	1.001026926498438e-131	2.6130017305138674e-134
9	-249170.4714371465	-0.001858490622145534	-9.303156171150226

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0%)

Accuracy

Total 2.2b remaining (96%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch27.0ms (0%)

Compiler: Compiled 638 to 368 computations (42.3% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	213	994
1	213	994

end0.0ms (0%)

sample30.4s (22.5%)

Algorithm

1×

intervals

Results

3.7s	4676×	body	1024	valid
755.0ms	1425×	body	512	valid
188.0ms	1358×	body	128	valid
168.0ms	525×	body	256	valid
23.0ms	16×	body	2048	valid

Compiler

Compiled 25674 to 18926 computations (26.3% saved)

Pareto

0.33471745006460984