Details

analyze1.3s (1.1%)

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)

sample159.0ms (0.1%)

Algorithm

1×

intervals

Results

110.0ms	142×	body	1024	valid
23.0ms	46×	body	512	valid
7.0ms	25×	body	256	valid
6.0ms	42×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify176.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5170	26

prune2.0ms (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

2.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 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	(/.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 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite43.0ms (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:

18.0ms	(*.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))

series943.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

694.0ms	(*.f64 (/.f64 (sin.f64 ky) (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)))
30.0ms	(pow.f64 (sin.f64 ky) 2)
27.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1426 to 1140 computations (20.1% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5392	3324

prune974.0ms (0.8%)

Pruning

87 alts after pruning (86 fresh and 1 done)

	Pruned	Kept	Total
New	57	86	143
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	57	87	144

Error

0.5b

Counts

144 → 87

Compiler

Compiled 5047 to 3318 computations (34.3% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 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	(/.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 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite50.0ms (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))
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))

series956.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

707.0ms	(*.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)))
32.0ms	(pow.f64 (sin.f64 kx) 2)
29.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1811 to 1525 computations (15.8% saved)

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5392	3324

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

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (pow.f64 kx 4) 1/3)
0.1b	(.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))
0.1b	(*.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))
0.3b	(/.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))))
5.6b	(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)))
19.3b	(-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3))
20.4b	(+.f64 (-.f64 (.f64 kx kx) (.f64 (pow.f64 kx 4) 1/3)) (*.f64 (pow.f64 kx 6) 2/45))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_78`
22×	`add-sqr-sqrt_binary64_100`
21×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84`
20×	`sqrt-prod_binary64_94`
11×	`add-log-exp_binary64_117`
7×	`associate-/r*_binary64_22`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`sqrt-div_binary64_95`
3×	`flip-+_binary64_52` `associate-/l*_binary64_23` `flip3-+_binary64_81`
2×	`diff-log_binary64_170` `associate-+l+_binary64_11` `associate-/r/_binary64_24` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `associate-+l-_binary64_13` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 88

Calls

8 calls:

18.0ms	(/.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))))
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)))
9.0ms	(+.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))
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))

series1.2s (1%)

Counts

4 → 38

Calls

4 calls:

655.0ms	(/.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))))
369.0ms	(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)))
81.0ms	(-.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))

Compiler

Compiled 2042 to 1766 computations (13.5% saved)

simplify83.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5205	5668

localize19.0ms (0%)

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 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))))) (sin.f64 th))
0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2)))))
0.0b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2)))
0.2b	(pow.f64 (sin.f64 kx) 2)
1.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))))
1.0b	(pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))
1.5b	(pow.f64 (sin.f64 ky) (sqrt.f64 2))

rewrite30.0ms (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:

10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))))
5.0ms	(pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))
4.0ms	(pow.f64 (sin.f64 ky) (sqrt.f64 2))
3.0ms	(pow.f64 (sin.f64 kx) 2)
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2)))

series1.3s (1.1%)

Counts

4 → 27

Calls

4 calls:

914.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))))
270.0ms	(pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))
120.0ms	(pow.f64 (sin.f64 ky) (sqrt.f64 2))
30.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2195 to 1920 computations (12.5% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4963	1766
1	4963	1766

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

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)))))
0.1b	(+.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))
0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite35.0ms (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:

12.0ms	(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)))
4.0ms	(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))

series464.0ms (0.4%)

Counts

4 → 34

Calls

4 calls:

200.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
195.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
36.0ms	(pow.f64 (sin.f64 ky) 2)
32.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1864 to 1388 computations (25.5% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4957	1784
1	4957	1784

prune11.0s (9.1%)

Pruning

322 alts after pruning (316 fresh and 6 done)

	Pruned	Kept	Total
New	243	237	480
Fresh	2	79	81
Picked	0	0	0
Done	0	6	6
Total	245	322	567

Error

0.5b

Counts

567 → 322

Compiler

Compiled 23872 to 16782 computations (29.7% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 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	(/.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 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite47.0ms (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:

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))
8.0ms	(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))

series966.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

699.0ms	(*.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)))
36.0ms	(pow.f64 (sin.f64 kx) 2)
29.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1646 to 1360 computations (17.4% saved)

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5392	3324

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(*.f64 (sin.f64 ky) (sin.f64 th))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.2b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.2b	(pow.f64 (sin.f64 ky) 2)
2.2b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.7b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite64.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`*-un-lft-identity_binary64_78`
47×	`times-frac_binary64_84`
42×	`sqrt-prod_binary64_94`
39×	`add-sqr-sqrt_binary64_100`
35×	`add-cube-cbrt_binary64_113`
24×	`associate-r_binary64_18`
23×	`unpow-prod-down_binary64_157`
20×	`distribute-lft-out_binary64_29`
14×	`add-exp-log_binary64_116`
13×	`pow1_binary64_139`
11×	`add-cbrt-cube_binary64_114`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-/l*_binary64_23` `pow-prod-down_binary64_149` `sqrt-div_binary64_95` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`div-exp_binary64_129` `inv-pow_binary64_163` `pow-flip_binary64_152` `sin-mult_binary64_233`
1×	`-commutative_binary64_9` `associate-l_binary64_19` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `unpow2_binary64_143` `frac-2neg_binary64_89` `1-exp_binary64_122` `sqr-pow_binary64_50` `frac-times_binary64_88` `pow-pow_binary64_150` `rec-exp_binary64_128` `associate-l/_binary64_21` `associate-*r/_binary64_20` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 137

Calls

8 calls:

19.0ms	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
15.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
10.0ms	(/.f64 1 (+.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))

series1.3s (1.1%)

Counts

4 → 44

Calls

4 calls:

721.0ms	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
288.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
257.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2140 to 1815 computations (15.2% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4976	4550
1	4976	4550

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (sin.f64 th) (sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx))))))))
0.0b	(.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx)))
0.0b	(+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx))))
0.4b	(/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx)))))
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.3b	(/.f64 (*.f64 ky ky) (sin.f64 kx))
13.6b	(sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx))))))

rewrite38.0ms (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 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx)))))
6.0ms	(sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx))))))
5.0ms	(/.f64 (*.f64 ky ky) (sin.f64 kx))
0.0ms	(+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx))))

series824.0ms (0.7%)

Counts

4 → 36

Calls

4 calls:

300.0ms	(/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx)))))
235.0ms	(sqrt.f64 (/.f64 (sin.f64 ky) (+.f64 (sin.f64 kx) (.f64 1/2 (/.f64 (.f64 ky ky) (sin.f64 kx))))))
173.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
116.0ms	(/.f64 (*.f64 ky ky) (sin.f64 kx))

Compiler

Compiled 2432 to 1771 computations (27.2% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5034	3312

localize23.0ms (0%)

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 (.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2))))) (sin.f64 th))
0.1b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2)))))
0.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2)))
1.5b	(pow.f64 (sin.f64 ky) (sqrt.f64 2))
10.9b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
10.9b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
10.9b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

rewrite19.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_109`
13×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
12×	`unpow-prod-down_binary64_157`
6×	`pow-unpow_binary64_155`
5×	`add-exp-log_binary64_116` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqr-pow_binary64_50`
3×	`sqrt-prod_binary64_94` `unpow2_binary64_143` `pow1/3_binary64_160`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow-pow_binary64_150`

Counts

4 → 68

Calls

8 calls:

3.0ms	(pow.f64 (sin.f64 ky) (sqrt.f64 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
0.0ms	(+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (pow.f64 (sin.f64 ky) (sqrt.f64 2)) (sqrt.f64 2)))

series460.0ms (0.4%)

Counts

4 → 23

Calls

4 calls:

121.0ms	(pow.f64 (sin.f64 ky) (sqrt.f64 2))
118.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
111.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
110.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

Compiler

Compiled 1392 to 1168 computations (16.1% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4919	1203
1	4919	1203

prune23.0s (19%)

Pruning

565 alts after pruning (554 fresh and 11 done)

	Pruned	Kept	Total
New	294	251	545
Fresh	8	303	311
Picked	0	0	0
Done	0	11	11
Total	302	565	867

Error

0.5b

Counts

867 → 565

Compiler

Compiled 34482 to 24197 computations (29.8% saved)

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 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	(/.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 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite51.0ms (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:

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))
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))

series972.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

719.0ms	(*.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)))
34.0ms	(pow.f64 (sin.f64 kx) 2)
30.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1866 to 1580 computations (15.3% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5392	3324

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:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(/.f64 1/2 (pow.f64 (sin.f64 kx) 2))
0.1b	(*.f64 ky (sin.f64 th))
0.1b	(+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)
2.7b	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
3.6b	(*.f64 (sin.f64 th) (pow.f64 ky 3))
3.9b	(-.f64 (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (.f64 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)))
5.6b	(.f64 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6))

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64_116`
22×	`add-sqr-sqrt_binary64_100`
20×	`add-cbrt-cube_binary64_114`
16×	`associate-r_binary64_18`
15×	`*-un-lft-identity_binary64_78`
13×	`add-cube-cbrt_binary64_113`
12×	`prod-exp_binary64_127`
10×	`associate-l_binary64_19`
6×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `div-exp_binary64_129` `times-frac_binary64_84` `pow1_binary64_139`
5×	`frac-sub_binary64_87` `unswap-sqr_binary64_46`
4×	`cbrt-undiv_binary64_112` `unpow-prod-down_binary64_157` `flip-+_binary64_52` `frac-times_binary64_88` `associate-*r/_binary64_20` `cube-prod_binary64_106` `flip3-+_binary64_81`
3×	`associate-l/_binary64_21` `associate-/r_binary64_22`
2×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `distribute-rgt-in_binary64_28` `sqr-pow_binary64_50` `div-inv_binary64_75` `associate--r+_binary64_14`
1×	`cube-mult_binary64_108` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `associate-/l*_binary64_23` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `distribute-lft-out_binary64_29` `unpow3_binary64_144` `sub-div_binary64_85` `sub-neg_binary64_71`

Counts

4 → 108

Calls

8 calls:

21.0ms	(.f64 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6))
9.0ms	(-.f64 (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (.f64 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)))
7.0ms	(*.f64 (sin.f64 th) (pow.f64 ky 3))
5.0ms	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
0.0ms	(+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)

series2.1s (1.8%)

Counts

4 → 47

Calls

4 calls:

1.1s	(-.f64 (/.f64 (.f64 ky (sin.f64 th)) (sin.f64 kx)) (.f64 (/.f64 (*.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6)))
659.0ms	(.f64 (/.f64 (.f64 (sin.f64 th) (pow.f64 ky 3)) (sin.f64 kx)) (+.f64 (/.f64 1/2 (pow.f64 (sin.f64 kx) 2)) 1/6))
252.0ms	(/.f64 (*.f64 ky (sin.f64 th)) (sin.f64 kx))
107.0ms	(*.f64 (sin.f64 th) (pow.f64 ky 3))

Compiler

Compiled 3133 to 2430 computations (22.4% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5267	4322

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (*.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))) (sin.f64 th))
0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))
1.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))
16.7b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
16.7b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
16.7b	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_109`
12×	`add-sqr-sqrt_binary64_100`
11×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`unpow-prod-down_binary64_157`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `unpow2_binary64_143` `pow1/3_binary64_160` `sqr-pow_binary64_50`
2×	`sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 63

Calls

8 calls:

5.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))))

series532.0ms (0.4%)

Counts

4 → 30

Calls

4 calls:

202.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 ky) 2)) (cbrt.f64 (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (pow.f64 (sin.f64 ky) 2)))))
115.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
109.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))
105.0ms	(cbrt.f64 (pow.f64 (sin.f64 ky) 2))

Compiler

Compiled 1240 to 1010 computations (18.5% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5004	1546

localize34.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 (pow.f64 (sin.f64 ky) 4) (*.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) 6) (pow.f64 (sin.f64 ky) 6))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.0b	(+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))
0.6b	(pow.f64 (sin.f64 kx) 6)
5.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))
5.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
5.3b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite73.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64_78`
85×	`sqrt-prod_binary64_94`
56×	`times-frac_binary64_84`
44×	`add-sqr-sqrt_binary64_100`
42×	`add-cube-cbrt_binary64_113`
28×	`distribute-lft-out_binary64_29`
21×	`unpow-prod-down_binary64_157`
8×	`associate-/l*_binary64_23` `sqrt-div_binary64_95`
7×	`associate-/r*_binary64_22` `add-exp-log_binary64_116` `pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`pow-unpow_binary64_155`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-/r/_binary64_24` `associate-/l/_binary64_25` `pow1/2_binary64_158`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `div-inv_binary64_75` `pow-pow_binary64_150` `sqrt-undiv_binary64_99` `clear-num_binary64_77`

Counts

4 → 138

Calls

8 calls:

20.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))
3.0ms	(pow.f64 (sin.f64 kx) 6)
0.0ms	(+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))

series1.8s (1.5%)

Counts

4 → 41

Calls

4 calls:

935.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6))) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
445.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 4) (-.f64 (pow.f64 (sin.f64 ky) 4) (*.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
341.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 6) (pow.f64 (sin.f64 ky) 6)))
64.0ms	(pow.f64 (sin.f64 kx) 6)

Compiler

Compiled 2562 to 2008 computations (21.6% saved)

simplify104.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5221	9066

prune31.7s (26.2%)

Pruning

822 alts after pruning (807 fresh and 15 done)

	Pruned	Kept	Total
New	295	275	570
Fresh	17	532	549
Picked	0	0	0
Done	1	15	16
Total	313	822	1135

Error

0.5b

Counts

1135 → 822

Compiler

Compiled 15759 to 9817 computations (37.7% saved)

simplify1.1s (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4989	61577
1	4989	61577

regimes21.5s (17.7%)

Compiler: Compiled 248286 to 185713 computations (25.2% saved)

bsearch0.0ms (0%)

regimes1.4s (1.2%)

Compiler: Compiled 6877 to 5989 computations (12.9% saved)

bsearch284.0ms (0.2%)

Steps

Iters	Range		Point
10	2.337829699065026e+165	2.4957889649797083e+175	1.0553320421210306e+166
6	2.8799265070588195e-20	3.7188437170632034e-19	3.6569678143575064e-19
8	-0.004296815640009351	-1.2715377982662133e-06	-0.004207042989973588

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes1.1s (0.9%)

Compiler: Compiled 4727 to 4347 computations (8% saved)

bsearch285.0ms (0.2%)

Steps

Iters	Range		Point
10	2.337829699065026e+165	2.4957889649797083e+175	4.386169214952346e+171
6	2.8799265070588195e-20	3.7188437170632034e-19	3.6569678143575064e-19
8	-0.004296815640009351	-1.2715377982662133e-06	-0.003338465294700686

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes822.0ms (0.7%)

Compiler: Compiled 3761 to 3482 computations (7.4% saved)

bsearch1.0ms (0%)

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

regimes706.0ms (0.6%)

Compiler: Compiled 1772 to 1748 computations (1.4% saved)

bsearch1.0ms (0%)

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

regimes524.0ms (0.4%)

Compiler: Compiled 1545 to 1517 computations (1.8% saved)

bsearch1.0ms (0%)

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

regimes504.0ms (0.4%)

Compiler: Compiled 1454 to 1433 computations (1.4% saved)

bsearch1.0ms (0%)

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

regimes405.0ms (0.3%)

Compiler: Compiled 1062 to 1080 computations (-1.7% saved)

bsearch1.0ms (0%)

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

regimes242.0ms (0.2%)

Compiler: Compiled 510 to 582 computations (-14.1% saved)

bsearch1.0ms (0%)

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

regimes224.0ms (0.2%)

Compiler: Compiled 197 to 295 computations (-49.7% saved)

bsearch134.0ms (0.1%)

Steps

Iters	Range		Point
9	1.5856102336962356e-39	3.714984628513282e-32	1.9010806566848318e-39
7	-3.2999395276986405	-0.18850954133291345	-3.1381468154648124

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes102.0ms (0.1%)

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

bsearch116.0ms (0.1%)

Steps

Iters	Range		Point
7	6.149779270512974e-156	2.4338250986912726e-154	6.2465106726532e-156
7	-3.2999395276986405	-0.18850954133291345	-3.1381468154648124

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes27.0ms (0%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch24.0ms (0%)

Compiler: Compiled 529 to 326 computations (38.4% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	188	800
1	188	800

end0.0ms (0%)

sample7.5s (6.2%)

Algorithm

1×

intervals

Results

3.7s	4587×	body	1024	valid
673.0ms	1394×	body	512	valid
201.0ms	1438×	body	128	valid
181.0ms	561×	body	256	valid
28.0ms	20×	body	2048	valid

Compiler

Compiled 28601 to 21303 computations (25.5% saved)