Details

analyze620.0ms (2.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 30 to 30 computations (0% saved)

sample98.0ms (0.4%)

Algorithm

1×

intervals

Results

33.0ms	189×	body	128	valid
29.0ms	30×	body	1024	valid
15.0ms	26×	body	512	valid
4.0ms	11×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify136.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5325	39

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.5b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
0.0b	(+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.3b	(pow.f64 (sin.f64 ky) 2)
0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
2.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.6b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_100`
30×	`*-un-lft-identity_binary64_78`
26×	`add-cube-cbrt_binary64_113`
21×	`times-frac_binary64_84`
19×	`add-exp-log_binary64_116`
15×	`sqrt-prod_binary64_94`
13×	`unpow-prod-down_binary64_157`
12×	`associate-l_binary64_19`
8×	`add-cbrt-cube_binary64_114`
6×	`prod-exp_binary64_127` `associate-/r*_binary64_22` `pow1_binary64_139`
5×	`associate-r_binary64_18`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
3×	`div-exp_binary64_129` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/l*_binary64_23` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`pow-to-exp_binary64_147` `div-inv_binary64_75` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `pow-pow_binary64_150` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 113

Calls

8 calls:

16.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
0.0ms	(+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

series3.4s (13.1%)

Counts

4 → 56

Calls

4 calls:

1.7s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
1.1s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
574.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
21.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4097 to 3742 computations (8.7% saved)

simplify79.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5125	5888

prune408.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	3	170

Error

0.0b

Counts

170 → 3

Compiler

Compiled 5844 to 4280 computations (26.8% saved)

localize22.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
0.0b	(+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
0.4b	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.4b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.6b	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))

rewrite71.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
32×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
29×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113`
24×	`times-frac_binary64_84`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
15×	`sqrt-prod_binary64_94`
14×	`associate-l_binary64_19`
12×	`pow1_binary64_139`
11×	`frac-times_binary64_88` `associate-*r/_binary64_20`
8×	`flip-+_binary64_52` `flip3-+_binary64_81`
6×	`associate-r_binary64_18` `associate-/r*_binary64_22`
5×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28`
4×	`add-log-exp_binary64_117` `associate-*l/_binary64_21` `pow-prod-down_binary64_149` `sqrt-div_binary64_95`
3×	`div-inv_binary64_75` `associate-/l*_binary64_23`
2×	`*-commutative_binary64_9` `unpow-prod-down_binary64_157` `associate-/r/_binary64_24` `distribute-lft-out_binary64_29`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `unswap-sqr_binary64_46` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 148

Calls

8 calls:

22.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
17.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
0.0ms	(+.f64 1/2 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))

series3.9s (15.1%)

Counts

4 → 67

Calls

4 calls:

1.7s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
1.1s	(sqrt.f64 (+.f64 1 (.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
589.0ms	(.f64 (/.f64 (.f64 2 l) Om) (.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
513.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4743 to 4321 computations (8.9% saved)

simplify125.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4972	8029
1	4972	8029

prune499.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	215	3	218

Error

0.0b

Counts

218 → 3

Compiler

Compiled 7822 to 5347 computations (31.6% saved)

localize26.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.1b	(+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))
0.0b	(sqrt.f64 (+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))))
0.0b	(+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))
0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
2.2b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
2.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.6b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_100`
42×	`*-un-lft-identity_binary64_78`
39×	`times-frac_binary64_84`
38×	`add-cube-cbrt_binary64_113`
25×	`log-pow_binary64_167`
24×	`sqrt-prod_binary64_94` `exp-prod_binary64_130`
18×	`add-exp-log_binary64_116`
12×	`associate-l_binary64_19`
10×	`unpow-prod-down_binary64_157`
8×	`add-cbrt-cube_binary64_114`
6×	`prod-exp_binary64_127` `associate-/r*_binary64_22` `sqrt-div_binary64_95` `pow1_binary64_139`
5×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `unswap-sqr_binary64_46` `associate-/r/_binary64_24` `flip3-+_binary64_81`
3×	`pow-exp_binary64_146` `div-exp_binary64_129` `div-inv_binary64_75` `associate-/l*_binary64_23` `log-prod_binary64_164`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `*-commutative_binary64_9` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `rem-log-exp_binary64_119` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 131

Calls

8 calls:

17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
7.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.0ms	(+.f64 1/2 (log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))))

series5.7s (22.3%)

Counts

4 → 69

Calls

4 calls:

2.6s	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
1.5s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
1.1s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
573.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 5407 to 4935 computations (8.7% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5104	7578

prune513.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	200	3	203

Error

0.0b

Counts

203 → 3

Compiler

Compiled 7537 to 5610 computations (25.6% saved)

localize34.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))
0.0b	(+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l)))
0.0b	(+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l)))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))
3.3b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
3.3b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
27.6b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
28.2b	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))

rewrite133.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`times-frac_binary64_84`
41×	`add-sqr-sqrt_binary64_100`
40×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
24×	`unpow-prod-down_binary64_157`
16×	`associate-/l*_binary64_23`
15×	`sqrt-prod_binary64_94`
14×	`add-exp-log_binary64_116`
11×	`pow1_binary64_139`
8×	`add-cbrt-cube_binary64_114` `unpow2_binary64_143` `sqr-pow_binary64_50` `sqrt-div_binary64_95`
7×	`associate-/r/_binary64_24`
6×	`sqrt-pow1_binary64_96` `div-exp_binary64_129` `frac-times_binary64_88` `associate-/r_binary64_22` `associate-r/_binary64_20`
4×	`frac-add_binary64_86` `add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`div-inv_binary64_75`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `pow-flip_binary64_152` `associate-*l/_binary64_21` `pow-prod-down_binary64_149` `clear-num_binary64_77` `pow1/2_binary64_158`
1×	`inv-pow_binary64_163` `rem-sqrt-square_binary64_91`

Counts

4 → 144

Calls

8 calls:

49.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
49.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
0.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (+.f64 (.f64 l (sqrt.f64 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) (.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))) l))))))

series1.5s (5.8%)

Counts

4 → 34

Calls

4 calls:

701.0ms	(sqrt.f64 (/.f64 1 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))))
549.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
116.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
116.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

Compiler

Compiled 3192 to 2558 computations (19.9% saved)

simplify77.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4956	3627
1	4956	3627

prune540.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	178	3	181

Error

0.0b

Counts

181 → 3

Compiler

Compiled 9774 to 6410 computations (34.4% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	344	1316
1	344	1316

regimes1.2s (4.8%)

Compiler: Compiled 15296 to 14332 computations (6.3% saved)

bsearch0.0ms (0%)

regimes944.0ms (3.7%)

Compiler: Compiled 10139 to 9912 computations (2.2% saved)

bsearch0.0ms (0%)

regimes740.0ms (2.9%)

Compiler: Compiled 4396 to 4409 computations (-0.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 5 computations (-150% saved)

regimes192.0ms (0.7%)

Compiler: Compiled 758 to 906 computations (-19.5% saved)

bsearch91.0ms (0.4%)

Steps

Iters	Range		Point
10	3.4719929211885745e-203	1.8483554494566125e-187	1.7604062973197394e-187
6	-8.040822055462166e-170	-5.206241069737631e-171	-7.836070606393636e-170

Compiler

Compiled 2 to 5 computations (-150% saved)

regimes224.0ms (0.9%)

Compiler: Compiled 408 to 536 computations (-31.4% saved)

bsearch120.0ms (0.5%)

Steps

Iters	Range	Point
8	7.65343094713454e-170	4.6179694833997445e-165	4.483079975783935e-165
5	-3.456086996578043e-186	-1.4744067752513707e-186	-3.4194323654837935e-186
10	-8.09362972759438e-94	-7.395334598994594e-104	-7.4862524034405e-104

Iters

Range

Point

7.65343094713454e-170

4.6179694833997445e-165

4.483079975783935e-165

-3.456086996578043e-186

-1.4744067752513707e-186

-3.4194323654837935e-186

-8.09362972759438e-94

-7.395334598994594e-104

-7.4862524034405e-104

Compiler

Compiled 2 to 5 computations (-150% saved)

regimes129.0ms (0.5%)

Compiler: Compiled 170 to 272 computations (-60% saved)

bsearch238.0ms (0.9%)

Steps

Iters	Range		Point
6	1.6967541409569276e-136	1.257801694052009e-135	4.89496005856651e-136
12	-1.385434715884739e-113	-1.3262825730878849e-160	-9.85489521685411e-146
9	-2.156787316921108e+195	-6.073213209174934e+186	-6.077199276602143e+194
7	-3.2453101456534925e+225	-9.532588643822812e+223	-9.71570446515414e+223

Compiler

Compiled 1 to 4 computations (-300% saved)

regimes35.0ms (0.1%)

Accuracy

Total 0.7b remaining (92.1%)

Threshold costs 0.7b (92.1%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch19.0ms (0.1%)

Compiler: Compiled 387 to 312 computations (19.4% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	154	463
1	154	463

end0.0ms (0%)

sample3.7s (14.2%)

Algorithm

1×

intervals

Results

1.2s	6428×	body	128	valid
664.0ms	787×	body	1024	valid
310.0ms	518×	body	512	valid
101.0ms	266×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 1174 to 1066 computations (9.2% saved)

Pareto

-0.03677900837231989

Details

analyze620.0ms (2.4%)

sample98.0ms (0.4%)

simplify136.0ms (0.5%)

prune8.0ms (0%)

localize20.0ms (0.1%)

rewrite43.0ms (0.2%)

series3.4s (13.1%)

simplify79.0ms (0.3%)

prune408.0ms (1.6%)

localize22.0ms (0.1%)

rewrite71.0ms (0.3%)

series3.9s (15.1%)

simplify125.0ms (0.5%)

prune499.0ms (1.9%)

localize26.0ms (0.1%)

rewrite56.0ms (0.2%)

series5.7s (22.3%)

simplify94.0ms (0.4%)

prune513.0ms (2%)

localize34.0ms (0.1%)

rewrite133.0ms (0.5%)

series1.5s (5.8%)

simplify77.0ms (0.3%)

prune540.0ms (2.1%)

simplify19.0ms (0.1%)

regimes1.2s (4.8%)

bsearch0.0ms (0%)

regimes944.0ms (3.7%)

bsearch0.0ms (0%)

regimes740.0ms (2.9%)

bsearch1.0ms (0%)

regimes192.0ms (0.7%)

bsearch91.0ms (0.4%)

regimes224.0ms (0.9%)

bsearch120.0ms (0.5%)

regimes129.0ms (0.5%)

bsearch238.0ms (0.9%)

regimes35.0ms (0.1%)

bsearch19.0ms (0.1%)

simplify9.0ms (0%)

end0.0ms (0%)

sample3.7s (14.2%)

Profiling