Details

analyze1.2s (9.9%)

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)

sample154.0ms (1.2%)

Algorithm

1×

intervals

Results

110.0ms	135×	body	1024	valid
18.0ms	37×	body	512	valid
8.0ms	62×	body	128	valid
7.0ms	22×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify238.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5170	26

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 3.4b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

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 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series619.0ms (5%)

Counts

4 → 12

Calls

4 calls:

405.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
163.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
27.0ms	(pow.f64 (sin.f64 ky) 2)
24.0ms	(pow.f64 (sin.f64 kx) 2)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5013	2288

prune170.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	10	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 2.4b

Counts

116 → 10

Compiler

Compiled 2951 to 1652 computations (44% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-r_binary64_18`
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-l_binary64_19` `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` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

22.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
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)

series616.0ms (5%)

Counts

4 → 12

Calls

4 calls:

401.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
165.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.0ms	(pow.f64 (sin.f64 ky) 2)
25.0ms	(pow.f64 (sin.f64 kx) 2)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4949	2129
1	4949	2129

prune141.0ms (1.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	114	11	125

Merged error: 2.4b

Counts

125 → 11

Compiler

Compiled 2864 to 1568 computations (45.3% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite53.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 113

Calls

4 calls:

15.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
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)

series840.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

350.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
303.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
163.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 ky) 2)

simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4931	3150
1	4931	3150

prune246.0ms (2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	125	11	136

Merged error: 2.4b

Counts

136 → 11

Compiler

Compiled 4819 to 2948 computations (38.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 ky))
0.6b	(cbrt.f64 (sin.f64 ky))
0.8b	(pow.f64 (cbrt.f64 (sin.f64 ky)) 4)
3.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`cbrt-prod_binary64_109`
6×	`unpow-prod-down_binary64_157` `pow1_binary64_139`
5×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `pow1/3_binary64_160` `pow-unpow_binary64_155`
2×	`pow-pow_binary64_150` `sqrt-div_binary64_95`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `sqr-pow_binary64_50` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 58

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))
4.0ms	(pow.f64 (cbrt.f64 (sin.f64 ky)) 4)
2.0ms	(cbrt.f64 (sin.f64 ky))
2.0ms	(cbrt.f64 (sin.f64 ky))

series570.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(pow.f64 (cbrt.f64 (sin.f64 ky)) 4)
164.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (*.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 4) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2))))
117.0ms	(cbrt.f64 (sin.f64 ky))
114.0ms	(cbrt.f64 (sin.f64 ky))

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4924	863
1	4924	863

prune87.0ms (0.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	70	11	81

Merged error: 2.4b

Counts

81 → 11

Compiler

Compiled 1823 to 962 computations (47.2% saved)

regimes777.0ms (6.3%)

Compiler: Compiled 8868 to 6991 computations (21.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	26
1	16	26

end0.0ms (0%)

sample6.1s (49.4%)

Algorithm

1×

intervals

Results

3.7s	4590×	body	1024	valid
695.0ms	1456×	body	512	valid
187.0ms	1416×	body	128	valid
160.0ms	521×	body	256	valid
27.0ms	17×	body	2048	valid

Compiler

Compiled 1009 to 797 computations (21% saved)

Details

analyze1.2s (9.9%)

sample154.0ms (1.2%)

simplify238.0ms (1.9%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite50.0ms (0.4%)

series619.0ms (5%)

simplify75.0ms (0.6%)

prune170.0ms (1.4%)

localize14.0ms (0.1%)

rewrite47.0ms (0.4%)

series616.0ms (5%)

simplify85.0ms (0.7%)

prune141.0ms (1.1%)

localize20.0ms (0.2%)

rewrite53.0ms (0.4%)

series840.0ms (6.8%)

simplify106.0ms (0.9%)

prune246.0ms (2%)

localize21.0ms (0.2%)

rewrite19.0ms (0.2%)

series570.0ms (4.6%)

simplify51.0ms (0.4%)

prune87.0ms (0.7%)

regimes777.0ms (6.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.1s (49.4%)

Profiling