Details

analyze599.0ms (3.1%)

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)

sample80.0ms (0.4%)

Algorithm

1×

intervals

Results

37.0ms	210×	body	128	valid
17.0ms	22×	body	1024	valid
10.0ms	18×	body	512	valid
2.0ms	6×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify134.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune6.0ms (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

0.0b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.8b	(/.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))))))
7.7b	(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)))))

rewrite309.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

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×	`pow1_binary64_139` `associate-/r*_binary64_22` `prod-exp_binary64_127`
5×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `pow-exp_binary64_146` `unswap-sqr_binary64_46`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `associate-/l*_binary64_23` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-unpow_binary64_155`
2×	`div-inv_binary64_75` `associate-/r/_binary64_24` `pow-to-exp_binary64_147` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `cbrt-unprod_binary64_111` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `pow-pow_binary64_150`

Counts

4 → 113

Calls

4 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	(pow.f64 (sin.f64 kx) 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)))))

Compiler

Compiled 4614 to 3499 computations (24.2% saved)

series3.4s (17.7%)

Error

0.0b

Counts

4 → 58

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))))))
1.0s	(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)))))
568.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 6332 to 5516 computations (12.9% saved)

simplify100.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5005	6187

prune384.0ms (2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	2	172

Error

Counts

172 → 2

Compiler

Compiled 5995 to 4384 computations (26.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
0.8b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
2.6b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
7.7b	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

rewrite436.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

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-r_binary64_18`
10×	`unpow-prod-down_binary64_157`
8×	`add-cbrt-cube_binary64_114`
6×	`pow1_binary64_139` `sqrt-div_binary64_95` `associate-/r*_binary64_22` `prod-exp_binary64_127`
5×	`associate-l_binary64_19`
4×	`add-log-exp_binary64_117` `flip3-+_binary64_81` `flip-+_binary64_52` `associate-/r/_binary64_24` `unswap-sqr_binary64_46`
3×	`div-inv_binary64_75` `log-prod_binary64_164` `div-exp_binary64_129` `associate-/l*_binary64_23` `pow-exp_binary64_146`
2×	`unpow2_binary64_143` `sqr-pow_binary64_50` `associate-*l/_binary64_21` `distribute-lft-out_binary64_29`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `rem-log-exp_binary64_119` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `*-commutative_binary64_9`

Counts

4 → 129

Calls

4 calls:

17.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))
8.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
6.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))

Compiler

Compiled 6069 to 4682 computations (22.9% saved)

series6.1s (31.7%)

Error

Counts

4 → 72

Calls

4 calls:

2.8s	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))))
1.5s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2)))))
1.0s	(sqrt.f64 (+.f64 1 (.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))))
566.0ms	(.f64 (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)) (pow.f64 (/.f64 (.f64 2 l) Om) 2))

Compiler

Compiled 8412 to 7354 computations (12.6% saved)

simplify116.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4948	7941
1	4948	7941

prune510.0ms (2.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	201	2	203

Error

Counts

203 → 2

Compiler

Compiled 7720 to 5761 computations (25.4% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.0b	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
5.5b	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
7.4b	(/.f64 (*.f64 l l) Om)
7.7b	(sqrt.f64 (+.f64 1 (.f64 4 (.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))

rewrite322.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

45×	`*-un-lft-identity_binary64_78`
43×	`times-frac_binary64_84`
36×	`add-sqr-sqrt_binary64_100`
31×	`add-cube-cbrt_binary64_113`
23×	`add-exp-log_binary64_116`
20×	`add-cbrt-cube_binary64_114`
18×	`unpow-prod-down_binary64_157`
11×	`associate-r_binary64_18`
9×	`associate-/l*_binary64_23`
7×	`pow1_binary64_139` `div-exp_binary64_129` `associate-l_binary64_19` `distribute-lft-out_binary64_29`
6×	`associate-/r*_binary64_22`
5×	`prod-exp_binary64_127` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111` `div-inv_binary64_75`
4×	`add-log-exp_binary64_117` `unpow2_binary64_143` `sqr-pow_binary64_50`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94` `frac-times_binary64_88` `associate-*r/_binary64_20`
2×	`sqrt-div_binary64_95` `frac-2neg_binary64_89` `clear-num_binary64_77` `frac-add_binary64_86` `unswap-sqr_binary64_46`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `pow-prod-down_binary64_149` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `associate-l/_binary64_21` `distribute-rgt-out_binary64_31` `-commutative_binary64_9`

Counts

4 → 129

Calls

4 calls:

50.0ms	(.f64 (/.f64 (.f64 l l) 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 ky) 2) Om)
5.0ms	(/.f64 (*.f64 l l) Om)
3.0ms	(sqrt.f64 (+.f64 1 (.f64 4 (.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))

Compiler

Compiled 5216 to 3128 computations (40% saved)

series1.9s (10.1%)

Error

Counts

4 → 48

Calls

4 calls:

1.0s	(sqrt.f64 (+.f64 1 (.f64 4 (.f64 (/.f64 (*.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))))
652.0ms	(.f64 (/.f64 (.f64 l l) Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om)))
107.0ms	(/.f64 (pow.f64 (sin.f64 ky) 2) Om)
79.0ms	(/.f64 (*.f64 l l) Om)

Compiler

Compiled 4945 to 4236 computations (14.3% saved)

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5632	4323

prune311.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	177	2	179

Error

Counts

179 → 2

Compiler

Compiled 6121 to 3722 computations (39.2% saved)

regimes1.1s (5.8%)

Accuracy

Total 0.4b remaining (39.2%)

Threshold costs 0.4b (39.2%)

Compiler

Compiled 10431 to 10301 computations (1.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	107
1	32	107

end0.0ms (0%)

sample3.2s (16.8%)

Algorithm

1×

intervals

Results

1.1s	6366×	body	128	valid
640.0ms	763×	body	1024	valid
332.0ms	558×	body	512	valid
130.0ms	311×	body	256	valid
3.0ms	2×	body	2048	valid

Compiler

Compiled 607 to 587 computations (3.3% saved)

Details

analyze599.0ms (3.1%)

sample80.0ms (0.4%)

simplify134.0ms (0.7%)

prune6.0ms (0%)

localize25.0ms (0.1%)

rewrite309.0ms (1.6%)

series3.4s (17.7%)

simplify100.0ms (0.5%)

prune384.0ms (2%)

localize25.0ms (0.1%)

rewrite436.0ms (2.3%)

series6.1s (31.7%)

simplify116.0ms (0.6%)

prune510.0ms (2.6%)

localize22.0ms (0.1%)

rewrite322.0ms (1.7%)

series1.9s (10.1%)

simplify71.0ms (0.4%)

prune311.0ms (1.6%)

regimes1.1s (5.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.2s (16.8%)

Profiling