Details

analyze604.0ms (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)

sample83.0ms (0.4%)

Algorithm

1×

intervals

Results

35.0ms	203×	body	128	valid
23.0ms	24×	body	1024	valid
9.0ms	16×	body	512	valid
5.0ms	13×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify143.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5325	39

prune5.0ms (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

Merged error: 1.0b

Counts

2 → 1

Compiler

Compiled 50 to 50 computations (0% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 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))))))
2.9b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.3b	(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)))))

rewrite45.0ms (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

4 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)))
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)))))
3.0ms	(pow.f64 (sin.f64 kx) 2)

series2.7s (14%)

Counts

4 → 39

Calls

4 calls:

1.4s	(/.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))))))
753.0ms	(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)))))
608.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5089	5604

prune338.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	3	153

Merged error: 0b

Counts

153 → 3

Compiler

Compiled 5580 to 4078 computations (26.9% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.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)))))))
2.6b	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.3b	(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 (0.4%)

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

4 calls:

21.0ms	(.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))))
18.0ms	(.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))))))

series3.3s (16.8%)

Counts

4 → 48

Calls

4 calls:

1.3s	(/.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)))))))
745.0ms	(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))))))
600.0ms	(.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))))
591.0ms	(.f64 (/.f64 (.f64 2 l) Om) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify123.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4959	7697
1	4959	7697

prune440.0ms (2.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	196	3	199

Merged error: 0b

Counts

199 → 3

Compiler

Compiled 7498 to 5108 computations (31.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

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))))))
2.9b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.9b	(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))))))))
7.3b	(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 (0.3%)

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

4 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)))
10.0ms	(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)))))

series4.8s (24.6%)

Counts

4 → 48

Calls

4 calls:

2.1s	(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))))))))
1.4s	(/.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))))))
733.0ms	(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)))))
636.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4987	7433
1	4987	7433

prune460.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	179	3	182

Merged error: 0b

Counts

182 → 3

Compiler

Compiled 7320 to 5413 computations (26.1% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.4b	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
5.4b	(/.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)))))
28.2b	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))

rewrite137.0ms (0.7%)

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

4 calls:

53.0ms	(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)))))
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))))
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
6.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

series1.7s (8.7%)

Counts

4 → 30

Calls

4 calls:

819.0ms	(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)))))
638.0ms	(sqrt.f64 (*.f64 (/.f64 4 Om) (+.f64 (/.f64 (pow.f64 (sin.f64 ky) 2) Om) (/.f64 (pow.f64 (sin.f64 kx) 2) Om))))
124.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)
113.0ms	(/.f64 (pow.f64 (sin.f64 kx) 2) Om)

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4960	3615
1	4960	3615

prune527.0ms (2.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	174	3	177

Merged error: 0b

Counts

177 → 3

Compiler

Compiled 9642 to 6326 computations (34.4% saved)

regimes721.0ms (3.7%)

Compiler: Compiled 8904 to 7967 computations (10.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	45
1	29	45

end0.0ms (0%)

sample2.9s (14.6%)

Algorithm

1×

intervals

Results

1.1s	6423×	body	128	valid
619.0ms	770×	body	1024	valid
296.0ms	521×	body	512	valid
103.0ms	286×	body	256	valid

Compiler

Compiled 483 to 432 computations (10.6% saved)

Details

analyze604.0ms (3.1%)

sample83.0ms (0.4%)

simplify143.0ms (0.7%)

prune5.0ms (0%)

localize19.0ms (0.1%)

rewrite45.0ms (0.2%)

series2.7s (14%)

simplify96.0ms (0.5%)

prune338.0ms (1.7%)

localize22.0ms (0.1%)

rewrite71.0ms (0.4%)

series3.3s (16.8%)

simplify123.0ms (0.6%)

prune440.0ms (2.3%)

localize26.0ms (0.1%)

rewrite56.0ms (0.3%)

series4.8s (24.6%)

simplify109.0ms (0.6%)

prune460.0ms (2.4%)

localize27.0ms (0.1%)

rewrite137.0ms (0.7%)

series1.7s (8.7%)

simplify79.0ms (0.4%)

prune527.0ms (2.7%)

regimes721.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.9s (14.6%)

Profiling