Details

analyze595.0ms (4.5%)

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 (0.6%)

Algorithm

1×

intervals

Results

39.0ms	209×	body	128	valid
17.0ms	19×	body	1024	valid
12.0ms	21×	body	512	valid
3.0ms	7×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify197.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

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)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.7b	(/.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))))))
2.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0b	(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 (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_98`
30×	`*-un-lft-identity_binary64_77`
26×	`add-cube-cbrt_binary64_109`
21×	`times-frac_binary64_83`
19×	`add-exp-log_binary64_112`
15×	`sqrt-prod_binary64_92`
13×	`unpow-prod-down_binary64_153`
12×	`associate-l_binary64_20`
8×	`add-cbrt-cube_binary64_110`
6×	`associate-/r*_binary64_23` `pow1_binary64_135` `prod-exp_binary64_123`
5×	`associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `sqrt-div_binary64_93` `pow-exp_binary64_142` `unswap-sqr_binary64_45`
3×	`flip-+_binary64_51` `sqr-pow_binary64_49` `flip3-+_binary64_80` `associate-/l*_binary64_24` `div-exp_binary64_125` `pow-unpow_binary64_151` `unpow2_binary64_139`
2×	`pow-to-exp_binary64_143` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30` `div-inv_binary64_74`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `distribute-lft-in_binary64_28` `*-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88` `pow-pow_binary64_146`

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)))
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 ky) 2)

series2.1s (16%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.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))))))
670.0ms	(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)))))
323.0ms	(.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 ky) 2)

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4954	4125
1	4954	4125

prune242.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 0b

Counts

126 → 4

Compiler

Compiled 4433 to 3375 computations (23.9% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 1/2 (cbrt.f64 (pow.f64 (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)))
2.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0b	(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)))))
10.9b	(cbrt.f64 (pow.f64 (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))

rewrite68.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`cbrt-prod_binary64_105`
67×	`add-sqr-sqrt_binary64_98`
66×	`times-frac_binary64_83`
64×	`*-un-lft-identity_binary64_77`
60×	`add-cube-cbrt_binary64_109`
40×	`unpow-prod-down_binary64_153`
33×	`sqrt-prod_binary64_92`
30×	`cube-prod_binary64_102`
21×	`associate-/r*_binary64_23`
18×	`add-exp-log_binary64_112`
12×	`associate-l_binary64_20`
7×	`add-cbrt-cube_binary64_110` `sqr-pow_binary64_49`
6×	`sqrt-div_binary64_93` `prod-exp_binary64_123`
5×	`pow1_binary64_135` `cube-mult_binary64_104` `associate-r_binary64_19` `unpow3_binary64_140`
4×	`add-log-exp_binary64_113` `flip-+_binary64_51` `cube-div_binary64_103` `flip3-+_binary64_80` `cbrt-div_binary64_106` `unswap-sqr_binary64_45`
3×	`pow-exp_binary64_142` `associate-/l*_binary64_24` `div-exp_binary64_125`
2×	`associate-*r/_binary64_21` `associate-/r/_binary64_25` `unpow2_binary64_139` `distribute-lft-out_binary64_30` `div-inv_binary64_74`
1×	`pow-to-exp_binary64_143` `rem-cbrt-cube_binary64_100` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `distribute-lft-in_binary64_28` `*-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `pow1/3_binary64_156` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88`

Counts

4 → 184

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)))
12.0ms	(/.f64 1/2 (cbrt.f64 (pow.f64 (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)))
6.0ms	(cbrt.f64 (pow.f64 (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))
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)))))

series2.7s (20.6%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1/2 (cbrt.f64 (pow.f64 (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)))
677.0ms	(cbrt.f64 (pow.f64 (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))
648.0ms	(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)))))
300.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5312	8767

prune552.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	196	4	200

Merged error: 0b

Counts

200 → 4

Compiler

Compiled 7986 to 6177 computations (22.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.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))))))
2.7b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(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))))))))
7.0b	(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)))))

rewrite55.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_98`
42×	`*-un-lft-identity_binary64_77`
39×	`times-frac_binary64_83`
38×	`add-cube-cbrt_binary64_109`
25×	`log-pow_binary64_163`
24×	`sqrt-prod_binary64_92` `exp-prod_binary64_126`
18×	`add-exp-log_binary64_112`
12×	`associate-l_binary64_20`
10×	`unpow-prod-down_binary64_153`
8×	`add-cbrt-cube_binary64_110`
6×	`associate-/r*_binary64_23` `sqrt-div_binary64_93` `pow1_binary64_135` `prod-exp_binary64_123`
5×	`associate-r_binary64_19`
4×	`add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `unswap-sqr_binary64_45` `associate-/r/_binary64_25`
3×	`log-prod_binary64_160` `pow-exp_binary64_142` `associate-/l*_binary64_24` `div-exp_binary64_125` `div-inv_binary64_74`
2×	`sqr-pow_binary64_49` `associate-*r/_binary64_21` `unpow2_binary64_139` `distribute-lft-out_binary64_30`
1×	`rem-log-exp_binary64_115` `pow-to-exp_binary64_143` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `distribute-lft-in_binary64_28` `*-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_88`

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)))))

series2.9s (21.7%)

Counts

4 → 12

Calls

4 calls:

1.1s	(/.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))))))
774.0ms	(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))))))))
677.0ms	(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)))))
298.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5032	5281

prune356.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	143	4	147

Merged error: 0b

Counts

147 → 4

Compiler

Compiled 5654 to 4363 computations (22.8% saved)

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms (0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Merged error: 0b

Counts

4 → 4

Compiler

Compiled 0 to 0 computations (0% saved)

regimes216.0ms (1.6%)

Compiler: Compiled 1137 to 1323 computations (-16.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	44
1	31	44

end0.0ms (0%)

sample2.7s (20.7%)

Algorithm

1×

intervals

Results

1.1s	6330×	body	128	valid
734.0ms	798×	body	1024	valid
343.0ms	566×	body	512	valid
116.0ms	306×	body	256	valid

Compiler

Compiled 121 to 133 computations (-9.9% saved)

Details

analyze595.0ms (4.5%)

sample83.0ms (0.6%)

simplify197.0ms (1.5%)

prune5.0ms (0%)

localize23.0ms (0.2%)

rewrite43.0ms (0.3%)

series2.1s (16%)

simplify91.0ms (0.7%)

prune242.0ms (1.8%)

localize27.0ms (0.2%)

rewrite68.0ms (0.5%)

series2.7s (20.6%)

simplify98.0ms (0.7%)

prune552.0ms (4.2%)

localize26.0ms (0.2%)

rewrite55.0ms (0.4%)

series2.9s (21.7%)

simplify87.0ms (0.7%)

prune356.0ms (2.7%)

localize2.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0%)

prune0.0ms (0%)

regimes216.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (20.7%)

Profiling