Details

analyze614.0ms (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)

sample81.0ms (0.5%)

Algorithm

1×

intervals

Results

37.0ms	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)

simplify206.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5325	39

prune8.0ms (0.1%)

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 104 to 104 computations (0% saved)

localize25.0ms (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)))))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_101`
30×	`*-un-lft-identity_binary64_79`
26×	`add-cube-cbrt_binary64_114`
21×	`times-frac_binary64_85`
19×	`add-exp-log_binary64_117`
15×	`sqrt-prod_binary64_95`
13×	`unpow-prod-down_binary64_158`
12×	`associate-l_binary64_20`
8×	`add-cbrt-cube_binary64_115`
6×	`associate-/r*_binary64_23` `prod-exp_binary64_128` `pow1_binary64_140`
5×	`associate-r_binary64_19`
4×	`pow-exp_binary64_147` `unswap-sqr_binary64_47` `sqrt-div_binary64_96` `add-log-exp_binary64_118`
3×	`div-exp_binary64_130` `pow-unpow_binary64_156` `flip-+_binary64_53` `unpow2_binary64_144` `sqr-pow_binary64_51` `associate-/l*_binary64_24` `flip3-+_binary64_82`
2×	`pow-to-exp_binary64_148` `div-inv_binary64_76` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
1×	`cbrt-undiv_binary64_113` `pow-pow_binary64_151` `distribute-lft-in_binary64_28` `cbrt-unprod_binary64_112` `rem-sqrt-square_binary64_92` `*-commutative_binary64_10` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

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 ky) 2)

series2.1s (13.8%)

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))))))
663.0ms	(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)))))
320.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 ky) 2)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4957	4125
1	4957	4125

prune316.0ms (2.1%)

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 5216 to 4118 computations (21.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_79`
19×	`sqrt-prod_binary64_95`
18×	`add-sqr-sqrt_binary64_101`
13×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
11×	`add-cube-cbrt_binary64_114`
10×	`sqrt-div_binary64_96`
9×	`pow1_binary64_140`
8×	`associate-r_binary64_19`
7×	`associate-l_binary64_20`
6×	`unpow-prod-down_binary64_158` `distribute-lft-out_binary64_30`
5×	`flip-+_binary64_53` `flip3-+_binary64_82`
4×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `add-log-exp_binary64_118`
3×	`times-frac_binary64_85` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `frac-times_binary64_89` `associate-*r/_binary64_21` `unswap-sqr_binary64_47`
1×	`div-inv_binary64_76` `associate-l/_binary64_22` `-commutative_binary64_10` `pow-prod-down_binary64_150`

Counts

4 → 86

Calls

4 calls:

18.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
12.0ms	(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)))
5.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))

series1.3s (8.8%)

Counts

4 → 12

Calls

4 calls:

673.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (/.f64 (*.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
359.0ms	(.f64 (/.f64 (.f64 2 l) Om) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
149.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
147.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5170	2575

prune241.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	98	4	102

Merged error: 0b

Counts

102 → 4

Compiler

Compiled 4600 to 3239 computations (29.6% saved)

localize25.0ms (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))

rewrite74.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`cbrt-prod_binary64_110`
67×	`add-sqr-sqrt_binary64_101`
66×	`times-frac_binary64_85`
64×	`*-un-lft-identity_binary64_79`
60×	`add-cube-cbrt_binary64_114`
40×	`unpow-prod-down_binary64_158`
33×	`sqrt-prod_binary64_95`
30×	`cube-prod_binary64_107`
21×	`associate-/r*_binary64_23`
18×	`add-exp-log_binary64_117`
12×	`associate-l_binary64_20`
7×	`add-cbrt-cube_binary64_115` `sqr-pow_binary64_51`
6×	`prod-exp_binary64_128` `sqrt-div_binary64_96`
5×	`cube-mult_binary64_109` `pow1_binary64_140` `associate-r_binary64_19` `unpow3_binary64_145`
4×	`cube-div_binary64_108` `flip-+_binary64_53` `cbrt-div_binary64_111` `unswap-sqr_binary64_47` `add-log-exp_binary64_118` `flip3-+_binary64_82`
3×	`pow-exp_binary64_147` `div-exp_binary64_130` `associate-/l*_binary64_24`
2×	`unpow2_binary64_144` `div-inv_binary64_76` `associate-*r/_binary64_21` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
1×	`cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `distribute-lft-in_binary64_28` `rem-cbrt-cube_binary64_103` `cbrt-unprod_binary64_112` `rem-sqrt-square_binary64_92` `*-commutative_binary64_10` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `pow1/3_binary64_161` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 184

Calls

4 calls:

18.0ms	(.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 (17.8%)

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)))
669.0ms	(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))
667.0ms	(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)))))
304.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5379	8767

prune534.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	196	4	200

Merged error: 0b

Counts

200 → 4

Compiler

Compiled 7980 to 6167 computations (22.7% saved)

localize24.0ms (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)))))

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_101`
42×	`*-un-lft-identity_binary64_79`
39×	`times-frac_binary64_85`
38×	`add-cube-cbrt_binary64_114`
25×	`log-pow_binary64_168`
24×	`sqrt-prod_binary64_95` `exp-prod_binary64_131`
18×	`add-exp-log_binary64_117`
12×	`associate-l_binary64_20`
10×	`unpow-prod-down_binary64_158`
8×	`add-cbrt-cube_binary64_115`
6×	`associate-/r*_binary64_23` `prod-exp_binary64_128` `sqrt-div_binary64_96` `pow1_binary64_140`
5×	`associate-r_binary64_19`
4×	`flip-+_binary64_53` `unswap-sqr_binary64_47` `associate-/r/_binary64_25` `add-log-exp_binary64_118` `flip3-+_binary64_82`
3×	`pow-exp_binary64_147` `div-exp_binary64_130` `div-inv_binary64_76` `associate-/l*_binary64_24` `log-prod_binary64_165`
2×	`unpow2_binary64_144` `sqr-pow_binary64_51` `associate-*r/_binary64_21` `distribute-lft-out_binary64_30`
1×	`rem-log-exp_binary64_120` `cbrt-undiv_binary64_113` `pow-to-exp_binary64_148` `distribute-lft-in_binary64_28` `cbrt-unprod_binary64_112` `rem-sqrt-square_binary64_92` `*-commutative_binary64_10` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 131

Calls

4 calls:

18.0ms	(.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 (19%)

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))))))
775.0ms	(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))))))))
674.0ms	(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)))))
316.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4988	5281
1	4988	5281

prune359.0ms (2.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

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

Merged error: 0b

Counts

147 → 4

Compiler

Compiled 5750 to 4453 computations (22.6% saved)

regimes304.0ms (2%)

Compiler: Compiled 2054 to 2110 computations (-2.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	65
1	29	65

end0.0ms (0%)

sample2.8s (18.6%)

Algorithm

1×

intervals

Results

1.2s	6330×	body	128	valid
723.0ms	798×	body	1024	valid
371.0ms	566×	body	512	valid
123.0ms	306×	body	256	valid

Compiler

Compiled 171 to 167 computations (2.3% saved)

Details

analyze614.0ms (4%)

sample81.0ms (0.5%)

simplify206.0ms (1.4%)

prune8.0ms (0.1%)

localize25.0ms (0.2%)

rewrite46.0ms (0.3%)

series2.1s (13.8%)

simplify80.0ms (0.5%)

prune316.0ms (2.1%)

localize22.0ms (0.1%)

rewrite58.0ms (0.4%)

series1.3s (8.8%)

simplify67.0ms (0.4%)

prune241.0ms (1.6%)

localize25.0ms (0.2%)

rewrite74.0ms (0.5%)

series2.7s (17.8%)

simplify99.0ms (0.7%)

prune534.0ms (3.5%)

localize24.0ms (0.2%)

rewrite62.0ms (0.4%)

series2.9s (19%)

simplify91.0ms (0.6%)

prune359.0ms (2.4%)

regimes304.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (18.6%)

Profiling