Details

analyze833.0ms (1.1%)

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)

sample133.0ms (0.2%)

Algorithm

1×

intervals

Results

59.0ms	211×	body	128	valid
36.0ms	28×	body	1024	valid
14.0ms	13×	body	512	valid
2.0ms	4×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify209.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5325	39

prune8.0ms (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: 0.8b

Counts

2 → 2

Compiler

Compiled 79 to 79 computations (0% saved)

localize21.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.6b	(/.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))))))
1.8b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.1b	(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)))))

rewrite63.0ms (0.1%)

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:

20.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(/.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)))))
4.0ms	(pow.f64 (sin.f64 ky) 2)

series1.5s (2%)

Counts

4 → 12

Calls

4 calls:

703.0ms	(/.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))))))
537.0ms	(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)))))
259.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
23.0ms	(pow.f64 (sin.f64 ky) 2)

simplify126.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5030	4123

prune1.4s (1.9%)

Pruning

37 alts after pruning (36 fresh and 1 done)

	Pruned	Kept	Total
New	89	36	125
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	90	37	127

Merged error: 0b

Counts

127 → 37

Compiler

Compiled 5958 to 4689 computations (21.3% saved)

localize33.0ms (0%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
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)))
7.1b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (*.f64 2 l) Om))))))

rewrite45.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_78`
19×	`sqrt-prod_binary64_94`
17×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113`
9×	`pow1_binary64_139`
8×	`associate-l_binary64_19` `sqrt-div_binary64_95`
6×	`add-cbrt-cube_binary64_114` `unpow-prod-down_binary64_157` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-r_binary64_18` `pow1/2_binary64_158`
2×	`associate-*l/_binary64_21` `unswap-sqr_binary64_46`
1×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`

Counts

4 → 75

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
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	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (*.f64 2 l) Om))))))

series1.2s (1.5%)

Counts

4 → 12

Calls

4 calls:

778.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (*.f64 2 l) Om))))))
185.0ms	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
112.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
95.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify95.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5114	2404

prune1.8s (2.3%)

Pruning

52 alts after pruning (50 fresh and 2 done)

	Pruned	Kept	Total
New	68	19	87
Fresh	4	31	35
Picked	0	1	1
Done	0	1	1
Total	72	52	124

Merged error: 0b

Counts

124 → 52

Compiler

Compiled 6668 to 5164 computations (22.6% saved)

localize27.0ms (0%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
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)))
7.1b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 (pow.f64 1 2)) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))))))

rewrite49.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_78`
19×	`sqrt-prod_binary64_94`
17×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113`
9×	`pow1_binary64_139`
8×	`associate-l_binary64_19` `sqrt-div_binary64_95`
6×	`add-cbrt-cube_binary64_114` `unpow-prod-down_binary64_157` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-r_binary64_18` `pow1/2_binary64_158`
2×	`associate-*l/_binary64_21` `unswap-sqr_binary64_46`
1×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`

Counts

4 → 75

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
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	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 (pow.f64 1 2)) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))))))

series1.1s (1.4%)

Counts

4 → 12

Calls

4 calls:

669.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 (pow.f64 1 2)) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))))))
167.0ms	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
128.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
115.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5132	2404

prune2.1s (2.7%)

Pruning

63 alts after pruning (60 fresh and 3 done)

	Pruned	Kept	Total
New	70	17	87
Fresh	6	43	49
Picked	0	1	1
Done	0	2	2
Total	76	63	139

Merged error: 0b

Counts

139 → 63

Compiler

Compiled 7667 to 6058 computations (21% saved)

localize43.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.6b	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
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)))
7.1b	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 1) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))))))

rewrite64.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_78`
19×	`sqrt-prod_binary64_94`
17×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113`
9×	`pow1_binary64_139`
8×	`associate-l_binary64_19` `sqrt-div_binary64_95`
6×	`add-cbrt-cube_binary64_114` `unpow-prod-down_binary64_157` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
4×	`add-log-exp_binary64_117` `flip-+_binary64_52` `flip3-+_binary64_81`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-r_binary64_18` `pow1/2_binary64_158`
2×	`associate-*l/_binary64_21` `unswap-sqr_binary64_46`
1×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`

Counts

4 → 75

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 1) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))))))

series1.1s (1.5%)

Counts

4 → 12

Calls

4 calls:

662.0ms	(sqrt.f64 (+.f64 1 (.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om))) (.f64 (sqrt.f64 1) (.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))))))
227.0ms	(.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (fabs.f64 (/.f64 (.f64 2 l) Om)))
124.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
118.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify108.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5132	2404

prune2.4s (3.1%)

Pruning

69 alts after pruning (65 fresh and 4 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	5	54	59
Picked	0	1	1
Done	0	3	3
Total	81	69	150

Merged error: 0b

Counts

150 → 69

Compiler

Compiled 4450 to 3300 computations (25.8% saved)

regimes20.2s (26.2%)

Compiler: Compiled 229748 to 199371 computations (13.2% saved)

bsearch19.8s (25.7%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	69
1	30	69

end0.0ms (0%)

sample22.5s (29.2%)

Algorithm

1×

intervals

Results

1.6s	6334×	body	128	valid
958.0ms	779×	body	1024	valid
516.0ms	573×	body	512	valid
205.0ms	313×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 11779 to 10197 computations (13.4% saved)

Pareto

Details

analyze833.0ms (1.1%)

sample133.0ms (0.2%)

simplify209.0ms (0.3%)

prune8.0ms (0%)

localize21.0ms (0%)

rewrite63.0ms (0.1%)

series1.5s (2%)

simplify126.0ms (0.2%)

prune1.4s (1.9%)

localize33.0ms (0%)

rewrite45.0ms (0.1%)

series1.2s (1.5%)

simplify95.0ms (0.1%)

prune1.8s (2.3%)

localize27.0ms (0%)

rewrite49.0ms (0.1%)

series1.1s (1.4%)

simplify105.0ms (0.1%)

prune2.1s (2.7%)

localize43.0ms (0.1%)

rewrite64.0ms (0.1%)

series1.1s (1.5%)

simplify108.0ms (0.1%)

prune2.4s (3.1%)

regimes20.2s (26.2%)

bsearch19.8s (25.7%)

simplify6.0ms (0%)

end0.0ms (0%)

sample22.5s (29.2%)

Profiling