Details

analyze1.4s (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
25%	74.9%	0.1%	8
54.6%	45.2%	0.1%	9
56.2%	43.7%	0.1%	10
62.4%	37.4%	0.1%	11
65.9%	33.9%	0.1%	12
66.3%	33.5%	0.1%	13
69%	30.8%	0.1%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample146.0ms (1.1%)

Algorithm

1×

intervals

Results

104.0ms	146×	body	1024	valid
20.0ms	48×	body	512	valid
6.0ms	43×	body	128	valid
5.0ms	19×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify171.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5170	26

prune3.0ms (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: 4.9b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.6b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_78`
27×	`add-sqr-sqrt_binary64_100`
26×	`add-cube-cbrt_binary64_113`
25×	`sqrt-prod_binary64_94`
24×	`times-frac_binary64_84`
16×	`unpow-prod-down_binary64_157`
10×	`distribute-lft-out_binary64_29`
8×	`associate-/r*_binary64_22` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-/l*_binary64_23`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 102

Calls

4 calls:

13.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series481.0ms (3.5%)

Counts

4 → 18

Calls

4 calls:

310.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
146.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
13.0ms	(pow.f64 (sin.f64 ky) 2)
12.0ms	(pow.f64 (sin.f64 kx) 2)

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5509	2414

prune174.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	110	10	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 1.6b

Counts

121 → 10

Compiler

Compiled 2900 to 1628 computations (43.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.6b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite57.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64_84`
150×	`*-un-lft-identity_binary64_78`
99×	`add-sqr-sqrt_binary64_100`
98×	`add-cube-cbrt_binary64_113`
65×	`sqrt-prod_binary64_94`
32×	`unpow-prod-down_binary64_157`
28×	`associate-/r*_binary64_22`
26×	`distribute-lft-out_binary64_29`
17×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
8×	`pow1_binary64_139`
7×	`div-exp_binary64_129`
6×	`pow-unpow_binary64_155`
5×	`div-inv_binary64_75`
4×	`add-log-exp_binary64_117`
3×	`cbrt-undiv_binary64_112` `associate-/l*_binary64_23`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `unpow2_binary64_143` `1-exp_binary64_122` `sqr-pow_binary64_50` `pow-pow_binary64_150` `rec-exp_binary64_128` `sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `inv-pow_binary64_163` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `pow-flip_binary64_152` `associate-/r/_binary64_24` `clear-num_binary64_77` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 189

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series474.0ms (3.4%)

Counts

4 → 18

Calls

4 calls:

301.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
149.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
12.0ms	(pow.f64 (sin.f64 ky) 2)
12.0ms	(pow.f64 (sin.f64 kx) 2)

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4956	5761
1	4956	5761

prune302.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	206	11	217

Merged error: 1.6b

Counts

217 → 11

Compiler

Compiled 5710 to 3343 computations (41.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
0.3b	(pow.f64 (sin.f64 ky) 2)
4.6b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite156.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

1029×	`times-frac_binary64_84`
639×	`*-un-lft-identity_binary64_78`
452×	`add-sqr-sqrt_binary64_100`
451×	`add-cube-cbrt_binary64_113`
235×	`sqrt-prod_binary64_94`
97×	`unpow-prod-down_binary64_157`
94×	`distribute-lft-out_binary64_29`
49×	`add-exp-log_binary64_116`
47×	`div-inv_binary64_75`
34×	`div-exp_binary64_129`
33×	`associate-/l*_binary64_23`
32×	`sqrt-div_binary64_95`
31×	`associate-/r/_binary64_24`
21×	`associate-/r*_binary64_22`
18×	`add-cbrt-cube_binary64_114`
16×	`flip-+_binary64_52` `flip3-+_binary64_81`
9×	`cbrt-undiv_binary64_112` `1-exp_binary64_122` `rec-exp_binary64_128`
8×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117`
3×	`pow-flip_binary64_152` `pow-unpow_binary64_155`
2×	`sqrt-pow1_binary64_96` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow1/2_binary64_158`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `inv-pow_binary64_163` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/l/_binary64_25`

Counts

4 → 555

Calls

4 calls:

29.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
12.0ms	(/.f64 1 (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	(pow.f64 (sin.f64 ky) 2)

series684.0ms (5%)

Counts

4 → 21

Calls

4 calls:

305.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
218.0ms	(/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
148.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
12.0ms	(pow.f64 (sin.f64 ky) 2)

simplify263.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

576 → 576

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4913	23468
1	4913	23468

prune1.3s (9.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	574	2	576
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	576	11	587

Merged error: 1.6b

Counts

587 → 11

Compiler

Compiled 18402 to 11439 computations (37.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b	(pow.f64 (sin.f64 ky) 2)
4.6b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64_78`
45×	`sqrt-prod_binary64_94`
41×	`add-sqr-sqrt_binary64_100`
34×	`times-frac_binary64_84`
28×	`add-cube-cbrt_binary64_113`
24×	`associate-r_binary64_18`
18×	`unpow-prod-down_binary64_157`
12×	`distribute-lft-out_binary64_29`
10×	`pow1_binary64_139`
8×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
3×	`associate-l_binary64_19` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `pow-pow_binary64_150` `sqrt-div_binary64_95` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `inv-pow_binary64_163` `pow-flip_binary64_152` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `pow1/2_binary64_158`

Counts

4 → 115

Calls

4 calls:

23.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
12.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series560.0ms (4.1%)

Counts

4 → 18

Calls

4 calls:

303.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
232.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
12.0ms	(pow.f64 (sin.f64 ky) 2)
12.0ms	(pow.f64 (sin.f64 kx) 2)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5007	2509

prune163.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	7	8
Picked	1	0	1
Done	0	2	2
Total	134	10	144

Merged error: 1.6b

Counts

144 → 10

Compiler

Compiled 3207 to 1908 computations (40.5% saved)

regimes1.2s (8.9%)

Compiler: Compiled 12214 to 9946 computations (18.6% saved)

bsearch4.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	117
1	36	117

end0.0ms (0%)

sample5.9s (42.5%)

Algorithm

1×

intervals

Results

3.2s	4630×	body	1024	valid
643.0ms	1432×	body	512	valid
179.0ms	1402×	body	128	valid
151.0ms	522×	body	256	valid
16.0ms	14×	body	2048	valid

Compiler

Compiled 1289 to 1035 computations (19.7% saved)

Details

analyze1.4s (9.8%)

sample146.0ms (1.1%)

simplify171.0ms (1.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite41.0ms (0.3%)

series481.0ms (3.5%)

simplify61.0ms (0.4%)

prune174.0ms (1.3%)

localize14.0ms (0.1%)

rewrite57.0ms (0.4%)

series474.0ms (3.4%)

simplify125.0ms (0.9%)

prune302.0ms (2.2%)

localize18.0ms (0.1%)

rewrite156.0ms (1.1%)

series684.0ms (5%)

simplify263.0ms (1.9%)

prune1.3s (9.5%)

localize14.0ms (0.1%)

rewrite52.0ms (0.4%)

series560.0ms (4.1%)

simplify67.0ms (0.5%)

prune163.0ms (1.2%)

regimes1.2s (8.9%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (42.5%)

Profiling