Details

analyze1.2s (8.6%)

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)

sample149.0ms (1%)

Algorithm

1×

intervals

Results

98.0ms	142×	body	1024	valid
28.0ms	50×	body	512	valid
6.0ms	20×	body	256	valid
5.0ms	44×	body	128	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify172.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

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

Error

5.0b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize19.0ms (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))))
0.3b	(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)))

rewrite37.0ms (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	(/.f64 (sin.f64 ky) (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 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series637.0ms (4.5%)

Counts

4 → 35

Calls

4 calls:

394.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
183.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 kx) 2)
29.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1170 to 967 computations (17.4% saved)

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5379	3116

prune210.0ms (1.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	125	12	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	12	138

Error

2.6b

Counts

138 → 12

Compiler

Compiled 3502 to 1989 computations (43.2% 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)))
0.3b	(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)))
11.0ms	(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)

series634.0ms (4.5%)

Counts

4 → 35

Calls

4 calls:

385.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
188.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)
30.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1234 to 1031 computations (16.5% saved)

simplify122.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4969	6463
1	4969	6463

prune486.0ms (3.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	223	1	224
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	226	10	236

Error

2.6b

Counts

236 → 10

Compiler

Compiled 6245 to 3659 computations (41.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite142.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

1005×	`times-frac_binary64_84`
608×	`*-un-lft-identity_binary64_78`
437×	`add-sqr-sqrt_binary64_100`
436×	`add-cube-cbrt_binary64_113`
215×	`sqrt-prod_binary64_94`
92×	`unpow-prod-down_binary64_157`
86×	`distribute-lft-out_binary64_29`
46×	`div-inv_binary64_75` `add-exp-log_binary64_116`
32×	`div-exp_binary64_129`
30×	`associate-/l*_binary64_23` `sqrt-div_binary64_95`
29×	`associate-/r/_binary64_24`
16×	`add-cbrt-cube_binary64_114`
15×	`flip-+_binary64_52` `flip3-+_binary64_81`
13×	`associate-/r*_binary64_22`
8×	`cbrt-undiv_binary64_112` `1-exp_binary64_122` `rec-exp_binary64_128`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25` `pow1/2_binary64_158`

Counts

4 → 518

Calls

4 calls:

32.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (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 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series636.0ms (4.5%)

Counts

4 → 35

Calls

4 calls:

386.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
188.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)
30.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1298 to 1095 computations (15.6% saved)

simplify248.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

553 → 553

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5037	22901

prune1.3s (8.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	552	1	553
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	554	9	563

Error

2.6b

Counts

563 → 9

Compiler

Compiled 17807 to 11021 computations (38.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (0.3%)

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:

20.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(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)

series756.0ms (5.3%)

Counts

4 → 35

Calls

4 calls:

404.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
294.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
31.0ms	(pow.f64 (sin.f64 ky) 2)
26.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 1258 to 1055 computations (16.1% saved)

simplify58.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5285	3295

prune190.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	150	9	159

Error

2.6b

Counts

159 → 9

Compiler

Compiled 3844 to 2304 computations (40.1% saved)

regimes1.0s (7.3%)

Accuracy

Total 1.1b remaining (34.8%)

Threshold costs 0b (0%)

Compiler

Compiled 11208 to 9187 computations (18% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	55
1	24	55

end0.0ms (0%)

sample6.0s (42.1%)

Algorithm

1×

intervals

Results

3.4s	4601×	body	1024	valid
621.0ms	1382×	body	512	valid
187.0ms	1492×	body	128	valid
147.0ms	516×	body	256	valid
11.0ms	9×	body	2048	valid

Compiler

Compiled 1287 to 1051 computations (18.3% saved)

Details

analyze1.2s (8.6%)

sample149.0ms (1%)

simplify172.0ms (1.2%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite37.0ms (0.3%)

series637.0ms (4.5%)

simplify59.0ms (0.4%)

prune210.0ms (1.5%)

localize14.0ms (0.1%)

rewrite57.0ms (0.4%)

series634.0ms (4.5%)

simplify122.0ms (0.9%)

prune486.0ms (3.4%)

localize15.0ms (0.1%)

rewrite142.0ms (1%)

series636.0ms (4.5%)

simplify248.0ms (1.7%)

prune1.3s (8.8%)

localize17.0ms (0.1%)

rewrite48.0ms (0.3%)

series756.0ms (5.3%)

simplify58.0ms (0.4%)

prune190.0ms (1.3%)

regimes1.0s (7.3%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.0s (42.1%)

Profiling