Details

analyze1.7s (6.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5547	104
0	3	3
1	3	3

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)

sample460.0ms (1.7%)

Algorithm

1×

intervals

Results

123.0ms	155×	body	1024	valid
20.0ms	40×	body	512	valid
9.0ms	17×	body	256	valid
6.0ms	44×	body	128	valid

Compiler

Compiled 4385 to 4640 computations (-5.8% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5170	26

prune4.0ms (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

2.9b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.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)
0.2b	(pow.f64 (sin.f64 ky) 2)
2.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite208.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

2.8b

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×	`add-exp-log_binary64_116` `associate-/r*_binary64_22`
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×	`flip3-+_binary64_81` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75`

Counts

4 → 102

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 ky) (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	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2664 to 1486 computations (44.2% saved)

series992.0ms (3.6%)

Error

1.6b

Counts

4 → 34

Calls

4 calls:

582.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
277.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
43.0ms	(pow.f64 (sin.f64 kx) 2)
38.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2002 to 1468 computations (26.7% saved)

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5005	2972

prune226.0ms (0.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	124	12	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	12	137

Error

1.6b

Counts

137 → 12

Compiler

Compiled 3407 to 1931 computations (43.3% saved)

localize16.0ms (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)
0.2b	(pow.f64 (sin.f64 ky) 2)
2.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite451.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

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×	`sqrt-div_binary64_95` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `1-exp_binary64_122` `rec-exp_binary64_128`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `inv-pow_binary64_163` `pow-flip_binary64_152` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/r/_binary64_24`

Counts

4 → 189

Calls

4 calls:

16.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
10.0ms	(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)

Compiler

Compiled 6091 to 3683 computations (39.5% saved)

series1.0s (3.7%)

Error

1.6b

Counts

4 → 34

Calls

4 calls:

605.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
262.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
44.0ms	(pow.f64 (sin.f64 kx) 2)
38.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2112 to 1578 computations (25.3% saved)

simplify82.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5032	6319

prune388.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	222	1	223
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	223	12	235

Error

1.6b

Counts

235 → 12

Compiler

Compiled 6207 to 3644 computations (41.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
2.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite230.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

43×	`*-un-lft-identity_binary64_78`
38×	`add-sqr-sqrt_binary64_100`
30×	`associate-r_binary64_18`
28×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
22×	`sqrt-prod_binary64_94`
15×	`add-exp-log_binary64_116`
14×	`unpow-prod-down_binary64_157`
9×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
5×	`unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `prod-exp_binary64_127`
3×	`associate-l_binary64_19`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `cbrt-unprod_binary64_111` `associate-/r/_binary64_24` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `1-exp_binary64_122` `rec-exp_binary64_128` `cbrt-undiv_binary64_112` `un-div-inv_binary64_76` `associate-r/_binary64_20` `div-inv_binary64_75` `-commutative_binary64_9`

Counts

4 → 108

Calls

4 calls:

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

Compiler

Compiled 3066 to 1891 computations (38.3% saved)

series1.0s (3.7%)

Error

1.6b

Counts

4 → 34

Calls

4 calls:

611.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
275.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
37.0ms	(pow.f64 (sin.f64 ky) 2)
37.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2112 to 1578 computations (25.3% saved)

simplify70.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4994	2719
1	4994	2719

prune225.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	142	12	154

Error

1.6b

Counts

154 → 12

Compiler

Compiled 3713 to 2228 computations (40% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
2.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
2.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite463.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

1.6b

Rules

104×	`sqrt-prod_binary64_94`
60×	`add-sqr-sqrt_binary64_100`
50×	`*-un-lft-identity_binary64_78`
34×	`sqrt-pow1_binary64_96`
30×	`pow1_binary64_139`
28×	`sqrt-div_binary64_95`
20×	`add-cube-cbrt_binary64_113`
19×	`swap-sqr_binary64_45`
18×	`pow1/2_binary64_158`
15×	`unpow-prod-down_binary64_157`
14×	`distribute-lft-out_binary64_29`
11×	`associate-l_binary64_19` `associate-r_binary64_18`
10×	`rem-sqrt-square_binary64_91`
9×	`pow-prod-up_binary64_148` `unswap-sqr_binary64_46`
8×	`flip3-+_binary64_81` `flip-+_binary64_52`
7×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114`
5×	`pow-prod-down_binary64_149` `pow-sqr_binary64_51`
4×	`add-log-exp_binary64_117` `sqr-abs_binary64_93` `frac-times_binary64_88`
3×	`pow-unpow_binary64_155`
2×	`associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`pow2_binary64_159` `pow-plus_binary64_141` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `sqrt-unprod_binary64_98` `rem-square-sqrt_binary64_90` `*-commutative_binary64_9` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 147

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 6119 to 3861 computations (36.9% saved)

series946.0ms (3.5%)

Error

1.6b

Counts

4 → 39

Calls

4 calls:

288.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
276.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
269.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
45.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3104 to 2188 computations (29.5% saved)

simplify115.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4951	3823
1	4951	3823

prune347.0ms (1.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	186	12	198

Error

1.6b

Counts

198 → 12

Compiler

Compiled 5629 to 3314 computations (41.1% saved)

regimes1.7s (6.2%)

Accuracy

Total 2.2b remaining (50.7%)

Threshold costs 0b (0%)

Compiler

Compiled 16977 to 13696 computations (19.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	26
1	16	26

end0.0ms (0%)

sample16.5s (60.4%)

Algorithm

1×

intervals

Results

3.7s	4655×	body	1024	valid
688.0ms	1343×	body	512	valid
214.0ms	1466×	body	128	valid
169.0ms	524×	body	256	valid
15.0ms	12×	body	2048	valid

Compiler

Compiled 137910 to 145542 computations (-5.5% saved)

Details

analyze1.7s (6.1%)

sample460.0ms (1.7%)

simplify78.0ms (0.3%)

prune4.0ms (0%)

localize15.0ms (0.1%)

rewrite208.0ms (0.8%)

series992.0ms (3.6%)

simplify71.0ms (0.3%)

prune226.0ms (0.8%)

localize16.0ms (0.1%)

rewrite451.0ms (1.7%)

series1.0s (3.7%)

simplify82.0ms (0.3%)

prune388.0ms (1.4%)

localize16.0ms (0.1%)

rewrite230.0ms (0.8%)

series1.0s (3.7%)

simplify70.0ms (0.3%)

prune225.0ms (0.8%)

localize18.0ms (0.1%)

rewrite463.0ms (1.7%)

series946.0ms (3.5%)

simplify115.0ms (0.4%)

prune347.0ms (1.3%)

regimes1.7s (6.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample16.5s (60.4%)

Profiling