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)

sample150.0ms (1.1%)

Algorithm

1×

intervals

Results

108.0ms	153×	body	1024	valid
19.0ms	43×	body	512	valid
8.0ms	44×	body	128	valid
4.0ms	15×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify177.0ms (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

Error

5.2b

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 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite35.0ms (0.2%)

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:

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

series697.0ms (4.9%)

Counts

4 → 29

Calls

4 calls:

404.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
231.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
35.0ms	(pow.f64 (sin.f64 kx) 2)
27.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1123 to 951 computations (15.3% saved)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4992	2687
1	4992	2687

prune201.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	13	132

Error

1.6b

Counts

132 → 13

Compiler

Compiled 3274 to 1882 computations (42.5% 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 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite56.0ms (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:

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

series712.0ms (5%)

Counts

4 → 29

Calls

4 calls:

430.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
219.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
35.0ms	(pow.f64 (sin.f64 kx) 2)
28.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 1185 to 1013 computations (14.5% saved)

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	6034
1	4954	6034

prune343.0ms (2.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	218	13	231

Error

1.6b

Counts

231 → 13

Compiler

Compiled 6080 to 3597 computations (40.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.8b	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
14.6b	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64_109`
12×	`add-sqr-sqrt_binary64_100`
11×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`unpow-prod-down_binary64_157`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `unpow2_binary64_143` `pow1/3_binary64_160` `sqr-pow_binary64_50`
2×	`sqrt-div_binary64_95`
1×	`sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 63

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
2.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

series624.0ms (4.4%)

Counts

4 → 28

Calls

4 calls:

234.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 kx) 2)) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (cbrt.f64 (pow.f64 (sin.f64 kx) 2))) (pow.f64 (sin.f64 ky) 2)))
135.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
132.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
123.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

Compiler

Compiled 1280 to 1066 computations (16.7% saved)

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4972	1435
1	4972	1435

prune151.0ms (1.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	91	13	104

Error

1.6b

Counts

104 → 13

Compiler

Compiled 3160 to 1909 computations (39.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.4b	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite126.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`sqrt-prod_binary64_94`
163×	`add-sqr-sqrt_binary64_100`
144×	`times-frac_binary64_84`
132×	`*-un-lft-identity_binary64_78`
72×	`add-cube-cbrt_binary64_113`
39×	`associate-l_binary64_19` `associate-r_binary64_18`
28×	`add-exp-log_binary64_116` `unswap-sqr_binary64_46`
24×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
18×	`add-cbrt-cube_binary64_114`
16×	`sqrt-div_binary64_95`
11×	`associate-/r*_binary64_22`
9×	`div-exp_binary64_129`
8×	`prod-exp_binary64_127` `pow1_binary64_139`
6×	`associate-/r/_binary64_24`
5×	`cbrt-undiv_binary64_112` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111`
3×	`div-inv_binary64_75` `associate-/l*_binary64_23`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `1-exp_binary64_122` `rec-exp_binary64_128` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 225

Calls

4 calls:

59.0ms	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
14.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.6s (11.3%)

Counts

4 → 38

Calls

4 calls:

711.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
428.0ms	(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
238.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
230.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 2416 to 1974 computations (18.3% saved)

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4930	8879
1	4930	8879

prune618.0ms (4.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	263	13	276

Error

1.6b

Counts

276 → 13

Compiler

Compiled 9955 to 6092 computations (38.8% saved)

regimes1.1s (7.7%)

Accuracy

Total 2.0b remaining (68.3%)

Threshold costs 0b (0%)

Compiler

Compiled 10218 to 8430 computations (17.5% 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	29	103
1	29	103

end0.0ms (0%)

sample5.9s (41.6%)

Algorithm

1×

intervals

Results

3.4s	4615×	body	1024	valid
631.0ms	1386×	body	512	valid
189.0ms	1444×	body	128	valid
146.0ms	536×	body	256	valid
35.0ms	19×	body	2048	valid

Compiler

Compiled 1188 to 967 computations (18.6% saved)

Details

analyze1.2s (8.6%)

sample150.0ms (1.1%)

simplify177.0ms (1.2%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite35.0ms (0.2%)

series697.0ms (4.9%)

simplify72.0ms (0.5%)

prune201.0ms (1.4%)

localize14.0ms (0.1%)

rewrite56.0ms (0.4%)

series712.0ms (5%)

simplify117.0ms (0.8%)

prune343.0ms (2.4%)

localize17.0ms (0.1%)

rewrite30.0ms (0.2%)

series624.0ms (4.4%)

simplify50.0ms (0.4%)

prune151.0ms (1.1%)

localize20.0ms (0.1%)

rewrite126.0ms (0.9%)

series1.6s (11.3%)

simplify147.0ms (1%)

prune618.0ms (4.3%)

regimes1.1s (7.7%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (41.6%)

Profiling