Details

analyze1.3s (3.5%)

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)

sample168.0ms (0.5%)

Algorithm

1×

intervals

Results

123.0ms	145×	body	1024	valid
21.0ms	43×	body	512	valid
6.0ms	48×	body	128	valid
6.0ms	20×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify233.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

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: 4.4b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize18.0ms (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)
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite38.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_77`
27×	`add-sqr-sqrt_binary64_98`
26×	`add-cube-cbrt_binary64_109`
25×	`sqrt-prod_binary64_92`
24×	`times-frac_binary64_83`
16×	`unpow-prod-down_binary64_153`
10×	`distribute-lft-out_binary64_30`
8×	`add-exp-log_binary64_112` `associate-/r*_binary64_23`
7×	`pow1_binary64_135`
6×	`add-cbrt-cube_binary64_110` `pow-unpow_binary64_151`
4×	`add-log-exp_binary64_113` `sqrt-div_binary64_93`
3×	`associate-/l*_binary64_24`
2×	`pow-to-exp_binary64_143` `flip-+_binary64_51` `sqr-pow_binary64_49` `flip3-+_binary64_80` `pow-exp_binary64_142` `associate-/r/_binary64_25` `unpow2_binary64_139` `pow-pow_binary64_146`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `div-exp_binary64_125` `pow1/2_binary64_154` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

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

series510.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

298.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
163.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 kx) 2)
24.0ms	(pow.f64 (sin.f64 ky) 2)

simplify74.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4963	2298
1	4963	2298

prune172.0ms (0.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 3.6b

Counts

115 → 11

Compiler

Compiled 2846 to 1618 computations (43.1% saved)

localize16.0ms (0%)

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)
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64_83`
150×	`*-un-lft-identity_binary64_77`
99×	`add-sqr-sqrt_binary64_98`
98×	`add-cube-cbrt_binary64_109`
65×	`sqrt-prod_binary64_92`
32×	`unpow-prod-down_binary64_153`
28×	`associate-/r*_binary64_23`
26×	`distribute-lft-out_binary64_30`
17×	`add-exp-log_binary64_112`
9×	`add-cbrt-cube_binary64_110`
8×	`pow1_binary64_135`
7×	`div-exp_binary64_125`
6×	`pow-unpow_binary64_151`
5×	`div-inv_binary64_74`
4×	`add-log-exp_binary64_113`
3×	`cbrt-undiv_binary64_108` `associate-/l*_binary64_24`
2×	`pow-to-exp_binary64_143` `sqrt-div_binary64_93` `1-exp_binary64_118` `sqr-pow_binary64_49` `pow-exp_binary64_142` `rec-exp_binary64_124` `unpow2_binary64_139` `pow-pow_binary64_146`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `flip-+_binary64_51` `flip3-+_binary64_80` `inv-pow_binary64_159` `associate-/r/_binary64_25` `pow1/2_binary64_154` `clear-num_binary64_76` `frac-2neg_binary64_88` `pow-flip_binary64_148`

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

series661.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

441.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
171.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.0ms	(pow.f64 (sin.f64 kx) 2)
24.0ms	(pow.f64 (sin.f64 ky) 2)

simplify127.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4928	5648
1	4928	5648

prune330.0ms (0.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	201	11	212

Merged error: 3.6b

Counts

212 → 11

Compiler

Compiled 5591 to 3290 computations (41.2% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite151.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

1005×	`times-frac_binary64_83`
608×	`*-un-lft-identity_binary64_77`
437×	`add-sqr-sqrt_binary64_98`
436×	`add-cube-cbrt_binary64_109`
215×	`sqrt-prod_binary64_92`
92×	`unpow-prod-down_binary64_153`
86×	`distribute-lft-out_binary64_30`
46×	`add-exp-log_binary64_112` `div-inv_binary64_74`
32×	`div-exp_binary64_125`
30×	`sqrt-div_binary64_93` `associate-/l*_binary64_24`
29×	`associate-/r/_binary64_25`
16×	`add-cbrt-cube_binary64_110`
15×	`flip-+_binary64_51` `flip3-+_binary64_80`
13×	`associate-/r*_binary64_23`
8×	`cbrt-undiv_binary64_108` `1-exp_binary64_118` `rec-exp_binary64_124`
7×	`pow1_binary64_135`
6×	`pow-unpow_binary64_151`
4×	`add-log-exp_binary64_113`
2×	`pow-to-exp_binary64_143` `sqr-pow_binary64_49` `pow-exp_binary64_142` `unpow2_binary64_139` `pow-pow_binary64_146`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `pow1/2_binary64_154` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88`

Counts

4 → 518

Calls

4 calls:

34.0ms	(/.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 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series510.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

300.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (/.f64 1 (sin.f64 ky)))
155.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
29.0ms	(pow.f64 (sin.f64 ky) 2)
26.0ms	(pow.f64 (sin.f64 kx) 2)

simplify241.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

530 → 530

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5136	22008

prune1.4s (3.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	528	2	530
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	531	10	541

Merged error: 3.6b

Counts

541 → 10

Compiler

Compiled 17085 to 10600 computations (38% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (sin.f64 ky))))
0.4b	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (sin.f64 ky)))
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite1.1s (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

4451×	`times-frac_binary64_83`
2451×	`sqrt-prod_binary64_92`
2325×	`add-sqr-sqrt_binary64_98`
2323×	`*-un-lft-identity_binary64_77`
1615×	`add-cube-cbrt_binary64_109`
731×	`associate-r_binary64_19`
687×	`cbrt-prod_binary64_105`
280×	`unpow-prod-down_binary64_153` `distribute-lft-out_binary64_30`
175×	`unswap-sqr_binary64_45`
116×	`div-inv_binary64_74`
97×	`sqrt-div_binary64_93`
94×	`associate-/r/_binary64_25`
48×	`flip-+_binary64_51` `flip3-+_binary64_80`
45×	`add-exp-log_binary64_112`
37×	`associate-l_binary64_20`
35×	`add-cbrt-cube_binary64_110`
33×	`associate-/l*_binary64_24`
22×	`associate-/r*_binary64_23`
18×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
12×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
8×	`pow1_binary64_135`
4×	`add-log-exp_binary64_113`
2×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `pow1/2_binary64_154`
1×	`pow-prod-down_binary64_145` `frac-times_binary64_87` `associate-l/_binary64_22` `associate-r/_binary64_21` `*-commutative_binary64_10` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88`

Counts

4 → 1804

Calls

4 calls:

515.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (sin.f64 ky))))
44.0ms	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (sin.f64 ky)))
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)))

series974.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

336.0ms	(/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (sin.f64 ky)))
304.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (.f64 (cbrt.f64 1) (cbrt.f64 1))) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (cbrt.f64 1) (sin.f64 ky))))
175.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
158.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify937.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1816 → 1816

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5566	120779

prune19.3s (54%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	1816	0	1816
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	1816	10	1826

Merged error: 3.6b

Counts

1826 → 10

Compiler

Compiled 114288 to 81100 computations (29% saved)

regimes924.0ms (2.6%)

Compiler: Compiled 10353 to 8485 computations (18% 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%)

sample6.5s (18.1%)

Algorithm

1×

intervals

Results

3.9s	4634×	body	1024	valid
719.0ms	1428×	body	512	valid
185.0ms	1400×	body	128	valid
163.0ms	516×	body	256	valid
35.0ms	22×	body	2048	valid

Compiler

Compiled 1174 to 963 computations (18% saved)

Details

analyze1.3s (3.5%)

sample168.0ms (0.5%)

simplify233.0ms (0.7%)

prune3.0ms (0%)

localize18.0ms (0.1%)

rewrite38.0ms (0.1%)

series510.0ms (1.4%)

simplify74.0ms (0.2%)

prune172.0ms (0.5%)

localize16.0ms (0%)

rewrite56.0ms (0.2%)

series661.0ms (1.9%)

simplify127.0ms (0.4%)

prune330.0ms (0.9%)

localize17.0ms (0%)

rewrite151.0ms (0.4%)

series510.0ms (1.4%)

simplify241.0ms (0.7%)

prune1.4s (3.8%)

localize24.0ms (0.1%)

rewrite1.1s (3.2%)

series974.0ms (2.7%)

simplify937.0ms (2.6%)

prune19.3s (54%)

regimes924.0ms (2.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.5s (18.1%)

Profiling