Details

analyze1.3s (10%)

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)

sample207.0ms (1.7%)

Algorithm

1×

intervals

Results

138.0ms	123×	body	1280	valid
43.0ms	66×	body	640	valid
9.0ms	19×	body	320	valid
5.0ms	41×	body	80	valid
2.0ms	7×	body	160	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify165.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	5171	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: 3.5b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.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)
3.2b	(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`
27×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
24×	`times-frac_binary64`
16×	`unpow-prod-down_binary64`
10×	`distribute-lft-out_binary64`
8×	`associate-/r*_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `associate-/r/_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 106

Calls

4 calls:

16.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)

series530.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

304.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
169.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 kx) 2)
27.0ms	(pow.f64 (sin.f64 ky) 2)

simplify129.0ms (1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4942	2355
1	4942	2355

prune181.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	107	11	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Merged error: 2.5b

Counts

119 → 11

Compiler

Compiled 2914 to 1658 computations (43.1% 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 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64`
150×	`*-un-lft-identity_binary64`
99×	`add-sqr-sqrt_binary64`
98×	`add-cube-cbrt_binary64`
65×	`sqrt-prod_binary64`
32×	`unpow-prod-down_binary64`
28×	`associate-/r*_binary64`
26×	`distribute-lft-out_binary64`
17×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
7×	`div-exp_binary64`
6×	`pow-unpow_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`pow-to-exp_binary64` `1-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rec-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `flip-+_binary64`

Counts

4 → 193

Calls

4 calls:

19.0ms	(/.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)))
4.0ms	(pow.f64 (sin.f64 kx) 2)
4.0ms	(pow.f64 (sin.f64 ky) 2)

series518.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

302.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
157.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 ky) 2)
29.0ms	(pow.f64 (sin.f64 kx) 2)

simplify209.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4931	5705
1	4931	5705

prune471.0ms (3.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	204	12	216

Merged error: 2.5b

Counts

216 → 12

Compiler

Compiled 5715 to 3369 computations (41% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (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)))))
3.5b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite63.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64` `times-frac_binary64`
45×	`sqrt-prod_binary64`
36×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`
23×	`unpow-prod-down_binary64`
20×	`distribute-lft-out_binary64`
11×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `insert-posit16`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`inv-pow_binary64` `div-exp_binary64` `pow-flip_binary64` `sqrt-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-exp_binary64` `-commutative_binary64`

Counts

4 → 142

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)))))
15.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
13.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(pow.f64 (sin.f64 kx) 2)

series731.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

291.0ms	(*.f64 (sin.f64 ky) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
243.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
168.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
29.0ms	(pow.f64 (sin.f64 kx) 2)

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5011	3240

prune215.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	155	11	166

Merged error: 2.5b

Counts

166 → 11

Compiler

Compiled 4067 to 2511 computations (38.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2))
3.2b	(pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2)

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64` `unpow-prod-down_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`add-exp-log_binary64`
9×	`pow-unpow_binary64` `associate-r_binary64`
7×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
5×	`sqr-pow_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `insert-posit16` `pow-exp_binary64`
3×	`pow-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`unpow2_binary64`
1×	`cbrt-unprod_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

17.0ms	(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2))
12.0ms	(pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2)
3.0ms	(pow.f64 (sin.f64 kx) 2)
3.0ms	(pow.f64 (sin.f64 ky) 2)

series595.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

294.0ms	(*.f64 (sin.f64 ky) (pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2))
239.0ms	(pow.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)) -1/2)
34.0ms	(pow.f64 (sin.f64 kx) 2)
27.0ms	(pow.f64 (sin.f64 ky) 2)

simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5104	1619

prune114.0ms (0.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	98	11	109

Merged error: 2.5b

Counts

109 → 11

Compiler

Compiled 2154 to 1227 computations (43% saved)

regimes193.0ms (1.5%)

Compiler: Compiled 1825 to 1552 computations (15% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	29
1	20	29

end0.0ms (0%)

sample6.6s (52.3%)

Algorithm

1×

intervals

Results

4.0s	3717×	body	1280	valid
1.4s	2083×	body	640	valid
323.0ms	691×	body	320	valid
156.0ms	1220×	body	80	valid
100.0ms	289×	body	160	valid

Compiler

Compiled 292 to 248 computations (15.1% saved)

Details

analyze1.3s (10%)

sample207.0ms (1.7%)

simplify165.0ms (1.3%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite41.0ms (0.3%)

series530.0ms (4.2%)

simplify129.0ms (1%)

prune181.0ms (1.4%)

localize16.0ms (0.1%)

rewrite52.0ms (0.4%)

series518.0ms (4.1%)

simplify209.0ms (1.7%)

prune471.0ms (3.8%)

localize17.0ms (0.1%)

rewrite63.0ms (0.5%)

series731.0ms (5.8%)

simplify90.0ms (0.7%)

prune215.0ms (1.7%)

localize22.0ms (0.2%)

rewrite39.0ms (0.3%)

series595.0ms (4.7%)

simplify109.0ms (0.9%)

prune114.0ms (0.9%)

regimes193.0ms (1.5%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample6.6s (52.3%)

Profiling