Details

analyze1.2s (11.2%)

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)

sample166.0ms (1.5%)

Algorithm

1×

intervals

Results

128.0ms	155×	body	1024	valid
17.0ms	37×	body	512	valid
7.0ms	54×	body	128	valid
3.0ms	10×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify81.0ms (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)

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)
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite39.0ms (0.4%)

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` `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 → 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)

series522.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

300.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
172.0ms	(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)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4963	2298
1	4963	2298

prune173.0ms (1.6%)

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: 3.5b

Counts

115 → 11

Compiler

Compiled 2838 to 1617 computations (43% 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)
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite62.0ms (0.6%)

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`
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 → 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)))
12.0ms	(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)

series506.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
160.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 ky) 2)
24.0ms	(pow.f64 (sin.f64 kx) 2)

simplify125.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4928	5648
1	4928	5648

prune303.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	201	11	212

Merged error: 3.5b

Counts

212 → 11

Compiler

Compiled 5613 to 3304 computations (41.1% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.0b	(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))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`unpow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`

Counts

4 → 63

Calls

4 calls:

17.0ms	(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)))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
3.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

series616.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
160.0ms	(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)))
148.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))
145.0ms	(cbrt.f64 (pow.f64 (sin.f64 kx) 2))

simplify81.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4880	1052
1	4880	1052

prune128.0ms (1.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	75	11	86

Merged error: 3.5b

Counts

86 → 11

Compiler

Compiled 2572 to 1556 computations (39.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`sqrt-prod_binary64`
56×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
32×	`add-cube-cbrt_binary64`
15×	`unpow-prod-down_binary64`
12×	`distribute-lft-out_binary64`
11×	`associate-/r*_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`

Counts

4 → 113

Calls

4 calls:

15.0ms	(/.f64 (sin.f64 ky) (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)))
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)

series703.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

355.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
167.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
155.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 kx) 2)

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5035	3194

prune224.0ms (2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	125	11	136

Merged error: 3.5b

Counts

136 → 11

Compiler

Compiled 4639 to 2766 computations (40.4% saved)

regimes226.0ms (2%)

Compiler: Compiled 2172 to 1806 computations (16.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	29
1	19	29

end0.0ms (0%)

sample5.6s (50.3%)

Algorithm

1×

intervals

Results

3.9s	4632×	body	1024	valid
686.0ms	1423×	body	512	valid
180.0ms	1408×	body	128	valid
159.0ms	524×	body	256	valid
23.0ms	13×	body	2048	valid

Compiler

Compiled 300 to 250 computations (16.7% saved)

Details

analyze1.2s (11.2%)

sample166.0ms (1.5%)

simplify81.0ms (0.7%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite39.0ms (0.4%)

series522.0ms (4.7%)

simplify72.0ms (0.7%)

prune173.0ms (1.6%)

localize16.0ms (0.1%)

rewrite62.0ms (0.6%)

series506.0ms (4.6%)

simplify125.0ms (1.1%)

prune303.0ms (2.7%)

localize22.0ms (0.2%)

rewrite34.0ms (0.3%)

series616.0ms (5.6%)

simplify81.0ms (0.7%)

prune128.0ms (1.2%)

localize18.0ms (0.2%)

rewrite56.0ms (0.5%)

series703.0ms (6.4%)

simplify57.0ms (0.5%)

prune224.0ms (2%)

regimes226.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.6s (50.3%)

Profiling