Details

analyze2.0s (2.9%)

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)

sample190.0ms (0.3%)

Algorithm

1×

intervals

Results

131.0ms	137×	body	1024	valid
29.0ms	49×	body	512	valid
9.0ms	25×	body	256	valid
7.0ms	45×	body	128	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify274.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (135.0ms)

Iter	Nodes	Cost
0	5170	26

prune8.0ms (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: 4.0b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize45.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite88.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

41.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
21.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.0ms	(pow.f64 (sin.f64 ky) 2)
5.0ms	(pow.f64 (sin.f64 kx) 2)

series470.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

287.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
128.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
34.0ms	(pow.f64 (sin.f64 ky) 2)
21.0ms	(pow.f64 (sin.f64 kx) 2)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5006	2288

prune721.0ms (1.1%)

Pruning

59 alts after pruning (58 fresh and 1 done)

	Pruned	Kept	Total
New	57	58	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	59	116

Merged error: 2.6b

Counts

116 → 59

Compiler

Compiled 4344 to 2729 computations (37.2% saved)

localize19.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite62.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

30.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
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)

series357.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

226.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
103.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify59.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5006	2288

prune1.5s (2.2%)

Pruning

113 alts after pruning (111 fresh and 2 done)

	Pruned	Kept	Total
New	58	57	115
Fresh	3	54	57
Picked	0	1	1
Done	0	1	1
Total	61	113	174

Merged error: 2.6b

Counts

174 → 113

Compiler

Compiled 7049 to 5090 computations (27.8% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.7b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite58.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_78`
34×	`add-sqr-sqrt_binary64_100`
30×	`associate-l_binary64_19`
26×	`times-frac_binary64_84`
25×	`add-cube-cbrt_binary64_113`
21×	`sqrt-prod_binary64_94`
14×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`associate-r_binary64_18` `unswap-sqr_binary64_46`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`-commutative_binary64_9` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `pow1/2_binary64_158`

Counts

4 → 103

Calls

4 calls:

32.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
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)

series497.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

328.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
139.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
16.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5006	2288

prune2.1s (3.1%)

Pruning

153 alts after pruning (150 fresh and 3 done)

	Pruned	Kept	Total
New	68	47	115
Fresh	7	103	110
Picked	0	1	1
Done	0	2	2
Total	75	153	228

Merged error: 2.6b

Counts

228 → 153

Compiler

Compiled 8202 to 5956 computations (27.4% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
0.2b	(*.f64 (sin.f64 kx) (sin.f64 kx))
0.3b	(pow.f64 (sin.f64 ky) 2)
3.7b	(sqrt.f64 (+.f64 (*.f64 (sin.f64 kx) (sin.f64 kx)) (pow.f64 (sin.f64 ky) 2)))

rewrite52.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_100`
27×	`associate-l_binary64_19`
25×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`times-frac_binary64_84`
15×	`pow1_binary64_139`
13×	`sqrt-prod_binary64_94`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
6×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `unswap-sqr_binary64_46` `sqrt-div_binary64_95`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unpow-prod-down_binary64_157` `swap-sqr_binary64_45` `pow-unpow_binary64_155`
2×	`*-commutative_binary64_9` `flip-+_binary64_52` `pow-prod-down_binary64_149` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`pow2_binary64_159` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `pow-sqr_binary64_51` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `sqr-sin-a_binary64_226` `pow-pow_binary64_150` `pow-prod-up_binary64_148` `associate-*l/_binary64_21` `sin-mult_binary64_233` `pow-plus_binary64_141` `pow1/2_binary64_158`

Counts

4 → 104

Calls

4 calls:

15.0ms	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
14.0ms	(sqrt.f64 (+.f64 (*.f64 (sin.f64 kx) (sin.f64 kx)) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(*.f64 (sin.f64 kx) (sin.f64 kx))
5.0ms	(pow.f64 (sin.f64 ky) 2)

series549.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (.f64 (sin.f64 kx) (sin.f64 kx)) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
137.0ms	(sqrt.f64 (+.f64 (*.f64 (sin.f64 kx) (sin.f64 kx)) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(*.f64 (sin.f64 kx) (sin.f64 kx))
25.0ms	(pow.f64 (sin.f64 ky) 2)

simplify159.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5008	2127

prune1.1s (1.5%)

Pruning

174 alts after pruning (170 fresh and 4 done)

	Pruned	Kept	Total
New	93	23	116
Fresh	2	147	149
Picked	0	1	1
Done	0	3	3
Total	95	174	269

Merged error: 2.5b

Counts

269 → 174

Compiler

Compiled 2758 to 1325 computations (52% saved)

regimes8.7s (12.7%)

Compiler: Compiled 73113 to 58855 computations (19.5% saved)

bsearch29.5s (43.1%)

Compiler: Compiled 13 to 12 computations (7.7% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	84
1	68	84

end0.0ms (0%)

sample19.8s (28.9%)

Algorithm

1×

intervals

Results

4.8s	4670×	body	1024	valid
915.0ms	1380×	body	512	valid
262.0ms	1404×	body	128	valid
213.0ms	525×	body	256	valid
35.0ms	21×	body	2048	valid

Compiler

Compiled 8108 to 6503 computations (19.8% saved)

Pareto

0.46677765275942124

Details

analyze2.0s (2.9%)

sample190.0ms (0.3%)

simplify274.0ms (0.4%)

prune8.0ms (0%)

localize45.0ms (0.1%)

rewrite88.0ms (0.1%)

series470.0ms (0.7%)

simplify74.0ms (0.1%)

prune721.0ms (1.1%)

localize19.0ms (0%)

rewrite62.0ms (0.1%)

series357.0ms (0.5%)

simplify59.0ms (0.1%)

prune1.5s (2.2%)

localize17.0ms (0%)

rewrite58.0ms (0.1%)

series497.0ms (0.7%)

simplify96.0ms (0.1%)

prune2.1s (3.1%)

localize14.0ms (0%)

rewrite52.0ms (0.1%)

series549.0ms (0.8%)

simplify159.0ms (0.2%)

prune1.1s (1.5%)

regimes8.7s (12.7%)

bsearch29.5s (43.1%)

simplify10.0ms (0%)

end0.0ms (0%)

sample19.8s (28.9%)

Profiling