Details

analyze1.3s (9.7%)

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)

sample170.0ms (1.3%)

Algorithm

1×

intervals

Results

123.0ms	154×	body	1024	valid
23.0ms	40×	body	512	valid
6.0ms	48×	body	128	valid
4.0ms	13×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify234.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5170	26

prune140.0ms (1.1%)

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: 4.2b

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 (/.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 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`*-un-lft-identity_binary64_77`
34×	`add-sqr-sqrt_binary64_98`
30×	`associate-l_binary64_20`
26×	`times-frac_binary64_83`
25×	`add-cube-cbrt_binary64_109`
21×	`sqrt-prod_binary64_92`
14×	`unpow-prod-down_binary64_153`
11×	`add-exp-log_binary64_112`
9×	`add-cbrt-cube_binary64_110` `pow1_binary64_135`
8×	`distribute-lft-out_binary64_30`
6×	`pow-unpow_binary64_151`
4×	`add-log-exp_binary64_113` `sqrt-div_binary64_93`
3×	`unswap-sqr_binary64_45` `associate-r_binary64_19`
2×	`pow-to-exp_binary64_143` `flip-+_binary64_51` `cbrt-unprod_binary64_107` `sqr-pow_binary64_49` `flip3-+_binary64_80` `pow-exp_binary64_142` `associate-/r/_binary64_25` `prod-exp_binary64_123` `unpow2_binary64_139` `pow-pow_binary64_146`
1×	`pow-prod-down_binary64_145` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `associate-l/_binary64_22` `div-exp_binary64_125` `-commutative_binary64_10` `pow1/2_binary64_154` `div-inv_binary64_74`

Counts

4 → 103

Calls

4 calls:

19.0ms	(*.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)

series612.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

400.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
163.0ms	(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)

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4952	2288
1	4952	2288

prune179.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	12	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Merged error: 3.1b

Counts

116 → 12

Compiler

Compiled 3007 to 1700 computations (43.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 kx) 2)
0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite61.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_77`
50×	`times-frac_binary64_83`
49×	`add-sqr-sqrt_binary64_98`
41×	`sqrt-prod_binary64_92`
40×	`add-cube-cbrt_binary64_109`
30×	`associate-r_binary64_19`
19×	`unpow-prod-down_binary64_153`
16×	`distribute-lft-out_binary64_30`
12×	`add-exp-log_binary64_112`
11×	`add-cbrt-cube_binary64_110`
8×	`associate-/r*_binary64_23` `pow1_binary64_135`
6×	`sqrt-div_binary64_93`
4×	`add-log-exp_binary64_113` `associate-/r/_binary64_25`
3×	`associate-l_binary64_20` `flip-+_binary64_51` `flip3-+_binary64_80` `associate-/l*_binary64_24` `pow-unpow_binary64_151` `unswap-sqr_binary64_45`
2×	`cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `div-exp_binary64_125` `prod-exp_binary64_123` `div-inv_binary64_74`
1×	`pow-to-exp_binary64_143` `pow-prod-down_binary64_145` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `sqr-pow_binary64_49` `pow-exp_binary64_142` `associate-r/_binary64_21` `-commutative_binary64_10` `pow1/2_binary64_154` `clear-num_binary64_76` `unpow2_binary64_139` `frac-2neg_binary64_88` `pow-pow_binary64_146`

Counts

4 → 134

Calls

4 calls:

21.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
13.0ms	(/.f64 (sin.f64 th) (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)

series929.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

393.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
350.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
162.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
24.0ms	(pow.f64 (sin.f64 kx) 2)

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5028	3544

prune195.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	147	11	158

Merged error: 3.1b

Counts

158 → 11

Compiler

Compiled 3803 to 2071 computations (45.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.8b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite72.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`sqrt-prod_binary64_92`
94×	`*-un-lft-identity_binary64_77`
66×	`times-frac_binary64_83`
56×	`add-sqr-sqrt_binary64_98`
54×	`add-cube-cbrt_binary64_109`
22×	`associate-/r*_binary64_23`
20×	`unpow-prod-down_binary64_153` `distribute-lft-out_binary64_30`
12×	`sqrt-div_binary64_93`
8×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`pow1_binary64_135` `associate-/l*_binary64_24`
4×	`add-log-exp_binary64_113` `flip-+_binary64_51` `flip3-+_binary64_80` `associate-/r/_binary64_25`
2×	`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 → 156

Calls

4 calls:

18.0ms	(/.f64 (sin.f64 th) (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)))))
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)))

series1.0s (8%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
347.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
156.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
153.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4943	5213
1	4943	5213

prune348.0ms (2.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	168	11	179

Merged error: 3.1b

Counts

179 → 11

Compiler

Compiled 6720 to 4034 computations (40% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
4.3b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.3b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite93.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-exp-log_binary64_112`
27×	`*-un-lft-identity_binary64_77`
25×	`add-cbrt-cube_binary64_110`
24×	`associate-l_binary64_20`
20×	`prod-exp_binary64_123`
18×	`cbrt-div_binary64_106`
15×	`cbrt-prod_binary64_105` `add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
12×	`times-frac_binary64_83`
10×	`cbrt-unprod_binary64_107` `div-exp_binary64_125`
9×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1_binary64_135`
8×	`sqrt-div_binary64_93` `associate-/r/_binary64_25`
6×	`unpow-prod-down_binary64_153` `distribute-lft-out_binary64_30`
5×	`cbrt-undiv_binary64_108` `frac-times_binary64_87` `associate-*r/_binary64_21`
4×	`add-log-exp_binary64_113`
3×	`sqrt-prod_binary64_92` `pow-prod-down_binary64_145` `1-exp_binary64_118` `rec-exp_binary64_124` `associate-*l/_binary64_22` `pow1/3_binary64_156`
1×	`-commutative_binary64_10` `associate-r*_binary64_19` `div-inv_binary64_74`

Counts

4 → 101

Calls

4 calls:

46.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
11.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series1.1s (8.4%)

Counts

4 → 12

Calls

4 calls:

429.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))))
223.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
218.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
216.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4981	4090
1	4981	4090

prune270.0ms (2.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	112	12	124

Merged error: 3.1b

Counts

124 → 12

Compiler

Compiled 5240 to 3323 computations (36.6% saved)

regimes296.0ms (2.3%)

Compiler: Compiled 2474 to 2099 computations (15.2% 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%)

sample5.5s (42.6%)

Algorithm

1×

intervals

Results

3.8s	4595×	body	1024	valid
728.0ms	1431×	body	512	valid
194.0ms	1432×	body	128	valid
163.0ms	528×	body	256	valid
23.0ms	14×	body	2048	valid

Compiler

Compiled 284 to 240 computations (15.5% saved)

Details

analyze1.3s (9.7%)

sample170.0ms (1.3%)

simplify234.0ms (1.8%)

prune140.0ms (1.1%)

localize15.0ms (0.1%)

rewrite44.0ms (0.3%)

series612.0ms (4.7%)

simplify89.0ms (0.7%)

prune179.0ms (1.4%)

localize17.0ms (0.1%)

rewrite61.0ms (0.5%)

series929.0ms (7.2%)

simplify67.0ms (0.5%)

prune195.0ms (1.5%)

localize17.0ms (0.1%)

rewrite72.0ms (0.6%)

series1.0s (8%)

simplify106.0ms (0.8%)

prune348.0ms (2.7%)

localize22.0ms (0.2%)

rewrite93.0ms (0.7%)

series1.1s (8.4%)

simplify92.0ms (0.7%)

prune270.0ms (2.1%)

regimes296.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample5.5s (42.6%)

Profiling