Details

analyze1.4s (10.9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5547	104
0	3	3
1	3	3

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)

sample154.0ms (1.2%)

Algorithm

1×

intervals

Results

114.0ms	156×	body	1024	valid
19.0ms	43×	body	512	valid
6.0ms	46×	body	128	valid
3.0ms	11×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify87.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

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

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))
0.3b	(pow.f64 (sin.f64 kx) 2)
0.3b	(pow.f64 (sin.f64 ky) 2)
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite47.0ms (0.4%)

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:

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))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
7.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

series354.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
93.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
15.0ms	(pow.f64 (sin.f64 ky) 2)
14.0ms	(pow.f64 (sin.f64 kx) 2)

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5006	2288

prune170.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	105	10	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Error

2.0b

Counts

116 → 10

Compiler

Compiled 2949 to 1651 computations (44% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 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)))))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`*-un-lft-identity_binary64_78`
50×	`times-frac_binary64_84`
49×	`add-sqr-sqrt_binary64_100`
41×	`sqrt-prod_binary64_94`
40×	`add-cube-cbrt_binary64_113`
30×	`associate-r_binary64_18`
19×	`unpow-prod-down_binary64_157`
16×	`distribute-lft-out_binary64_29`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
8×	`associate-/r*_binary64_22` `pow1_binary64_139`
6×	`sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`associate-l_binary64_19` `flip-+_binary64_52` `associate-/l*_binary64_23` `unswap-sqr_binary64_46` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75`
1×	`-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 134

Calls

4 calls:

22.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
12.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series665.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

334.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
226.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
92.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)

simplify108.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4967	3544
1	4967	3544

prune183.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	144	12	156

Error

2.0b

Counts

156 → 12

Compiler

Compiled 3807 to 2073 computations (45.5% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
0.3b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite119.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

164×	`sqrt-prod_binary64_94`
130×	`add-sqr-sqrt_binary64_100`
123×	`times-frac_binary64_84`
120×	`*-un-lft-identity_binary64_78`
72×	`add-cube-cbrt_binary64_113`
39×	`associate-l_binary64_19` `associate-r_binary64_18`
24×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
18×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
16×	`unswap-sqr_binary64_46` `sqrt-div_binary64_95`
11×	`associate-/r*_binary64_22`
8×	`pow1_binary64_139`
6×	`associate-/r/_binary64_24`
5×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `flip3-+_binary64_81`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
3×	`div-inv_binary64_75` `associate-/l*_binary64_23`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 209

Calls

4 calls:

51.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
13.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

series628.0ms (5%)

Counts

4 → 12

Calls

4 calls:

232.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))) (/.f64 (sin.f64 th) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
216.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
93.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
86.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

simplify160.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4941	7977
1	4941	7977

prune499.0ms (4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	220	1	221
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	221	12	233

Error

2.0b

Counts

233 → 12

Compiler

Compiled 8617 to 5058 computations (41.3% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.4b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.4b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_78`
18×	`add-sqr-sqrt_binary64_100`
16×	`cbrt-prod_binary64_109`
12×	`add-cube-cbrt_binary64_113`
11×	`associate-r_binary64_18`
10×	`sqrt-prod_binary64_94`
9×	`unpow-prod-down_binary64_157`
7×	`add-exp-log_binary64_116` `pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `distribute-lft-out_binary64_29`
4×	`add-log-exp_binary64_117`
3×	`associate-l_binary64_19` `flip-+_binary64_52` `unswap-sqr_binary64_46` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95` `associate-*r/_binary64_20`
1×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-prod-down_binary64_149`

Counts

4 → 78

Calls

4 calls:

15.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

series455.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sqrt.f64 (cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
130.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
125.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
14.0ms	(pow.f64 (sin.f64 ky) 2)

simplify81.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4881	2396
1	4881	2396

prune158.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	89	13	102

Error

2.0b

Counts

102 → 13

Compiler

Compiled 3316 to 2047 computations (38.3% saved)

regimes1.1s (8.7%)

Accuracy

Total 0.4b remaining (13.6%)

Threshold costs 0.4b (13.6%)

Compiler

Compiled 12564 to 9887 computations (21.3% saved)

bsearch4.0ms (0%)

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

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	84
1	63	84

end0.0ms (0%)

sample5.9s (47.6%)

Algorithm

1×

intervals

Results

3.3s	4604×	body	1024	valid
635.0ms	1390×	body	512	valid
192.0ms	1442×	body	128	valid
154.0ms	552×	body	256	valid
13.0ms	12×	body	2048	valid

Compiler

Compiled 1410 to 1104 computations (21.7% saved)

Details

analyze1.4s (10.9%)

sample154.0ms (1.2%)

simplify87.0ms (0.7%)

prune3.0ms (0%)

localize15.0ms (0.1%)

rewrite47.0ms (0.4%)

series354.0ms (2.8%)

simplify60.0ms (0.5%)

prune170.0ms (1.4%)

localize14.0ms (0.1%)

rewrite58.0ms (0.5%)

series665.0ms (5.3%)

simplify108.0ms (0.9%)

prune183.0ms (1.5%)

localize17.0ms (0.1%)

rewrite119.0ms (0.9%)

series628.0ms (5%)

simplify160.0ms (1.3%)

prune499.0ms (4%)

localize21.0ms (0.2%)

rewrite44.0ms (0.3%)

series455.0ms (3.6%)

simplify81.0ms (0.6%)

prune158.0ms (1.3%)

regimes1.1s (8.7%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (47.6%)

Profiling