Details

analyze1.4s (7.2%)

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)

sample152.0ms (0.8%)

Algorithm

1×

intervals

Results

109.0ms	151×	body	1024	valid
17.0ms	38×	body	512	valid
6.0ms	47×	body	128	valid
5.0ms	20×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify85.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5170	26

prune7.0ms (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

3.2b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.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)
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite211.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

3.0b

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×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
8×	`distribute-lft-out_binary64_29`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
3×	`unswap-sqr_binary64_46` `associate-r_binary64_18`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-l/_binary64_21` `div-inv_binary64_75` `-commutative_binary64_9`

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 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2766 to 1522 computations (45% saved)

series956.0ms (5%)

Error

1.2b

Counts

4 → 39

Calls

4 calls:

646.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
196.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
32.0ms	(pow.f64 (sin.f64 ky) 2)
30.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2393 to 1709 computations (28.6% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4993	3140
1	4993	3140

prune218.0ms (1.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	128	14	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	14	143

Error

1.1b

Counts

143 → 14

Compiler

Compiled 3704 to 2076 computations (44% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))))
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))))
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite263.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

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×	`pow1_binary64_139` `associate-/r*_binary64_22`
6×	`sqrt-div_binary64_95`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `associate-/l_binary64_23` `pow-unpow_binary64_155` `unswap-sqr_binary64_46` `associate-l*_binary64_19`
2×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `div-inv_binary64_75` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `-commutative_binary64_9`

Counts

4 → 134

Calls

4 calls:

24.0ms	(*.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 ky) 2)

Compiler

Compiled 3846 to 2108 computations (45.2% saved)

series1.4s (7.3%)

Error

1.1b

Counts

4 → 49

Calls

4 calls:

608.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
524.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
185.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
28.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3247 to 2294 computations (29.4% saved)

simplify93.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4978	4875
1	4978	4875

prune244.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	185	12	197

Error

1.1b

Counts

197 → 12

Compiler

Compiled 4819 to 2620 computations (45.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))))
0.3b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite688.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

346×	`times-frac_binary64_84`
262×	`*-un-lft-identity_binary64_78`
193×	`add-sqr-sqrt_binary64_100`
171×	`add-cube-cbrt_binary64_113`
112×	`sqrt-prod_binary64_94`
89×	`associate-r_binary64_18`
47×	`unpow-prod-down_binary64_157`
44×	`distribute-lft-out_binary64_29`
35×	`add-exp-log_binary64_116`
28×	`associate-/r*_binary64_22`
18×	`add-cbrt-cube_binary64_114`
14×	`div-exp_binary64_129`
9×	`pow1_binary64_139` `div-inv_binary64_75`
7×	`prod-exp_binary64_127` `unswap-sqr_binary64_46`
6×	`cbrt-undiv_binary64_112`
4×	`add-log-exp_binary64_117` `1-exp_binary64_122` `rec-exp_binary64_128`
3×	`associate-/l_binary64_23` `pow-unpow_binary64_155` `cbrt-unprod_binary64_111` `associate-l*_binary64_19`
2×	`sqrt-div_binary64_95` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `inv-pow_binary64_163` `pow-flip_binary64_152` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-prod-down_binary64_149` `un-div-inv_binary64_76` `associate-r/_binary64_20` `-commutative_binary64_9`

Counts

4 → 291

Calls

4 calls:

41.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))))
17.0ms	(/.f64 1 (/.f64 (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 ky) 2)

Compiler

Compiled 10028 to 6062 computations (39.5% saved)

series1.4s (7.5%)

Error

1.1b

Counts

4 → 49

Calls

4 calls:

635.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))))
540.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
173.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
31.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3329 to 2380 computations (28.5% saved)

simplify148.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	10541
1	4965	10541

prune605.0ms (3.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	337	3	340
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	339	13	352

Error

1.1b

Counts

352 → 13

Compiler

Compiled 10042 to 5676 computations (43.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 ky) (/.f64 (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)
2.9b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite345.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

180×	`times-frac_binary64_84`
150×	`*-un-lft-identity_binary64_78`
99×	`add-sqr-sqrt_binary64_100`
98×	`add-cube-cbrt_binary64_113`
65×	`sqrt-prod_binary64_94`
32×	`unpow-prod-down_binary64_157`
28×	`associate-/r*_binary64_22`
26×	`distribute-lft-out_binary64_29`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
7×	`pow1_binary64_139`
6×	`pow-unpow_binary64_155`
5×	`div-inv_binary64_75`
4×	`add-log-exp_binary64_117`
3×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/l*_binary64_23`
2×	`sqrt-div_binary64_95` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/r/_binary64_24`

Counts

4 → 183

Calls

4 calls:

17.0ms	(/.f64 (sin.f64 ky) (/.f64 (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)

Compiler

Compiled 5704 to 2980 computations (47.8% saved)

series947.0ms (4.9%)

Error

1.1b

Counts

4 → 39

Calls

4 calls:

648.0ms	(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
190.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
29.0ms	(pow.f64 (sin.f64 kx) 2)
28.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2393 to 1709 computations (28.6% saved)

simplify128.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4953	7265
1	4953	7265

prune283.0ms (1.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	223	12	235

Error

1.1b

Counts

235 → 12

Compiler

Compiled 5885 to 2983 computations (49.3% saved)

regimes2.0s (10.2%)

Accuracy

Total 1.3b remaining (42.3%)

Threshold costs 0b (0%)

Compiler

Compiled 23259 to 18385 computations (21% saved)

bsearch6.0ms (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	20	55
1	20	55

end0.0ms (0%)

sample7.5s (39.1%)

Algorithm

1×

intervals

Results

3.3s	4581×	body	1024	valid
689.0ms	1470×	body	512	valid
191.0ms	1416×	body	128	valid
146.0ms	524×	body	256	valid
12.0ms	9×	body	2048	valid

Compiler

Compiled 2626 to 2073 computations (21.1% saved)

Details

analyze1.4s (7.2%)

sample152.0ms (0.8%)

simplify85.0ms (0.4%)

prune7.0ms (0%)

localize15.0ms (0.1%)

rewrite211.0ms (1.1%)

series956.0ms (5%)

simplify77.0ms (0.4%)

prune218.0ms (1.1%)

localize14.0ms (0.1%)

rewrite263.0ms (1.4%)

series1.4s (7.3%)

simplify93.0ms (0.5%)

prune244.0ms (1.3%)

localize15.0ms (0.1%)

rewrite688.0ms (3.6%)

series1.4s (7.5%)

simplify148.0ms (0.8%)

prune605.0ms (3.1%)

localize14.0ms (0.1%)

rewrite345.0ms (1.8%)

series947.0ms (4.9%)

simplify128.0ms (0.7%)

prune283.0ms (1.5%)

regimes2.0s (10.2%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.5s (39.1%)

Profiling