Details

analyze1.9s (7.5%)

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)

sample214.0ms (0.8%)

Algorithm

1×

intervals

Results

142.0ms	133×	body	1024	valid
37.0ms	60×	body	512	valid
9.0ms	25×	body	256	valid
6.0ms	37×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify106.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5170	26

prune5.0ms (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

2.7b

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 kx) 2)
0.2b	(pow.f64 (sin.f64 ky) 2)
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite254.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

2.5b

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:

33.0ms	(*.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)

series1.2s (4.6%)

Error

1.2b

Counts

4 → 39

Calls

4 calls:

817.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
229.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
39.0ms	(pow.f64 (sin.f64 kx) 2)
27.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2393 to 1709 computations (28.6% saved)

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4993	3140
1	4993	3140

prune236.0ms (0.9%)

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 3715 to 2081 computations (44% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(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)))))
0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite308.0ms (1.2%)

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` `unswap-sqr_binary64_46` `associate-l*_binary64_19` `pow-unpow_binary64_155`
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-prod-down_binary64_149` `associate-r/_binary64_20` `-commutative_binary64_9` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 134

Calls

4 calls:

23.0ms	(*.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))))
11.0ms	(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)

series1.7s (6.8%)

Error

1.1b

Counts

4 → 49

Calls

4 calls:

751.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
640.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
220.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
44.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3247 to 2294 computations (29.4% saved)

simplify104.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4978	4875
1	4978	4875

prune307.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	185	12	197

Error

1.1b

Counts

197 → 12

Compiler

Compiled 4809 to 2612 computations (45.7% saved)

localize14.0ms (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	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
0.3b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite935.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

370×	`times-frac_binary64_84`
293×	`*-un-lft-identity_binary64_78`
208×	`add-sqr-sqrt_binary64_100`
186×	`add-cube-cbrt_binary64_113`
132×	`sqrt-prod_binary64_94`
89×	`associate-r_binary64_18`
52×	`unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
36×	`add-exp-log_binary64_116`
31×	`associate-/r*_binary64_22`
20×	`add-cbrt-cube_binary64_114`
15×	`div-exp_binary64_129`
11×	`associate-/l*_binary64_23`
10×	`div-inv_binary64_75`
8×	`pow1_binary64_139`
7×	`cbrt-undiv_binary64_112` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `1-exp_binary64_122` `rec-exp_binary64_128`
3×	`cbrt-unprod_binary64_111` `associate-l_binary64_19`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `inv-pow_binary64_163` `pow-flip_binary64_152` `pow-prod-down_binary64_149` `un-div-inv_binary64_76` `associate-r/_binary64_20` `-commutative_binary64_9`

Counts

4 → 322

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))))
27.0ms	(/.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)))
11.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 11170 to 6716 computations (39.9% saved)

series2.4s (9.2%)

Error

1.1b

Counts

4 → 60

Calls

4 calls:

778.0ms	(*.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))))
685.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
591.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))
210.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

Compiler

Compiled 4301 to 3015 computations (29.9% saved)

simplify158.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

382 → 382

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5025	12554

prune770.0ms (3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	379	3	382
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	380	14	394

Error

1.1b

Counts

394 → 14

Compiler

Compiled 11478 to 6471 computations (43.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.3b	(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
0.3b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))
2.5b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite473.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

204×	`times-frac_binary64_84`
181×	`*-un-lft-identity_binary64_78`
114×	`add-sqr-sqrt_binary64_100`
113×	`add-cube-cbrt_binary64_113`
85×	`sqrt-prod_binary64_94`
37×	`unpow-prod-down_binary64_157`
34×	`distribute-lft-out_binary64_29`
31×	`associate-/r*_binary64_22`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23`
6×	`pow1_binary64_139` `div-inv_binary64_75`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`pow-unpow_binary64_155`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `associate-/r/_binary64_24` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50`

Counts

4 → 214

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)))
16.0ms	(/.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)))
4.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 6784 to 3567 computations (47.4% saved)

series1.6s (6.4%)

Error

1.1b

Counts

4 → 50

Calls

4 calls:

717.0ms	(/.f64 (sin.f64 ky) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th)))
541.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 th))
223.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
54.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3311 to 2292 computations (30.8% saved)

simplify189.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4949	9274
1	4949	9274

prune439.0ms (1.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	265	13	278

Error

1.1b

Counts

278 → 13

Compiler

Compiled 7189 to 3668 computations (49% saved)

regimes2.5s (9.8%)

Accuracy

Total 2.2b remaining (54.7%)

Threshold costs 0b (0%)

Compiler

Compiled 25014 to 19573 computations (21.8% 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%)

sample9.6s (37.5%)

Algorithm

1×

intervals

Results

4.3s	4622×	body	1024	valid
829.0ms	1428×	body	512	valid
235.0ms	1409×	body	128	valid
196.0ms	521×	body	256	valid
34.0ms	20×	body	2048	valid

Compiler

Compiled 2803 to 2195 computations (21.7% saved)

Details

analyze1.9s (7.5%)

sample214.0ms (0.8%)

simplify106.0ms (0.4%)

prune5.0ms (0%)

localize15.0ms (0.1%)

rewrite254.0ms (1%)

series1.2s (4.6%)

simplify90.0ms (0.4%)

prune236.0ms (0.9%)

localize13.0ms (0.1%)

rewrite308.0ms (1.2%)

series1.7s (6.8%)

simplify104.0ms (0.4%)

prune307.0ms (1.2%)

localize14.0ms (0.1%)

rewrite935.0ms (3.7%)

series2.4s (9.2%)

simplify158.0ms (0.6%)

prune770.0ms (3%)

localize16.0ms (0.1%)

rewrite473.0ms (1.9%)

series1.6s (6.4%)

simplify189.0ms (0.7%)

prune439.0ms (1.7%)

regimes2.5s (9.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample9.6s (37.5%)

Profiling