Details

analyze1.5s (8.4%)

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 (0.9%)

Algorithm

1×

intervals

Results

102.0ms	142×	body	1024	valid
20.0ms	43×	body	512	valid
10.0ms	14×	body	256	valid
7.0ms	56×	body	128	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

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

4.4b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize13.0ms (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)
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite219.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

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:

18.0ms	(*.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)))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2766 to 1522 computations (45% saved)

series963.0ms (5.6%)

Error

2.0b

Counts

4 → 34

Calls

4 calls:

665.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
198.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
30.0ms	(pow.f64 (sin.f64 kx) 2)
25.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2227 to 1576 computations (29.2% saved)

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5389	3013

prune197.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	10	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

1.9b

Counts

138 → 10

Compiler

Compiled 3432 to 1891 computations (44.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.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 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.1b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite249.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

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` `unswap-sqr_binary64_46` `associate-l_binary64_19` `pow-unpow_binary64_155` `associate-/l*_binary64_23`
2×	`div-exp_binary64_129` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `div-inv_binary64_75`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `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` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 134

Calls

4 calls:

19.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
15.0ms	(/.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)

Compiler

Compiled 3846 to 2108 computations (45.2% saved)

series1.4s (8.4%)

Error

1.9b

Counts

4 → 44

Calls

4 calls:

649.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
540.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
183.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
22.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3040 to 2133 computations (29.8% saved)

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5003	4730

prune239.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	178	10	188

Error

1.9b

Counts

188 → 10

Compiler

Compiled 4565 to 2445 computations (46.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 kx))
0.6b	(cbrt.f64 (sin.f64 kx))
0.7b	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
4.1b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))

rewrite140.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

11×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`cbrt-prod_binary64_109`
6×	`pow1_binary64_139` `unpow-prod-down_binary64_157`
5×	`add-exp-log_binary64_116`
4×	`add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
3×	`sqrt-prod_binary64_94` `pow-unpow_binary64_155` `pow1/3_binary64_160`
2×	`sqrt-div_binary64_95` `pow-pow_binary64_150`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `sqr-pow_binary64_50`

Counts

4 → 58

Calls

4 calls:

13.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
2.0ms	(cbrt.f64 (sin.f64 kx))
2.0ms	(cbrt.f64 (sin.f64 kx))

Compiler

Compiled 1827 to 913 computations (50% saved)

series516.0ms (3%)

Error

1.9b

Counts

4 → 24

Calls

4 calls:

195.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 kx)) 4) (pow.f64 (cbrt.f64 (sin.f64 kx)) 2)) (pow.f64 (sin.f64 ky) 2)))
133.0ms	(pow.f64 (cbrt.f64 (sin.f64 kx)) 4)
91.0ms	(cbrt.f64 (sin.f64 kx))
68.0ms	(cbrt.f64 (sin.f64 kx))

Compiler

Compiled 1621 to 1207 computations (25.5% saved)

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5043	1032

prune110.0ms (0.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	82	10	92

Error

1.9b

Counts

92 → 10

Compiler

Compiled 2201 to 1197 computations (45.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
0.3b	(pow.f64 (sin.f64 ky) 2)
2.0b	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
4.1b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite246.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.9b

Rules

76×	`*-un-lft-identity_binary64_78`
47×	`times-frac_binary64_84`
42×	`sqrt-prod_binary64_94`
39×	`add-sqr-sqrt_binary64_100`
35×	`add-cube-cbrt_binary64_113`
24×	`associate-r_binary64_18`
23×	`unpow-prod-down_binary64_157`
20×	`distribute-lft-out_binary64_29`
14×	`add-exp-log_binary64_116`
13×	`pow1_binary64_139`
11×	`add-cbrt-cube_binary64_114`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `pow-unpow_binary64_155` `associate-/l*_binary64_23`
2×	`inv-pow_binary64_163` `pow-flip_binary64_152` `sin-mult_binary64_233` `div-exp_binary64_129`
1×	`pow1/2_binary64_158` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20` `associate-l_binary64_19` `*-commutative_binary64_9` `pow-pow_binary64_150` `pow-to-exp_binary64_147` `pow-exp_binary64_146` `unpow2_binary64_143` `sqr-pow_binary64_50` `1-exp_binary64_122` `rec-exp_binary64_128` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

4 → 137

Calls

4 calls:

20.0ms	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
10.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 3949 to 2354 computations (40.4% saved)

series1.2s (7%)

Error

1.9b

Counts

4 → 39

Calls

4 calls:

645.0ms	(.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
268.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
217.0ms	(/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
25.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2667 to 1903 computations (28.6% saved)

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5034	4282

prune223.0ms (1.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	175	11	186

Error

1.9b

Counts

186 → 11

Compiler

Compiled 4431 to 2491 computations (43.8% saved)

regimes2.3s (13.1%)

Accuracy

Total 1.4b remaining (44.5%)

Threshold costs 0b (0%)

Compiler

Compiled 21904 to 17071 computations (22.1% 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	23	65
1	23	65

end0.0ms (0%)

sample7.2s (41.8%)

Algorithm

1×

intervals

Results

3.5s	4639×	body	1024	valid
636.0ms	1330×	body	512	valid
196.0ms	1506×	body	128	valid
155.0ms	510×	body	256	valid
20.0ms	15×	body	2048	valid

Compiler

Compiled 2403 to 1870 computations (22.2% saved)

Details

analyze1.5s (8.4%)

sample154.0ms (0.9%)

simplify88.0ms (0.5%)

prune3.0ms (0%)

localize13.0ms (0.1%)

rewrite219.0ms (1.3%)

series963.0ms (5.6%)

simplify60.0ms (0.3%)

prune197.0ms (1.1%)

localize13.0ms (0.1%)

rewrite249.0ms (1.4%)

series1.4s (8.4%)

simplify94.0ms (0.5%)

prune239.0ms (1.4%)

localize18.0ms (0.1%)

rewrite140.0ms (0.8%)

series516.0ms (3%)

simplify66.0ms (0.4%)

prune110.0ms (0.6%)

localize14.0ms (0.1%)

rewrite246.0ms (1.4%)

series1.2s (7%)

simplify69.0ms (0.4%)

prune223.0ms (1.3%)

regimes2.3s (13.1%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.2s (41.8%)

Profiling