Details

analyze1.3s (7.5%)

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)

sample158.0ms (0.9%)

Algorithm

1×

intervals

Results

110.0ms	148×	body	1024	valid
26.0ms	57×	body	512	valid
5.0ms	38×	body	128	valid
4.0ms	13×	body	256	valid

Compiler

Compiled 33 to 32 computations (3% saved)

simplify174.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

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

3.5b

Counts

2 → 1

Compiler

Compiled 32 to 28 computations (12.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.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)
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite281.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

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))
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)

series1.1s (6.4%)

Error

1.3b

Counts

4 → 40

Calls

4 calls:

669.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
263.0ms	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
46.0ms	(pow.f64 (sin.f64 kx) 2)
42.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2561 to 1798 computations (29.8% saved)

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5150	3386

prune201.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	134	9	143
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	134	10	144

Error

1.2b

Counts

144 → 10

Compiler

Compiled 3753 to 2075 computations (44.7% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
1.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
3.2b	(sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite136.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

25×	`*-un-lft-identity_binary64_78`
15×	`sqrt-prod_binary64_94`
14×	`add-sqr-sqrt_binary64_100`
13×	`add-cube-cbrt_binary64_113`
12×	`unpow-prod-down_binary64_157`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
8×	`times-frac_binary64_84` `associate-/r*_binary64_22`
7×	`pow1_binary64_139`
6×	`distribute-lft-out_binary64_29` `pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
2×	`flip3-+_binary64_81` `flip-+_binary64_52` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r/_binary64_24` `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` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `sin-mult_binary64_233` `associate-/l/_binary64_25` `associate-/l*_binary64_23`

Counts

4 → 87

Calls

4 calls:

14.0ms	(/.f64 (*.f64 (sin.f64 ky) (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)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 2170 to 1157 computations (46.7% saved)

series958.0ms (5.7%)

Error

1.2b

Counts

4 → 40

Calls

4 calls:

658.0ms	(/.f64 (*.f64 (sin.f64 ky) (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)))
29.0ms	(pow.f64 (sin.f64 kx) 2)
29.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2561 to 1775 computations (30.7% saved)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5067	2868

prune147.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	127	10	137

Error

1.2b

Counts

137 → 10

Compiler

Compiled 3093 to 1633 computations (47.2% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 ky))
3.6b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.6b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
3.6b	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))

rewrite178.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

20×	`*-un-lft-identity_binary64_78`
18×	`cbrt-prod_binary64_109`
8×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100`
6×	`cbrt-div_binary64_110` `unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
4×	`pow1/3_binary64_160` `pow1_binary64_139` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`flip3-+_binary64_81` `flip-+_binary64_52`

Counts

4 → 56

Calls

4 calls:

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)))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
1.0ms	(cbrt.f64 (sin.f64 ky))

Compiler

Compiled 3320 to 1799 computations (45.8% saved)

series1.5s (9.1%)

Error

1.2b

Counts

4 → 42

Calls

4 calls:

448.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
439.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
432.0ms	(cbrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
87.0ms	(cbrt.f64 (sin.f64 ky))

Compiler

Compiled 6548 to 4398 computations (32.8% saved)

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4941	2702
1	4941	2702

prune274.0ms (1.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	98	10	108

Error

1.2b

Counts

108 → 10

Compiler

Compiled 5934 to 3318 computations (44.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
1.6b	(.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)))))
3.2b	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))

rewrite190.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

52×	`*-un-lft-identity_binary64_78`
42×	`sqrt-prod_binary64_94`
32×	`times-frac_binary64_84`
31×	`add-sqr-sqrt_binary64_100`
27×	`add-cube-cbrt_binary64_113`
24×	`associate-r_binary64_18`
18×	`unpow-prod-down_binary64_157`
13×	`pow1_binary64_139`
12×	`distribute-lft-out_binary64_29`
11×	`add-exp-log_binary64_116`
9×	`add-cbrt-cube_binary64_114`
6×	`pow-unpow_binary64_155`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`sqrt-pow1_binary64_96` `sqrt-div_binary64_95` `rem-sqrt-square_binary64_91` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
2×	`div-inv_binary64_75` `flip3-+_binary64_81` `flip-+_binary64_52` `sin-mult_binary64_233` `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` `inv-pow_binary64_163` `pow-flip_binary64_152` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20` `associate-l_binary64_19` `*-commutative_binary64_9`

Counts

4 → 114

Calls

4 calls:

19.0ms	(.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)))))
10.0ms	(sqrt.f64 (/.f64 1 (+.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 3209 to 1893 computations (41% saved)

series1.1s (6.3%)

Error

1.2b

Counts

4 → 40

Calls

4 calls:

663.0ms	(.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)))))
290.0ms	(sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))
29.0ms	(pow.f64 (sin.f64 kx) 2)
27.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 2721 to 1935 computations (28.9% saved)

simplify102.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4958	3643
1	4958	3643

prune195.0ms (1.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	154	10	164

Error

1.2b

Counts

164 → 10

Compiler

Compiled 3909 to 2182 computations (44.2% saved)

regimes1.7s (10%)

Accuracy

Total 1.5b remaining (44.1%)

Threshold costs 0b (0%)

Compiler

Compiled 20964 to 16108 computations (23.2% 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%)

sample6.9s (41.1%)

Algorithm

1×

intervals

Results

3.3s	4561×	body	1024	valid
662.0ms	1450×	body	512	valid
187.0ms	585×	body	256	valid
183.0ms	1399×	body	128	valid
6.0ms	5×	body	2048	valid

Compiler

Compiled 2371 to 1820 computations (23.2% saved)

Details

analyze1.3s (7.5%)

sample158.0ms (0.9%)

simplify174.0ms (1%)

prune7.0ms (0%)

localize13.0ms (0.1%)

rewrite281.0ms (1.7%)

series1.1s (6.4%)

simplify59.0ms (0.4%)

prune201.0ms (1.2%)

localize13.0ms (0.1%)

rewrite136.0ms (0.8%)

series958.0ms (5.7%)

simplify58.0ms (0.3%)

prune147.0ms (0.9%)

localize24.0ms (0.1%)

rewrite178.0ms (1.1%)

series1.5s (9.1%)

simplify97.0ms (0.6%)

prune274.0ms (1.6%)

localize14.0ms (0.1%)

rewrite190.0ms (1.1%)

series1.1s (6.3%)

simplify102.0ms (0.6%)

prune195.0ms (1.2%)

regimes1.7s (10%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.9s (41.1%)

Profiling