Details

analyze1.9s (13.5%)

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 20 to 15 computations (25% saved)

sample8.2s (58.9%)

Results

6.2s	4769×	body	1024	valid
1.2s	1486×	body	512	valid
362.0ms	1425×	body	128	valid
321.0ms	562×	body	256	valid
32.0ms	14×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

645×	`associate-/r*_binary64`
634×	`sqr-pow_binary64`
394×	`associate-l_binary64`
373×	`cube-prod_binary64`
368×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	26	18
2	40	18
3	68	18
4	141	18
5	348	18
6	1055	18
7	1796	18
8	2484	18
9	2697	18
10	2968	18
11	3311	18
12	3705	18
13	4603	18
14	4799	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Compiler

Compiled 58 to 35 computations (39.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	0.2b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series286.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

160.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
103.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
23.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite86.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
330×	`prod-diff_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
180×	`pow3_binary64`

Counts

3 → 91

Calls

3 calls:

84.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
84.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
84.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	203	39
2	2514	39
3	4923	39
4	5348	39

simplify91.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

852×	`fma-def_binary64`
469×	`cancel-sign-sub-inv_binary64`
357×	`fma-neg_binary64`
281×	`neg-mul-1_binary64`
205×	`sub-neg_binary64`

Counts

175 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	2944
1	720	2800
2	2663	2590
3	4579	2590
4	4978	2590

prune143.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	8	148
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Error

Counts

149 → 8

Alt Table

Status	Error	Program
	2.5b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.5b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	2.4b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))))
▶	0.2b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	24.9b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) 3))
	9.5b	(*.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3)) (sin.f64 th))
	1.4b	(pow.f64 (cbrt.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) 3)
	0.2b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))

Compiler

Compiled 3971 to 1841 computations (53.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

series219.0ms (1.6%)

Counts

2 → 72

Calls

2 calls:

154.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
64.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`log-prod_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
183×	`log-pow_binary64`
171×	`prod-diff_binary64`

Counts

2 → 84

Calls

2 calls:

55.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
55.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	209	31
2	2728	31
3	5176	31

simplify67.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

929×	`associate-/l*_binary64`
770×	`fma-def_binary64`
382×	`cancel-sign-sub-inv_binary64`
232×	`associate-/r/_binary64`
138×	`fma-neg_binary64`

Counts

156 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2827
1	621	2459
2	2348	2219
3	5753	2219

prune136.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	170	7	177

Error

Counts

177 → 7

Alt Table

Status	Error	Program
	0.2b	(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (sin.f64 th)))
	0.3b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))))
	2.5b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.3b	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th))))
	17.8b	(/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)) 3)))
▶	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.2b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))

Compiler

Compiled 4459 to 1881 computations (57.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.2b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series355.0ms (2.5%)

Counts

2 → 72

Calls

2 calls:

207.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
147.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite79.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
330×	`prod-diff_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
180×	`pow3_binary64`

Counts

2 → 67

Calls

2 calls:

78.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
78.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	203	31
2	2512	31
3	4919	31
4	5344	31

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
411×	`cancel-sign-sub-inv_binary64`
368×	`associate-/r/_binary64`
177×	`fma-neg_binary64`
174×	`times-frac_binary64`

Counts

139 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2908
1	607	2884
2	2353	2627
3	4992	2627

prune133.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	153	7	160

Error

Counts

160 → 7

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (sin.f64 th)))
	0.3b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))))
	2.5b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.3b	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th))))
	17.8b	(/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)) 3)))
✓	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.2b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))

Compiler

Compiled 4236 to 1952 computations (53.9% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (sin.f64 th)))
✓	0.2b	(/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series263.0ms (1.9%)

Counts

2 → 60

Calls

2 calls:

155.0ms	(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (sin.f64 th)))
108.0ms	(/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite87.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`log-prod_binary64`
333×	`prod-diff_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`
179×	`log-pow_binary64`

Counts

2 → 74

Calls

2 calls:

85.0ms	(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (sin.f64 th)))
85.0ms	(/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	249	31
2	2638	31
3	4880	31
4	5269	31

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

893×	`times-frac_binary64`
715×	`fma-def_binary64`
455×	`fma-neg_binary64`
303×	`cancel-sign-sub-inv_binary64`
170×	`sub-neg_binary64`

Counts

134 → 116

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	2422
1	581	2406
2	2120	2395
3	4953	2393
4	5210	2393

prune110.0ms (0.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	155	7	162

Error

Counts

162 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (neg.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (neg.f64 (sin.f64 th)))
	0.3b	(log1p.f64 (expm1.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))))
	2.5b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.3b	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th))))
	17.8b	(/.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)) 3)))
✓	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.2b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))

Compiler

Compiled 4166 to 1876 computations (55% saved)

regimes1.4s (9.7%)

Accuracy

Total 0.2b remaining (86.5%)

Threshold costs 0.2b (86.5%)

Counts

127 → 1

Compiler

Compiled 20742 to 14127 computations (31.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	10	18

end109.0ms (0.8%)

Compiler: Compiled 147 to 96 computations (34.7% saved)

Details

analyze1.9s (13.5%)

sample8.2s (58.9%)

simplify80.0ms (0.6%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series286.0ms (2.1%)

rewrite86.0ms (0.6%)

simplify91.0ms (0.7%)

prune143.0ms (1%)

localize10.0ms (0.1%)

series219.0ms (1.6%)

rewrite57.0ms (0.4%)

simplify67.0ms (0.5%)

prune136.0ms (1%)

localize9.0ms (0.1%)

series355.0ms (2.5%)

rewrite79.0ms (0.6%)

simplify73.0ms (0.5%)

prune133.0ms (1%)

localize11.0ms (0.1%)

series263.0ms (1.9%)

rewrite87.0ms (0.6%)

simplify87.0ms (0.6%)

prune110.0ms (0.8%)

regimes1.4s (9.7%)

simplify2.0ms (0%)

end109.0ms (0.8%)

Profiling