Details

analyze1.8s (9%)

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)

sample9.2s (46.6%)

Results

7.1s	4752×	body	1024	valid
1.2s	1479×	body	512	valid
401.0ms	1467×	body	128	valid
284.0ms	545×	body	256	valid
32.0ms	13×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify98.0ms (0.5%)

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

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.7b	(*.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	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series344.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

194.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
122.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
27.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite251.0ms (1.3%)

Algorithm

3×	egg-rewrite

Rules

48×	`egg`
43×	`egg`
35×	`egg`

Counts

3 → 126

Calls

3 calls:

88.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
83.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
78.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	143	13
2	1760	13
3	4946	13
4	5000	13
0	10	18
1	203	18
2	2514	18
3	4923	18
4	5348	18
0	6	8
1	117	8
2	1305	8
3	4985	8
4	5633	8

simplify108.0ms (0.5%)

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

210 → 182

Iterations

Useful iterations: 2 (0.0ms)

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

prune353.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Error

0.0b

Counts

184 → 8

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2) (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
▶	0.2b	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	5.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	31.2b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.7b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

Compiler

Compiled 4713 to 2034 computations (56.8% 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))
✓	0.1b	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	0.2b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series206.0ms (1%)

Counts

1 → 36

Calls

1 calls:

205.0ms

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

rewrite93.0ms (0.5%)

Algorithm

1×	egg-rewrite

Rules

47× egg

Counts

1 → 47

Calls

1 calls:

92.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	203	18
2	2512	18
3	4919	18
4	5344	18

simplify88.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
471×	`associate-/l*_binary64`
445×	`fma-neg_binary64`
434×	`fma-def_binary64`
411×	`associate-/r*_binary64`

Counts

83 → 72

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1586
1	393	1574
2	1426	1406
3	4909	1406
4	5222	1406

prune312.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	181	8	189

Error

0.0b

Counts

189 → 8

Alt Table

Status	Error	Program
	0.7b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2) (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
✓	0.2b	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	5.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	31.2b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
▶	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.7b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

Compiler

Compiled 4679 to 2022 computations (56.8% saved)

localize10.0ms (0%)

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 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
✓	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

series344.0ms (1.7%)

Counts

2 → 60

Calls

2 calls:

243.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
100.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite143.0ms (0.7%)

Algorithm

2×	egg-rewrite

Rules

58×	`egg`
43×	`egg`

Counts

2 → 101

Calls

2 calls:

82.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
59.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	143	13
2	1760	13
3	4946	13
4	5000	13
0	10	18
1	209	18
2	2728	18
3	5176	18

simplify99.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

852×	`times-frac_binary64`
776×	`fma-def_binary64`
346×	`cancel-sign-sub-inv_binary64`
322×	`fma-neg_binary64`
138×	`sub-neg_binary64`

Counts

161 → 142

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	2346
1	585	2158
2	2154	2148
3	4982	2146
4	5141	2146

prune206.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	189	3	192
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	192	8	200

Error

Counts

200 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	5.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	0.7b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2) (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.7b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.7b	(/.f64 (sin.f64 th) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2)) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
▶	0.2b	(expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
	9.3b	(/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) 3)))

Compiler

Compiled 4964 to 2090 computations (57.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.1b	(log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

series2.8s (14.1%)

Counts

1 → 36

Calls

1 calls:

2.8s	(log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

rewrite95.0ms (0.5%)

Algorithm

1×	egg-rewrite

Rules

16× egg

Counts

1 → 16

Calls

1 calls:

95.0ms

(log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	227	20
2	2906	20
3	4892	20
4	5403	20

simplify144.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-def_binary64`
278×	`cancel-sign-sub-inv_binary64`
244×	`fma-neg_binary64`
202×	`unswap-sqr_binary64`
152×	`times-frac_binary64`

Counts

52 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1952
1	537	1944
2	2364	1829
3	4862	1825
4	4979	1825
5	5000	1825
6	4980	1825

prune270.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	234	8	242

Error

Counts

242 → 8

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	5.4b	(.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (.f64 (sin.f64 th) (sin.f64 ky)))
	0.7b	(.f64 (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2) (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.7b	(.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.7b	(/.f64 (sin.f64 th) (*.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2) (pow.f64 (cbrt.f64 (sin.f64 ky)) 2)) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
✓	0.2b	(expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))))
	9.3b	(/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) 3)))

Compiler

Compiled 7044 to 3388 computations (51.9% saved)

regimes2.6s (13.3%)

Accuracy

Total 0.2b remaining (86.8%)

Threshold costs 0.2b (86.8%)

Counts

262 → 1

Compiler

Compiled 44264 to 29519 computations (33.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	21	22
2	31	22
3	39	22
4	44	22
5	47	22
6	48	22
7	48	22

end135.0ms (0.7%)

Compiler: Compiled 203 to 130 computations (36% saved)

Details

analyze1.8s (9%)

sample9.2s (46.6%)

simplify98.0ms (0.5%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series344.0ms (1.7%)

rewrite251.0ms (1.3%)

simplify108.0ms (0.5%)

prune353.0ms (1.8%)

localize10.0ms (0.1%)

series206.0ms (1%)

rewrite93.0ms (0.5%)

simplify88.0ms (0.4%)

prune312.0ms (1.6%)

localize10.0ms (0%)

series344.0ms (1.7%)

rewrite143.0ms (0.7%)

simplify99.0ms (0.5%)

prune206.0ms (1%)

localize11.0ms (0.1%)

series2.8s (14.1%)

rewrite95.0ms (0.5%)

simplify144.0ms (0.7%)

prune270.0ms (1.4%)

regimes2.6s (13.3%)

simplify3.0ms (0%)

end135.0ms (0.7%)

Profiling