Details

analyze1.8s (12.9%)

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)

sample8.0s (58.1%)

Results

6.1s	4722×	body	1024	valid
1.2s	1481×	body	512	valid
366.0ms	1508×	body	128	valid
267.0ms	530×	body	256	valid
36.0ms	15×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify45.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

389×	`associate-l_binary64`
330×	`sqr-pow_binary64`
320×	`*-commutative_binary64`
275×	`associate-/r/_binary64`
269×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	26	18
2	51	18
3	79	18
4	160	18
5	450	18
6	1702	18
7	3048	18
8	3896	18
9	4149	18
10	4488	18
11	4978	18

Stop Event

1×	node limit

Counts

1 → 2

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

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	4.1b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	2.0b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 96 to 63 computations (34.4% 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) (sin.f64 th))
✓	2.0b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series188.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

155.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
24.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
8.0ms	(*.f64 (sin.f64 ky) (sin.f64 th))

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

373×	`prod-diff_binary64`
202×	`expm1-udef_binary64`
202×	`log1p-udef_binary64`
183×	`log-pow_binary64`
149×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	34
1	210	34
2	2913	34

Stop Event

1×	node limit

Counts

3 → 82

Calls

3 calls:

60.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
60.0ms	(*.f64 (sin.f64 ky) (sin.f64 th))
60.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
504×	`cancel-sign-sub-inv_binary64`
213×	`associate-/r/_binary64`
186×	`fma-neg_binary64`
168×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	2472
1	637	2312
2	2395	2085

Stop Event

1×	node limit

Counts

166 → 139

prune129.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	132	7	139
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	7	141

Error

Counts

141 → 7

Alt Table

Status	Error	Program
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	5.1b	(.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)))
	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	2.3b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (.f64 (sin.f64 ky) (sin.f64 th)) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (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))
	2.0b	(/.f64 (log1p.f64 (expm1.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 3504 to 1520 computations (56.6% 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))
✓	0.1b	(/.f64 (sin.f64 ky) (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))

series245.0ms (1.8%)

Counts

2 → 60

Calls

2 calls:

149.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
95.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

rewrite49.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
178×	`log-pow_binary64`
169×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	203	31
2	2623	31

Stop Event

1×	node limit

Counts

2 → 66

Calls

2 calls:

47.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
47.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
675×	`fma-def_binary64`
333×	`cancel-sign-sub-inv_binary64`
154×	`sub-neg_binary64`
131×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2390
1	592	2374
2	2243	2361

Stop Event

1×	node limit

Counts

126 → 107

prune122.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	143	6	149

Error

Counts

149 → 6

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (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))
	2.0b	(/.f64 (log1p.f64 (expm1.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	5.1b	(.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)))
▶	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

Compiler

Compiled 3893 to 1831 computations (53% 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))
✓	0.1b	(/.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)))

series202.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

154.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
48.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	209	31
2	2860	31

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

49.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
49.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

852×	`times-frac_binary64`
764×	`fma-def_binary64`
346×	`cancel-sign-sub-inv_binary64`
138×	`sub-neg_binary64`
127×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	2346
1	604	2158
2	2283	2150

Stop Event

1×	node limit

Counts

142 → 123

prune142.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	158	6	164

Error

Counts

164 → 6

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (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))
	2.0b	(/.f64 (log1p.f64 (expm1.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
▶	0.2b	(/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1))
	5.1b	(.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)))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Compiler

Compiled 4179 to 1825 computations (56.3% 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	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1)
✓	0.2b	(/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1))

series328.0ms (2.4%)

Counts

2 → 60

Calls

2 calls:

175.0ms	(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1)
153.0ms	(/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1))

rewrite66.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

602×	`log-prod_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
207×	`log-pow_binary64`
174×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	249	31
2	3204	31

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

65.0ms	(pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1)
65.0ms	(/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1))

simplify50.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

852×	`times-frac_binary64`
764×	`fma-def_binary64`
346×	`cancel-sign-sub-inv_binary64`
138×	`sub-neg_binary64`
127×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	2346
1	604	2158
2	2283	2150

Stop Event

1×	node limit

Counts

142 → 123

prune178.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	211	6	217

Error

Counts

217 → 6

Alt Table

Status	Error	Program
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 th) (sqrt.f64 (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))
	2.0b	(/.f64 (log1p.f64 (expm1.f64 (*.f64 (sin.f64 ky) (sin.f64 th)))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(/.f64 (sin.f64 th) (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) -1))
	5.1b	(.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)))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

Compiler

Compiled 5617 to 2535 computations (54.9% saved)

regimes1.8s (13.3%)

Accuracy

Total 0.2b remaining (81.7%)

Threshold costs 0.2b (81.7%)

Counts

178 → 1

Compiler

Compiled 28282 to 19629 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	11	18

Stop Event

1×

saturated

end105.0ms (0.8%)

Compiler: Compiled 131 to 85 computations (35.1% saved)

Details

analyze1.8s (12.9%)

sample8.0s (58.1%)

simplify45.0ms (0.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series188.0ms (1.4%)

rewrite61.0ms (0.4%)

simplify53.0ms (0.4%)

prune129.0ms (0.9%)

localize9.0ms (0.1%)

series245.0ms (1.8%)

rewrite49.0ms (0.4%)

simplify56.0ms (0.4%)

prune122.0ms (0.9%)

localize9.0ms (0.1%)

series202.0ms (1.5%)

rewrite51.0ms (0.4%)

simplify54.0ms (0.4%)

prune142.0ms (1%)

localize11.0ms (0.1%)

series328.0ms (2.4%)

rewrite66.0ms (0.5%)

simplify50.0ms (0.4%)

prune178.0ms (1.3%)

regimes1.8s (13.3%)

simplify2.0ms (0%)

end105.0ms (0.8%)

Profiling