Details

analyze1.9s (13.6%)

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)

sample8.3s (58.7%)

Results

6.3s	4758×	body	1024	valid
1.3s	1498×	body	512	valid
366.0ms	1455×	body	128	valid
261.0ms	530×	body	256	valid
35.0ms	15×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify84.0ms (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

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
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.7b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize8.0ms (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)))
✓	0.1b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

series318.0ms (2.2%)

Counts

3 → 84

Calls

3 calls:

170.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
124.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
23.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite89.0ms (0.6%)

Algorithm

2×	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 (sin.f64 ky) (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))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify89.0ms (0.6%)

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 → 145

Iterations

Useful iterations: 2 (0.0ms)

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

prune135.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	140	7	147

Error

Counts

147 → 7

Alt Table

Status	Error	Program
	5.3b	(.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)))
	1.3b	(.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (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)))
	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (sin.f64 th))
	4.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))

Compiler

Compiled 3883 to 1801 computations (53.6% saved)

localize8.0ms (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))
✓	0.1b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series217.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

172.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
45.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite57.0ms (0.4%)

Algorithm

2×	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 ky))
55.0ms	(/.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	10	31
1	209	31
2	2728	31
3	5176	31
0	0	0
1	0	0

simplify84.0ms (0.6%)

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

144 → 125

Iterations

Useful iterations: 3 (0.0ms)

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

prune156.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	164	7	171

Error

Counts

171 → 7

Alt Table

Status	Error	Program
	5.3b	(.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)))
	1.3b	(.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (/.f64 (sin.f64 ky) (cbrt.f64 (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)))
▶	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	0.6b	(*.f64 (/.f64 (sin.f64 ky) (pow.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (sin.f64 th))
	4.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))

Compiler

Compiled 4325 to 1880 computations (56.5% 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))
✓	0.3b	(/.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)))

series237.0ms (1.7%)

Counts

2 → 72

Calls

2 calls:

168.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
69.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))

rewrite60.0ms (0.4%)

Algorithm

2×	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:

58.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
58.0ms	(/.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
0	0	0
1	0	0

simplify69.0ms (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

prune137.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	169	7	176

Error

Counts

176 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	0.5b	(/.f64 (sin.f64 ky) (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2) (sin.f64 th)))
▶	0.4b	(/.f64 (sin.f64 ky) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th))))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	5.3b	(.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)))

Compiler

Compiled 4413 to 1862 computations (57.8% saved)

localize10.0ms (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 1 (sin.f64 th))
✓	0.3b	(/.f64 (sin.f64 ky) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th))))
✓	0.4b	(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th)))

series245.0ms (1.7%)

Counts

3 → 76

Calls

3 calls:

166.0ms	(/.f64 (sin.f64 ky) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th))))
72.0ms	(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th)))
6.0ms	(/.f64 1 (sin.f64 th))

rewrite67.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

617×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
202×	`log-pow_binary64`
162×	`prod-diff_binary64`

Counts

3 → 102

Calls

3 calls:

64.0ms	(/.f64 1 (sin.f64 th))
64.0ms	(/.f64 (sin.f64 ky) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th))))
64.0ms	(*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	245	37
2	2990	37
3	5561	37
0	0	0
1	0	0

simplify125.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
429×	`fma-neg_binary64`
382×	`cancel-sign-sub-inv_binary64`
232×	`associate-/r/_binary64`
136×	`sub-neg_binary64`

Counts

178 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2882
1	646	2512
2	2412	2262
3	4695	2262
4	4987	2262
5	4999	2262
6	4968	2262

prune140.0ms (1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	196	7	203

Error

Counts

203 → 7

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))
	0.5b	(/.f64 (sin.f64 ky) (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2) (sin.f64 th)))
✓	0.4b	(/.f64 (sin.f64 ky) (*.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (/.f64 1 (sin.f64 th))))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.8b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	5.3b	(.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)))

Compiler

Compiled 4836 to 2117 computations (56.2% saved)

regimes1.5s (10.3%)

Accuracy

Total 0.2b remaining (86.7%)

Threshold costs 0.2b (86.7%)

Counts

144 → 1

Compiler

Compiled 23869 to 16435 computations (31.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	13	22
2	13	22

end110.0ms (0.8%)

Compiler: Compiled 149 to 104 computations (30.2% saved)

Details

analyze1.9s (13.6%)

sample8.3s (58.7%)

simplify84.0ms (0.6%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series318.0ms (2.2%)

rewrite89.0ms (0.6%)

simplify89.0ms (0.6%)

prune135.0ms (1%)

localize8.0ms (0.1%)

series217.0ms (1.5%)

rewrite57.0ms (0.4%)

simplify84.0ms (0.6%)

prune156.0ms (1.1%)

localize9.0ms (0.1%)

series237.0ms (1.7%)

rewrite60.0ms (0.4%)

simplify69.0ms (0.5%)

prune137.0ms (1%)

localize10.0ms (0.1%)

series245.0ms (1.7%)

rewrite67.0ms (0.5%)

simplify125.0ms (0.9%)

prune140.0ms (1%)

regimes1.5s (10.3%)

simplify2.0ms (0%)

end110.0ms (0.8%)

Profiling