Details

analyze2.0s (11.7%)

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 (48.3%)

Results

6.3s	4819×	body	1024	valid
1.1s	1422×	body	512	valid
418.0ms	1446×	body	128	valid
278.0ms	556×	body	256	valid
30.0ms	13×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify82.0ms (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
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	3.8b	(*.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)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 th)
✓	0.0b	(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))

series298.0ms (1.7%)

Counts

4 → 88

Calls

4 calls:

172.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
101.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
24.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
1.0ms	(sin.f64 th)

rewrite95.0ms (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

4 → 111

Calls

4 calls:

91.0ms	(sin.f64 th)
91.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
91.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
91.0ms	(*.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	42
1	203	42
2	2514	42
3	4923	42
4	5348	42

simplify94.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

907×	`fma-def_binary64`
531×	`cancel-sign-sub-inv_binary64`
272×	`fma-neg_binary64`
218×	`sub-neg_binary64`
153×	`distribute-rgt-neg-in_binary64`

Counts

199 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	241	2996
1	748	2852
2	2760	2831
3	4955	2829
4	5023	2829

prune173.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	163	9	172
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	9	174

Error

Counts

174 → 9

Alt Table

Status	Error	Program
	24.4b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 th))) (cbrt.f64 (exp.f64 (sin.f64 th))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 th))))))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2)) (sin.f64 th))
	3.7b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	6.3b	(.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)))
▶	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.8b	(.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))
	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (expm1.f64 (log1p.f64 (sin.f64 th))))
	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

Compiler

Compiled 4642 to 2111 computations (54.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (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 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
✓	1.0b	(log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series1.4s (7.9%)

Counts

3 → 84

Calls

3 calls:

1.1s

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

168.0ms

(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

104.0ms

(expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

551×	`log-prod_binary64`
314×	`prod-diff_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
192×	`log-pow_binary64`

Counts

3 → 96

Calls

3 calls:

59.0ms

(expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

59.0ms

(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

59.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	220	46
2	2640	46
3	5198	46

simplify93.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

861×	`fma-def_binary64`
426×	`cancel-sign-sub-inv_binary64`
366×	`fma-neg_binary64`
287×	`neg-mul-1_binary64`
211×	`sub-neg_binary64`

Counts

180 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	3153
1	700	3115
2	2526	2890
3	4666	2889
4	5069	2889

prune188.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	205	9	214

Error

Counts

214 → 9

Alt Table

Status	Error	Program
	24.4b	(.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (sin.f64 th))) (cbrt.f64 (exp.f64 (sin.f64 th))))) (log.f64 (cbrt.f64 (exp.f64 (sin.f64 th))))))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2)) (sin.f64 th))
	3.7b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	6.3b	(.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)))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.8b	(.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))
▶	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (expm1.f64 (log1p.f64 (sin.f64 th))))
	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

Compiler

Compiled 5736 to 2678 computations (53.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 th)
	0.0b	(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)))

series215.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

172.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
43.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite56.0ms (0.3%)

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 → 82

Calls

2 calls:

54.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
54.0ms	(/.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

simplify79.0ms (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

142 → 123

Iterations

Useful iterations: 3 (0.0ms)

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

prune179.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	192	8	200

Error

Counts

200 → 8

Alt Table

Status	Error	Program
	3.7b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	6.3b	(.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)))
	0.8b	(.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))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (expm1.f64 (log1p.f64 (sin.f64 th))))
	3.9b	(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 ky))))
	32.7b	(/.f64 (sin.f64 th) (pow.f64 (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 2))
▶	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

Compiler

Compiled 4900 to 2100 computations (57.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sin.f64 th)
	0.0b	(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)))

series243.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

174.0ms	(/.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))

rewrite59.0ms (0.3%)

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 → 82

Calls

2 calls:

57.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
57.0ms	(/.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

simplify66.0ms (0.4%)

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

154 → 128

Iterations

Useful iterations: 2 (0.0ms)

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

prune173.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	196	8	204

Error

Counts

204 → 8

Alt Table

Status	Error	Program
	3.7b	(/.f64 (/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (pow.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 2)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	6.3b	(.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)))
	0.8b	(.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))
✓	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
	0.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (expm1.f64 (log1p.f64 (sin.f64 th))))
	3.9b	(/.f64 (sin.f64 th) (*.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (/.f64 1 (sin.f64 ky))))
	32.7b	(/.f64 (sin.f64 th) (pow.f64 (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 2))
✓	0.3b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

Compiler

Compiled 4879 to 2034 computations (58.3% saved)

regimes3.2s (18.6%)

Accuracy

Total 0.2b remaining (86.1%)

Threshold costs 0.2b (86.1%)

Counts

251 → 1

Compiler

Compiled 41665 to 28120 computations (32.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	21	22
2	30	22
3	39	22
4	44	22
5	47	22
6	48	22
7	48	22

end126.0ms (0.7%)

Compiler: Compiled 189 to 126 computations (33.3% saved)

Details

analyze2.0s (11.7%)

sample8.3s (48.3%)

simplify82.0ms (0.5%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series298.0ms (1.7%)

rewrite95.0ms (0.6%)

simplify94.0ms (0.5%)

prune173.0ms (1%)

localize13.0ms (0.1%)

series1.4s (7.9%)

rewrite61.0ms (0.4%)

simplify93.0ms (0.5%)

prune188.0ms (1.1%)

localize9.0ms (0.1%)

series215.0ms (1.3%)

rewrite56.0ms (0.3%)

simplify79.0ms (0.5%)

prune179.0ms (1%)

localize10.0ms (0.1%)

series243.0ms (1.4%)

rewrite59.0ms (0.3%)

simplify66.0ms (0.4%)

prune173.0ms (1%)

regimes3.2s (18.6%)

simplify3.0ms (0%)

end126.0ms (0.7%)

Profiling