Details

analyze1.8s (10.4%)

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)

sample8.1s (46.1%)

Results

6.1s	4752×	body	1024	valid
1.2s	1479×	body	512	valid
403.0ms	1467×	body	128	valid
269.0ms	545×	body	256	valid
32.0ms	13×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify84.0ms (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))
	3.7b	(*.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)

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 (/.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)))

series366.0ms (2.1%)

Counts

3 → 84

Calls

3 calls:

203.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
132.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
30.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite92.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

88× egg-rr

Counts

3 → 88

Calls

2 calls:

90.0ms	((/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.0ms	()

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

simplify139.0ms (0.8%)

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

172 → 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

prune147.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Error

0.0b

Counts

147 → 8

Alt Table

Status	Error	Program
	23.3b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3) (pow.f64 (sin.f64 th) 3)))
▶	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))
	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)))
	2.6b	(/.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))))
	3.4b	(/.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))))
	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	0.3b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))

Compiler

Compiled 3976 to 1865 computations (53.1% 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 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))

series341.0ms (1.9%)

Counts

2 → 60

Calls

2 calls:

286.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
54.0ms	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))

rewrite62.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

82× egg-rr

Counts

2 → 82

Calls

2 calls:

60.0ms	((/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
0.0ms	()

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

simplify88.0ms (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

prune175.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	161	8	169

Error

Counts

169 → 8

Alt Table

Status	Error	Program
	23.3b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3) (pow.f64 (sin.f64 th) 3)))
	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))
	9.3b	(/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) 3)))
	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)))))
	0.3b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))
	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)))
	3.7b	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
▶	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

Compiler

Compiled 4402 to 1952 computations (55.7% saved)

localize12.0ms (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 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	0.1b	(log1p.f64 (*.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)))

series2.3s (13%)

Counts

1 → 36

Calls

1 calls:

2.3s	(log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

rewrite53.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

21× egg-rr

Counts

1 → 21

Calls

2 calls:

52.0ms	((log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	221	20
2	2692	20
3	5490	20
0	0	0
1	0	0

simplify114.0ms (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

57 → 45

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

prune824.0ms (4.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	190	8	198

Error

Counts

198 → 8

Alt Table

Status	Error	Program
	23.3b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3) (pow.f64 (sin.f64 th) 3)))
	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))
	9.3b	(/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) 3)))
	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)))))
▶	0.3b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))
	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)))
	3.7b	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
✓	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

Compiler

Compiled 6254 to 3219 computations (48.5% saved)

localize12.0ms (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 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))
	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	0.2b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1)

series391.0ms (2.2%)

Counts

2 → 60

Calls

2 calls:

242.0ms	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))
148.0ms	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1)

rewrite70.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

64× egg-rr

Counts

2 → 64

Calls

2 calls:

68.0ms	((pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	243	31
2	2826	31
3	5135	31
0	0	0
1	0	0

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

892×	`times-frac_binary64`
687×	`fma-def_binary64`
356×	`fma-neg_binary64`
333×	`cancel-sign-sub-inv_binary64`
154×	`sub-neg_binary64`

Counts

124 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	2390
1	571	2374
2	2102	2359
3	4993	2357
4	5183	2357

prune182.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	195	8	203

Error

Counts

203 → 8

Alt Table

Status	Error	Program
	23.3b	(cbrt.f64 (*.f64 (pow.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 3) (pow.f64 (sin.f64 th) 3)))
	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))
	9.3b	(/.f64 (sin.f64 th) (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) 3)))
	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)))))
✓	0.3b	(*.f64 (pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)) -1) (sin.f64 th))
	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)))
	3.7b	(/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))) (sin.f64 ky)))
✓	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

Compiler

Compiled 5380 to 2526 computations (53% saved)

regimes1.9s (11%)

Accuracy

Total 0.2b remaining (81.6%)

Threshold costs 0.2b (81.6%)

Counts

177 → 1

Compiler

Compiled 28864 to 19747 computations (31.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	15	18
2	14	18

end150.0ms (0.9%)

Compiler: Compiled 196 to 132 computations (32.7% saved)

Details

analyze1.8s (10.4%)

sample8.1s (46.1%)

simplify84.0ms (0.5%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series366.0ms (2.1%)

rewrite92.0ms (0.5%)

simplify139.0ms (0.8%)

prune147.0ms (0.8%)

localize9.0ms (0.1%)

series341.0ms (1.9%)

rewrite62.0ms (0.4%)

simplify88.0ms (0.5%)

prune175.0ms (1%)

localize12.0ms (0.1%)

series2.3s (13%)

rewrite53.0ms (0.3%)

simplify114.0ms (0.7%)

prune824.0ms (4.7%)

localize12.0ms (0.1%)

series391.0ms (2.2%)

rewrite70.0ms (0.4%)

simplify91.0ms (0.5%)

prune182.0ms (1%)

regimes1.9s (11%)

simplify2.0ms (0%)

end150.0ms (0.9%)

Profiling