Details

analyze1.8s (12.6%)

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)

sample8.0s (56.1%)

Results

6.1s	4802×	body	1024	valid
1.1s	1438×	body	512	valid
378.0ms	1450×	body	128	valid
285.0ms	545×	body	256	valid
50.0ms	21×	body	2048	valid

Compiler

Compiled 40 to 30 computations (25% saved)

preprocess42.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

739×	`associate-/r/_binary64`
592×	`associate-*r/_binary64`
430×	`associate-l_binary64`
352×	`associate-r_binary64`
348×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	104
1	54	72
2	114	72
3	221	72
4	648	72
5	2866	72
6	4530	72
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify49.0ms (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

1.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.9b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 th))
▶	2.5b	(/.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
✓	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (sin.f64 ky) (sin.f64 th))
✓	2.5b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series201.0ms (1.4%)

Counts

3 → 84

Calls

21 calls:

25.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	kx	-inf
25.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	ky	-inf
25.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	kx	inf
24.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	th	-inf
22.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	ky	inf

rewrite50.0ms (0.3%)

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

simplify52.0ms (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

prune127.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	8	139
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	132	9	141

Error

0.0b

Counts

141 → 9

Alt Table

Status	Error	Program
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
	0.3b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	0.5b	(*.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)))))
	32.6b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))) 1)
	0.2b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	2.6b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
	3.9b	(*.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	(pow.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	2.6b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 3558 to 1566 computations (56% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))
✓	0.2b	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))

series254.0ms (1.8%)

Counts

2 → 72

Calls

18 calls:

27.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))	kx	-inf
25.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))	kx	inf
25.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))	ky	inf
24.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))	ky	-inf
24.0ms	(/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))	th	-inf

rewrite52.0ms (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

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2827
1	642	2459
2	2481	2219

Stop Event

1×	node limit

Counts

154 → 131

prune167.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	167	8	175

Error

Counts

175 → 8

Alt Table

Status	Error	Program
	2.6b	(pow.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (*.f64 (sin.f64 ky) (sin.f64 th))) -1)
	1.4b	(pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (.f64 (cbrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) 1)
	2.6b	(pow.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th)))) 1)
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
	1.3b	(pow.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 3)
✓	0.2b	(pow.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	0.5b	(*.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)))))
	2.6b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

Compiler

Compiled 4771 to 2248 computations (52.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.2b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series321.0ms (2.2%)

Counts

2 → 72

Calls

18 calls:

25.0ms	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))	kx	-inf
25.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	ky	inf
24.0ms	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))	kx	inf
24.0ms	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))	th	-inf
24.0ms	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))	ky	inf

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

549×	`log-prod_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
184×	`log-pow_binary64`
176×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	249	31
2	2890	31

Stop Event

1×	node limit

Counts

2 → 84

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
411×	`cancel-sign-sub-inv_binary64`
368×	`associate-/r/_binary64`
177×	`fma-neg_binary64`
174×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	192	2908
1	628	2884
2	2493	2627

Stop Event

1×	node limit

Counts

156 → 133

prune157.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	169	7	176

Error

Counts

176 → 7

Alt Table

Status	Error	Program
	29.5b	(*.f64 (/.f64 (sin.f64 ky) 1) (pow.f64 (sqrt.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2))
	2.6b	(pow.f64 (*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (/.f64 1 (sin.f64 th)))) 1)
	0.4b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
	1.4b	(pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (.f64 (cbrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) 1)
▶	0.3b	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
✓	0.2b	(pow.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	0.5b	(*.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)))))

Compiler

Compiled 4690 to 2246 computations (52.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.1b	(/.f64 1 (sin.f64 ky))
	0.2b	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))

series172.0ms (1.2%)

Counts

2 → 40

Calls

12 calls:

26.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))	kx	-inf
24.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))	th	-inf
23.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))	kx	inf
23.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))	ky	inf
23.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))	ky	-inf

rewrite50.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
207×	`log-pow_binary64`
168×	`prod-diff_binary64`
164×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	250	24
2	3309	24

Stop Event

1×	node limit

Counts

2 → 66

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
471×	`associate-/l*_binary64`
470×	`fma-def_binary64`
407×	`associate-/r*_binary64`
230×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1641
1	435	1627
2	1588	1455

Stop Event

1×	node limit

Counts

106 → 98

prune167.0ms (1.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	193	7	200

Error

Counts

200 → 7

Alt Table

Status	Error	Program
	29.5b	(*.f64 (/.f64 (sin.f64 ky) 1) (pow.f64 (sqrt.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) 2))
	0.4b	(*.f64 (/.f64 (sin.f64 ky) 1) (/.f64 (sin.f64 th) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))))
	1.4b	(pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 ky)) 2) (.f64 (cbrt.f64 (sin.f64 ky)) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) 1)
	0.3b	(.f64 (sin.f64 th) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky)))
✓	0.3b	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
✓	0.2b	(pow.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))) 1)
	0.5b	(*.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)))))

Compiler

Compiled 5106 to 2386 computations (53.3% saved)

regimes2.2s (15.5%)

Accuracy

Total 0.2b remaining (83.5%)

Threshold costs 0.2b (83.5%)

Counts

195 → 1

Compiler

Compiled 32048 to 22368 computations (30.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	18	18

Stop Event

1×

saturated

end130.0ms (0.9%)

Stop Event

1×

fuel

Compiler

Compiled 158 to 104 computations (34.2% saved)

Details

analyze1.8s (12.6%)

sample8.0s (56.1%)

preprocess42.0ms (0.3%)

simplify49.0ms (0.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series201.0ms (1.4%)

rewrite50.0ms (0.3%)

simplify52.0ms (0.4%)

prune127.0ms (0.9%)

localize11.0ms (0.1%)

series254.0ms (1.8%)

rewrite52.0ms (0.4%)

simplify69.0ms (0.5%)

prune167.0ms (1.2%)

localize10.0ms (0.1%)

series321.0ms (2.2%)

rewrite52.0ms (0.4%)

simplify66.0ms (0.5%)

prune157.0ms (1.1%)

localize10.0ms (0.1%)

series172.0ms (1.2%)

rewrite50.0ms (0.4%)

simplify38.0ms (0.3%)

prune167.0ms (1.2%)

regimes2.2s (15.5%)

simplify2.0ms (0%)

end130.0ms (0.9%)

Profiling