Details

analyze1.8s (12.2%)

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 (54.4%)

Results

6.2s	4743×	body	1024	valid
1.2s	1456×	body	512	valid
364.0ms	1457×	body	128	valid
296.0ms	584×	body	256	valid
39.0ms	16×	body	2048	valid

Compiler

Compiled 40 to 30 computations (25% saved)

preprocess38.0ms (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)

simplify44.0ms (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

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	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))
▶	3.3b	(/.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)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 ky)
✓	0.0b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(*.f64 (sin.f64 ky) (sin.f64 th))
✓	3.3b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series179.0ms (1.2%)

Counts

4 → 88

Calls

24 calls:

23.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	kx	-inf
22.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	kx	inf
22.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	ky	-inf
21.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	th	inf
20.0ms	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))	ky	inf

rewrite56.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	210	37
2	2890	37
0	10	37

Stop Event

1×	saturated
1×	node limit

Counts

4 → 101

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-def_binary64`
558×	`cancel-sign-sub-inv_binary64`
213×	`associate-/r/_binary64`
205×	`fma-neg_binary64`
181×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	2524
1	664	2364
2	2488	2125

Stop Event

1×	node limit

Counts

189 → 165

prune166.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	184	7	191
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	185	8	193

Error

Counts

193 → 8

Alt Table

Status	Error	Program
	28.3b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 2) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	27.5b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
▶	0.3b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	18.1b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (log.f64 (exp.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
	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))
	7.2b	(.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)))
	0.5b	(*.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 4370 to 1857 computations (57.5% 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))
✓	0.2b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.2b	(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series331.0ms (2.2%)

Counts

3 → 84

Calls

21 calls:

23.0ms	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))	kx	-inf
22.0ms	(*.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))	kx	-inf
22.0ms	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))	th	inf
22.0ms	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))	kx	inf
22.0ms	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))	ky	-inf

rewrite51.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

580×	`log-prod_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
186×	`log-pow_binary64`
160×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
1	239	42
2	2888	42
0	12	48

Stop Event

1×	saturated
1×	node limit

Counts

3 → 77

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

427×	`cancel-sign-sub-inv_binary64`
206×	`sub-neg_binary64`
194×	`fma-def_binary64`
176×	`fma-neg_binary64`
168×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	3062
1	741	3038
2	2884	2849

Stop Event

1×	node limit

Counts

161 → 134

prune228.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	170	7	177

Error

Counts

177 → 7

Alt Table

Status	Error	Program
	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))
	0.5b	(.f64 (sin.f64 th) (.f64 (sin.f64 ky) (pow.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) -1/2) 2)))
	28.3b	(/.f64 (pow.f64 (sqrt.f64 (*.f64 (sin.f64 ky) (sin.f64 th))) 2) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	27.5b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
▶	0.2b	(*.f64 (sin.f64 th) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
	7.2b	(.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 4686 to 2379 computations (49.2% saved)

localize11.0ms (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 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	0.2b	(*.f64 (sin.f64 th) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
✓	0.2b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series296.0ms (2%)

Counts

3 → 84

Calls

21 calls:

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

rewrite59.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

608×	`log-prod_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
191×	`log-pow_binary64`
153×	`prod-diff_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	245	44
2	3100	44
0	12	50

Stop Event

1×	saturated
1×	node limit

Counts

3 → 108

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

994×	`times-frac_binary64`
449×	`cancel-sign-sub-inv_binary64`
227×	`fma-def_binary64`
206×	`sub-neg_binary64`
160×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	231	3150
1	760	2958
2	2897	2958

Stop Event

1×	node limit

Counts

192 → 164

prune167.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	199	7	206

Error

Counts

206 → 7

Alt Table

Status	Error	Program
	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
	7.4b	(*.f64 (sin.f64 th) (/.f64 1 (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) 3)) (sin.f64 ky))))
	27.5b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
	0.7b	(*.f64 (sin.f64 th) (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 3)))
▶	0.2b	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
✓	0.2b	(*.f64 (sin.f64 th) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
	7.2b	(.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 5485 to 2568 computations (53.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series181.0ms (1.2%)

Counts

1 → 36

Calls

9 calls:

27.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))	ky	inf
26.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))	ky	-inf
26.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))	kx	inf
25.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))	th	0
24.0ms	(/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))	kx	-inf

rewrite46.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	209	18
2	2834	18
0	10	18

Stop Event

1×	saturated
1×	node limit

Counts

1 → 46

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1586
1	412	1574
2	1521	1406

Stop Event

1×	node limit

Counts

82 → 71

prune181.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	210	6	216

Error

Counts

216 → 6

Alt Table

Status	Error	Program
	27.5b	(pow.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th)))) 2)
	0.7b	(*.f64 (sin.f64 th) (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) 3)))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 th))))
✓	0.2b	(*.f64 (sin.f64 th) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
	7.2b	(.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)))
	7.3b	(/.f64 (sin.f64 th) (/.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) 3)) (sin.f64 ky)))

Compiler

Compiled 4838 to 2064 computations (57.3% saved)

regimes2.6s (17.2%)

Accuracy

Total 0.2b remaining (79.9%)

Threshold costs 0.2b (79.9%)

Counts

265 → 1

Compiler

Compiled 41075 to 28572 computations (30.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	16	18

Stop Event

1×

saturated

end105.0ms (0.7%)

Stop Event

1×

fuel

Compiler

Compiled 134 to 94 computations (29.9% saved)

Details

analyze1.8s (12.2%)

sample8.1s (54.4%)

preprocess38.0ms (0.3%)

simplify44.0ms (0.3%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series179.0ms (1.2%)

rewrite56.0ms (0.4%)

simplify55.0ms (0.4%)

prune166.0ms (1.1%)

localize10.0ms (0.1%)

series331.0ms (2.2%)

rewrite51.0ms (0.3%)

simplify64.0ms (0.4%)

prune228.0ms (1.5%)

localize11.0ms (0.1%)

series296.0ms (2%)

rewrite59.0ms (0.4%)

simplify68.0ms (0.5%)

prune167.0ms (1.1%)

localize8.0ms (0.1%)

series181.0ms (1.2%)

rewrite46.0ms (0.3%)

simplify38.0ms (0.3%)

prune181.0ms (1.2%)

regimes2.6s (17.2%)

simplify2.0ms (0%)

end105.0ms (0.7%)

Profiling