Details

analyze1.8s (7.1%)

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)

sample8.8s (34.9%)

Results

6.6s	4781×	body	1024	valid
1.2s	1394×	body	512	valid
487.0ms	1506×	body	128	valid
326.0ms	557×	body	256	valid
40.0ms	18×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify95.0ms (0.4%)

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

prune8.0ms (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
	6.1b	(*.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	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series702.0ms (2.8%)

Counts

4 → 88

Calls

4 calls:

387.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
249.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
62.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
3.0ms	(sin.f64 th)

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
19×	`times-frac_binary64`
13×	`associate-l_binary64`

Counts

4 → 82

Calls

4 calls:

11.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
5.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms	(sin.f64 th)
1.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify303.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

541×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
225×	`sub-neg_binary64`
206×	`fma-def_binary64`
167×	`*-commutative_binary64`

Counts

170 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	335	4692
1	934	4356
2	3244	4356
3	4863	4352
4	4998	4352
5	4955	4352

prune349.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	192	6	198
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	194	6	200

Error

Counts

200 → 6

Alt Table

Status	Error	Program
	0.8b	(.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	8.0b	(.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)))
	23.4b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	2.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
▶	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))

Compiler

Compiled 5444 to 2016 computations (63% saved)

localize20.0ms (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 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))
✓	0.1b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
✓	0.2b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series720.0ms (2.9%)

Counts

3 → 84

Calls

3 calls:

384.0ms

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

234.0ms

(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

102.0ms

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

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
103×	`add-sqr-sqrt_binary64`
91×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

3 → 181

Calls

3 calls:

22.0ms

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

9.0ms

(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

5.0ms

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

simplify334.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

453×	`cancel-sign-sub-inv_binary64`
248×	`associate-r_binary64`
232×	`fma-def_binary64`
219×	`sub-neg_binary64`
198×	`*-commutative_binary64`

Counts

265 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	369	7761
1	1001	7004
2	3670	6977
3	4959	6977

prune700.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	375	2	377
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	377	6	383

Error

Counts

383 → 6

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	0.8b	(.f64 (/.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (/.f64 (cbrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (cbrt.f64 (sin.f64 ky)))) (sin.f64 th))
	8.0b	(.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)))
	23.4b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
▶	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	1.2b	(.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))

Compiler

Compiled 10714 to 3871 computations (63.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series778.0ms (3.1%)

Counts

3 → 96

Calls

3 calls:

377.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
349.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
51.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 73

Calls

3 calls:

10.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
5.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
1.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

simplify313.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

555×	`cancel-sign-sub-inv_binary64`
257×	`fma-neg_binary64`
228×	`times-frac_binary64`
214×	`sub-neg_binary64`
201×	`associate-r_binary64`

Counts

169 → 149

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	326	5096
1	920	4768
2	3574	4768
3	4914	4768
4	4986	4768
5	5000	4768
6	4959	4768

prune287.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	165	6	171

Error

Counts

171 → 6

Alt Table

Status	Error	Program
	23.4b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
▶	0.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
	8.0b	(.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)))
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	1.2b	(.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))

Compiler

Compiled 4953 to 2052 computations (58.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
✓	0.3b	(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	0.3b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
✓	0.3b	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))

series1.2s (4.7%)

Counts

4 → 120

Calls

4 calls:

426.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
374.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
293.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
89.0ms	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

rewrite85.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
61×	`*-un-lft-identity_binary64`
61×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`

Counts

4 → 172

Calls

4 calls:

32.0ms	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
7.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
7.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
2.0ms	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

simplify412.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

386×	`fma-neg_binary64`
381×	`associate-r_binary64`
341×	`fma-def_binary64`
279×	`associate-l_binary64`
200×	`associate-*l/_binary64`

Counts

292 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	492	10360
1	1402	9508
2	4952	9506
3	5271	9506

prune519.0ms (2.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	295	6	301

Error

Counts

301 → 6

Alt Table

Status	Error	Program
	23.4b	(cbrt.f64 (.f64 (.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)) (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))) (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
✓	0.4b	(*.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
	8.0b	(.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)))
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	1.2b	(.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (/.f64 (sin.f64 ky) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))

Compiler

Compiled 11056 to 3680 computations (66.7% saved)

regimes7.4s (29.3%)

Accuracy

Total 0.2b remaining (83.8%)

Threshold costs 0.2b (83.8%)

Counts

365 → 1

Compiler

Compiled 77137 to 44710 computations (42% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	16	18
2	15	18

end203.0ms (0.8%)

Compiler: Compiled 171 to 91 computations (46.8% saved)

Details

analyze1.8s (7.1%)

sample8.8s (34.9%)

simplify95.0ms (0.4%)

prune8.0ms (0%)

localize18.0ms (0.1%)

series702.0ms (2.8%)

rewrite27.0ms (0.1%)

simplify303.0ms (1.2%)

prune349.0ms (1.4%)

localize20.0ms (0.1%)

series720.0ms (2.9%)

rewrite75.0ms (0.3%)

simplify334.0ms (1.3%)

prune700.0ms (2.8%)

localize19.0ms (0.1%)

series778.0ms (3.1%)

rewrite27.0ms (0.1%)

simplify313.0ms (1.2%)

prune287.0ms (1.1%)

localize24.0ms (0.1%)

series1.2s (4.7%)

rewrite85.0ms (0.3%)

simplify412.0ms (1.6%)

prune519.0ms (2.1%)

regimes7.4s (29.3%)

simplify5.0ms (0%)

end203.0ms (0.8%)

Profiling