Details

analyze1.9s (9.7%)

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)

sample8.2s (41.6%)

Results

6.2s	4777×	body	1024	valid
1.2s	1485×	body	512	valid
391.0ms	1422×	body	128	valid
297.0ms	557×	body	256	valid
44.0ms	15×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify80.0ms (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

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))
	1.9b	(*.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 (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))

series374.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

201.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
144.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
28.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

5.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
2.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
0.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
479×	`cancel-sign-sub-inv_binary64`
212×	`sub-neg_binary64`
168×	`fma-neg_binary64`
164×	`*-commutative_binary64`

Counts

157 → 182

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	4580
1	903	4251
2	3145	4236
3	5043	4236

prune180.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Error

0.0b

Counts

184 → 8

Alt Table

Status	Error	Program
	2.7b	(.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)))
	28.5b	(cbrt.f64 (.f64 (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (*.f64 (sin.f64 th) (sin.f64 th)) (sin.f64 th))))
	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	2.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
▶	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	1.5b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))

Compiler

Compiled 5233 to 1962 computations (62.5% saved)

localize10.0ms (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))
✓	0.2b	(*.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)))

series378.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

200.0ms

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

123.0ms

(/.f64 1 (/.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))

rewrite40.0ms (0.2%)

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:

12.0ms

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

5.0ms

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

2.0ms

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

simplify162.0ms (0.8%)

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

prune400.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	375	2	377
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	377	8	385

Error

Counts

385 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	2.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	1.5b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	28.5b	(cbrt.f64 (.f64 (/.f64 (.f64 (.f64 (sin.f64 ky) (sin.f64 ky)) (sin.f64 ky)) (.f64 (.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (*.f64 (sin.f64 th) (sin.f64 th)) (sin.f64 th))))
▶	0.4b	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky)))) (sin.f64 th))
	32.2b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))

Compiler

Compiled 10777 to 3918 computations (63.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series430.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

195.0ms	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky)))) (sin.f64 th))
122.0ms	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky))))
111.0ms	(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms	(/.f64 1 (/.f64 1 (sin.f64 ky)))

rewrite88.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

371×	`add-exp-log_binary64`
203×	`times-frac_binary64`
180×	`div-exp_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`prod-exp_binary64`

Counts

4 → 353

Calls

4 calls:

20.0ms	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky))))
15.0ms	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky)))) (sin.f64 th))
6.0ms	(/.f64 1 (/.f64 1 (sin.f64 ky)))
3.0ms	(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify214.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

528×	`cancel-sign-sub-inv_binary64`
248×	`associate-r_binary64`
237×	`fma-neg_binary64`
234×	`sub-neg_binary64`
215×	`associate-l_binary64`

Counts

449 → 503

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	426	9306
1	1041	8712
2	3839	8712
3	5034	8712

prune471.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	502	1	503
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	503	8	511

Error

Counts

511 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	2.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	1.5b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
✓	0.4b	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky)))) (sin.f64 th))
▶	0.4b	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
	32.2b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))

Compiler

Compiled 13794 to 6945 computations (49.7% saved)

localize11.0ms (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 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)))

series382.0ms (1.9%)

Counts

3 → 76

Calls

3 calls:

192.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
184.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
6.0ms	(/.f64 1 (sin.f64 ky))

rewrite55.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

439×	`times-frac_binary64`
215×	`*-un-lft-identity_binary64`
215×	`add-sqr-sqrt_binary64`
215×	`add-cube-cbrt_binary64`
31×	`div-inv_binary64`

Counts

3 → 283

Calls

3 calls:

10.0ms	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
2.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
2.0ms	(/.f64 1 (sin.f64 ky))

simplify950.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
295×	`associate-/l/_binary64`
245×	`associate-/r*_binary64`
218×	`associate-*l/_binary64`
217×	`times-frac_binary64`

Counts

359 → 400

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	434	13125
1	1195	12447
2	4080	12431
3	4993	12431
4	4971	12431

prune363.0ms (1.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	433	0	433
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	433	8	441

Error

Counts

441 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (*.f64 (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
	2.2b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	1.5b	(.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
✓	0.4b	(.f64 (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (/.f64 1 (sin.f64 ky)))) (sin.f64 th))
✓	0.4b	(/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 1 (sin.f64 ky)))
	32.2b	(*.f64 (/.f64 1 (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))) (/.f64 (sin.f64 th) (sqrt.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))

Compiler

Compiled 13028 to 4550 computations (65.1% saved)

regimes4.8s (24.1%)

Accuracy

Total 0.2b remaining (88.2%)

Threshold costs 0.2b (88.2%)

Counts

408 → 1

Compiler

Compiled 87770 to 55689 computations (36.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	10	18

end116.0ms (0.6%)

Compiler: Compiled 196 to 116 computations (40.8% saved)

Details

analyze1.9s (9.7%)

sample8.2s (41.6%)

simplify80.0ms (0.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series374.0ms (1.9%)

rewrite13.0ms (0.1%)

simplify104.0ms (0.5%)

prune180.0ms (0.9%)

localize10.0ms (0.1%)

series378.0ms (1.9%)

rewrite40.0ms (0.2%)

simplify162.0ms (0.8%)

prune400.0ms (2%)

localize13.0ms (0.1%)

series430.0ms (2.2%)

rewrite88.0ms (0.4%)

simplify214.0ms (1.1%)

prune471.0ms (2.4%)

localize11.0ms (0.1%)

series382.0ms (1.9%)

rewrite55.0ms (0.3%)

simplify950.0ms (4.8%)

prune363.0ms (1.8%)

regimes4.8s (24.1%)

simplify2.0ms (0%)

end116.0ms (0.6%)

Profiling