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 (46.3%)

Results

6.2s	4865×	body	1024	valid
1.1s	1447×	body	512	valid
363.0ms	1414×	body	128	valid
282.0ms	514×	body	256	valid
35.0ms	16×	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)

localize11.0ms (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 (/.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)))

series358.0ms (2%)

Counts

4 → 88

Calls

4 calls:

199.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
128.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
29.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
2.0ms	(sin.f64 th)

rewrite15.0ms (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:

5.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
3.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	(sin.f64 th)
0.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify168.0ms (1%)

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 → 200

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

prune813.0ms (4.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	193	7	200
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	195	7	202

Error

0.0b

Counts

202 → 7

Alt Table

Status	Error	Program
	31.7b	(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	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (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))
	5.2b	(.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)))
	0.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	3.0b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	0.3b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

Compiler

Compiled 5449 to 2056 computations (62.3% 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 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
✓	0.1b	(/.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)))

series421.0ms (2.4%)

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))

167.0ms

(/.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))

rewrite39.0ms (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))

6.0ms

(/.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))

simplify188.0ms (1.1%)

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

prune340.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	376	1	377
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	377	7	384

Error

Counts

384 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (/.f64 (sin.f64 th) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))
	0.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.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))
	31.7b	(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))))
	5.2b	(.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)))
	3.0b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
▶	0.3b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

Compiler

Compiled 10730 to 3898 computations (63.7% 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))
✓	0.2b	(/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.2b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
✓	0.3b	(*.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

series490.0ms (2.8%)

Counts

3 → 96

Calls

3 calls:

196.0ms

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

183.0ms

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

111.0ms

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

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
27×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 95

Calls

3 calls:

9.0ms

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

6.0ms

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

2.0ms

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

simplify156.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

505×	`cancel-sign-sub-inv_binary64`
260×	`fma-neg_binary64`
258×	`associate-r_binary64`
224×	`times-frac_binary64`
221×	`associate-/l*_binary64`

Counts

191 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	324	5455
1	919	5141
2	3589	5141
3	4979	5141
4	4969	5141

prune277.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	227	7	234

Error

Counts

234 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (/.f64 (sin.f64 th) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))
▶	0.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.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))
	1.7b	(.f64 (sin.f64 ky) (.f64 (expm1.f64 (log1p.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th)))
	5.2b	(.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)))
	3.0b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

Compiler

Compiled 6634 to 3096 computations (53.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
✓	0.3b	(/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.3b	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series676.0ms (3.9%)

Counts

4 → 108

Calls

4 calls:

246.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
155.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
147.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
127.0ms	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))

rewrite57.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64`
94×	`times-frac_binary64`
67×	`*-un-lft-identity_binary64`
64×	`add-exp-log_binary64`
61×	`add-cube-cbrt_binary64`

Counts

4 → 206

Calls

4 calls:

15.0ms	(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
10.0ms	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
4.0ms	(/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
4.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify234.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

405×	`associate-r_binary64`
324×	`associate-l_binary64`
311×	`fma-def_binary64`
294×	`fma-neg_binary64`
198×	`associate-/l*_binary64`

Counts

314 → 323

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	487	10948
1	1339	9179
2	4821	9179
3	5055	9179

prune279.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	323	7	330

Error

Counts

330 → 7

Alt Table

Status	Error	Program
	0.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (/.f64 (sin.f64 th) (cbrt.f64 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))
✓	0.6b	(.f64 (.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (sqrt.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))
	1.7b	(.f64 (sin.f64 ky) (.f64 (expm1.f64 (log1p.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th)))
	5.2b	(.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)))
	3.0b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
✓	0.3b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

Compiler

Compiled 11531 to 3987 computations (65.4% saved)

regimes2.7s (15.4%)

Accuracy

Total 0.2b remaining (84.5%)

Threshold costs 0.2b (84.5%)

Counts

251 → 1

Compiler

Compiled 51310 to 30518 computations (40.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	10	18

end206.0ms (1.2%)

Compiler: Compiled 174 to 108 computations (37.9% saved)

Details

analyze1.8s (10.4%)

sample8.1s (46.3%)

simplify84.0ms (0.5%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series358.0ms (2%)

rewrite15.0ms (0.1%)

simplify168.0ms (1%)

prune813.0ms (4.6%)

localize10.0ms (0.1%)

series421.0ms (2.4%)

rewrite39.0ms (0.2%)

simplify188.0ms (1.1%)

prune340.0ms (1.9%)

localize11.0ms (0.1%)

series490.0ms (2.8%)

rewrite24.0ms (0.1%)

simplify156.0ms (0.9%)

prune277.0ms (1.6%)

localize12.0ms (0.1%)

series676.0ms (3.9%)

rewrite57.0ms (0.3%)

simplify234.0ms (1.3%)

prune279.0ms (1.6%)

regimes2.7s (15.4%)

simplify2.0ms (0%)

end206.0ms (1.2%)

Profiling