Details

analyze3.4s (15.1%)

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)

sample400.0ms (1.8%)

Algorithm

1×

intervals

Results

295.0ms	153×	body	1024	valid
45.0ms	39×	body	512	valid
19.0ms	27×	body	256	valid
14.0ms	35×	body	128	valid
7.0ms	2×	body	2048	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify100.0ms (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
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	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))

Compiler

Compiled 96 to 63 computations (34.4% saved)

localize19.0ms (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))

series667.0ms (3%)

Counts

3 → 84

Calls

3 calls:

373.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
244.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
49.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite30.0ms (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:

16.0ms	(*.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)))
1.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify194.0ms (0.9%)

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

prune324.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	174	8	182
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	175	9	184

Error

0.0b

Counts

184 → 9

Alt Table

Status	Error	Program
	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)))
	1.3b	(.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)))
	33.2b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	1.3b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
▶	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	0.9b	(.f64 (.f64 (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (/.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))) (sin.f64 th))
	4.1b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))

Compiler

Compiled 5217 to 1979 computations (62.1% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series791.0ms (3.5%)

Counts

3 → 96

Calls

3 calls:

386.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
351.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
54.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite27.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

11.0ms	(*.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))

simplify355.0ms (1.6%)

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 → 147

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

prune321.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	149	7	156

Error

Counts

156 → 7

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
	1.3b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
	0.6b	(*.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)))))
	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)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.1b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	11.0b	(*.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 4628 to 1990 computations (57% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series792.0ms (3.5%)

Counts

3 → 108

Calls

3 calls:

343.0ms

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

304.0ms

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

144.0ms

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

rewrite76.0ms (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-r_binary64`

Counts

3 → 182

Calls

3 calls:

24.0ms

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

8.0ms

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

6.0ms

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

simplify475.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

280×	`fma-neg_binary64`
261×	`times-frac_binary64`
260×	`associate-r_binary64`
245×	`associate-/l*_binary64`
228×	`associate-/r*_binary64`

Counts

290 → 334

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	8816
1	1085	7862
2	4295	7835
3	4870	7835
4	4977	7835
5	4948	7835

prune333.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	361	0	361
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	361	7	368

Error

Counts

368 → 7

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
	1.3b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
▶	0.6b	(*.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)))))
	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)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.1b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	11.0b	(*.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 10648 to 3924 computations (63.1% saved)

localize23.0ms (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 (5.2%)

Counts

4 → 120

Calls

4 calls:

415.0ms	(/.f64 (sin.f64 th) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
360.0ms	(*.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)))))
296.0ms	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
90.0ms	(sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))

rewrite85.0ms (0.4%)

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:

30.0ms	(*.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)))))
8.0ms	(/.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)))

simplify387.0ms (1.7%)

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

prune465.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	295	7	302

Error

Counts

302 → 7

Alt Table

Status	Error	Program
✓	0.4b	(*.f64 (sin.f64 ky) (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 th))))
	1.3b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (*.f64 (cbrt.f64 (sin.f64 th)) (cbrt.f64 (sin.f64 th)))) (cbrt.f64 (sin.f64 th)))
✓	0.6b	(*.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)))))
	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)))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
	4.1b	(.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))) (sin.f64 ky)) (sin.f64 th))
	11.0b	(*.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 11046 to 3693 computations (66.6% saved)

regimes2.4s (10.5%)

Accuracy

Total 0.2b remaining (86.4%)

Threshold costs 0.2b (86.4%)

Counts

138 → 1

Compiler

Compiled 23426 to 14836 computations (36.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	11	18
2	11	18

end1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

sample9.7s (43%)

Algorithm

1×

intervals

Results

7.2s	4592×	body	1024	valid
1.3s	1411×	body	512	valid
347.0ms	1431×	body	128	valid
325.0ms	553×	body	256	valid
41.0ms	13×	body	2048	valid

Compiler

Compiled 170 to 113 computations (33.5% saved)

Details

analyze3.4s (15.1%)

sample400.0ms (1.8%)

simplify100.0ms (0.4%)

prune8.0ms (0%)

localize19.0ms (0.1%)

series667.0ms (3%)

rewrite30.0ms (0.1%)

simplify194.0ms (0.9%)

prune324.0ms (1.4%)

localize18.0ms (0.1%)

series791.0ms (3.5%)

rewrite27.0ms (0.1%)

simplify355.0ms (1.6%)

prune321.0ms (1.4%)

localize25.0ms (0.1%)

series792.0ms (3.5%)

rewrite76.0ms (0.3%)

simplify475.0ms (2.1%)

prune333.0ms (1.5%)

localize23.0ms (0.1%)

series1.2s (5.2%)

rewrite85.0ms (0.4%)

simplify387.0ms (1.7%)

prune465.0ms (2.1%)

regimes2.4s (10.5%)

simplify4.0ms (0%)

end1.0ms (0%)

sample9.7s (43%)

Profiling