Details

analyze2.8s (11.1%)

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
25%	74.9%	0.1%	5
43.7%	56.2%	0.1%	6
43.7%	56.2%	0.1%	7
53%	46.8%	0.1%	8
60.8%	39%	0.1%	9
60.8%	39%	0.1%	10
64.7%	35.1%	0.1%	11
68.3%	31.6%	0.1%	12
68.3%	31.6%	0.1%	13
70%	29.8%	0.1%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample13.3s (51.6%)

Results

10.1s	4780×	body	1024	valid
1.8s	1503×	body	512	valid
594.0ms	1407×	body	128	valid
457.0ms	553×	body	256	valid
50.0ms	13×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify147.0ms (0.6%)

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
	1.8b	(*.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)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sin.f64 kx)
✓	0.1b	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
✓	0.2b	(/.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))

series654.0ms (2.5%)

Counts

4 → 88

Calls

4 calls:

341.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
233.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
76.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))
3.0ms	(sin.f64 kx)

rewrite32.0ms (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:

9.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
4.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	(sin.f64 kx)
1.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify465.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

539×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
224×	`sub-neg_binary64`
206×	`fma-def_binary64`
167×	`*-commutative_binary64`

Counts

170 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	343	4685
1	947	4356
2	3270	4356
3	4915	4352
4	4990	4352

prune421.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	189	9	198
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	191	9	200

Error

0.0b

Counts

200 → 9

Alt Table

Status	Error	Program
	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	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)))
	0.7b	(.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)))
	2.3b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	3.4b	(.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)))
	29.7b	(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))))

Compiler

Compiled 5518 to 2117 computations (61.6% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.2b	(/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
✓	0.3b	(expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series612.0ms (2.4%)

Counts

4 → 108

Calls

4 calls:

319.0ms	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
178.0ms	(/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
79.0ms	(expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
35.0ms	(log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite31.0ms (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 → 85

Calls

4 calls:

10.0ms	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
5.0ms	(/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
1.0ms	(expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	(log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

simplify237.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

308×	`sub-neg_binary64`
270×	`fma-def_binary64`
239×	`times-frac_binary64`
230×	`associate-/l*_binary64`
205×	`fma-neg_binary64`

Counts

193 → 222

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	414	5691
1	1191	5180
2	4280	5180
3	4972	5180

prune366.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	222	9	231

Error

0.0b

Counts

231 → 9

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	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)))
	0.7b	(.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)))
	2.3b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	3.4b	(.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)))
	29.7b	(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))))

Compiler

Compiled 6861 to 2597 computations (62.1% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

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

series764.0ms (3%)

Counts

3 → 96

Calls

3 calls:

382.0ms	(/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))
340.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
42.0ms	(hypot.f64 (sin.f64 kx) (sin.f64 ky))

rewrite31.0ms (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:

18.0ms	(*.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))

simplify329.0ms (1.3%)

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

prune354.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	163	9	172

Error

Counts

172 → 9

Alt Table

Status	Error	Program
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (log1p.f64 (expm1.f64 (sin.f64 kx))) (sin.f64 ky))))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (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)))
	5.1b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (log.f64 (exp.f64 (sin.f64 kx))) (sin.f64 ky))))
	3.4b	(.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 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))
	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)))
	2.3b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 4941 to 2148 computations (56.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(expm1.f64 (log1p.f64 (sin.f64 kx)))
✓	0.2b	(/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
✓	0.3b	(log1p.f64 (sin.f64 kx))
✓	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))

series979.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

356.0ms	(/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
316.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
302.0ms	(log1p.f64 (sin.f64 kx))
3.0ms	(expm1.f64 (log1p.f64 (sin.f64 kx)))

rewrite26.0ms (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-r_binary64`

Counts

4 → 85

Calls

4 calls:

15.0ms	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
3.0ms	(/.f64 (sin.f64 th) (hypot.f64 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky)))
0.0ms	(expm1.f64 (log1p.f64 (sin.f64 kx)))
0.0ms	(log1p.f64 (sin.f64 kx))

simplify188.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

857×	`fma-def_binary64`
507×	`cancel-sign-sub-inv_binary64`
252×	`fma-neg_binary64`
196×	`associate-r_binary64`
190×	`times-frac_binary64`

Counts

181 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	4720
1	861	4526
2	3234	4506
3	4996	4506
4	4981	4506

prune220.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	201	9	210

Error

Counts

210 → 9

Alt Table

Status	Error	Program
	0.3b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (log1p.f64 (expm1.f64 (sin.f64 kx))) (sin.f64 ky))))
✓	0.2b	(*.f64 (/.f64 (sin.f64 ky) (log1p.f64 (expm1.f64 (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)))
	5.1b	(*.f64 (sin.f64 ky) (/.f64 (sin.f64 th) (hypot.f64 (log.f64 (exp.f64 (sin.f64 kx))) (sin.f64 ky))))
	3.4b	(.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 (expm1.f64 (log1p.f64 (sin.f64 kx))) (sin.f64 ky))))
	1.3b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (cbrt.f64 (pow.f64 (sin.f64 kx) 3)))) (sin.f64 th))
	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)))
	2.3b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

Compiler

Compiled 5630 to 2034 computations (63.9% saved)

regimes3.5s (13.4%)

Accuracy

Total 0.2b remaining (89.1%)

Threshold costs 0.2b (89.1%)

Counts

181 → 1

Compiler

Compiled 33237 to 20139 computations (39.4% 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

end186.0ms (0.7%)

Compiler: Compiled 184 to 123 computations (33.2% saved)

Details

analyze2.8s (11.1%)

sample13.3s (51.6%)

simplify147.0ms (0.6%)

prune8.0ms (0%)

localize19.0ms (0.1%)

series654.0ms (2.5%)

rewrite32.0ms (0.1%)

simplify465.0ms (1.8%)

prune421.0ms (1.6%)

localize25.0ms (0.1%)

series612.0ms (2.4%)

rewrite31.0ms (0.1%)

simplify237.0ms (0.9%)

prune366.0ms (1.4%)

localize9.0ms (0%)

series764.0ms (3%)

rewrite31.0ms (0.1%)

simplify329.0ms (1.3%)

prune354.0ms (1.4%)

localize25.0ms (0.1%)

series979.0ms (3.8%)

rewrite26.0ms (0.1%)

simplify188.0ms (0.7%)

prune220.0ms (0.9%)

regimes3.5s (13.4%)

simplify4.0ms (0%)

end186.0ms (0.7%)

Profiling