Details

analyze1.9s (10.1%)

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)

sample8.6s (46.5%)

Results

6.5s	4699×	body	1024	valid
1.1s	1461×	body	512	valid
477.0ms	1524×	body	128	valid
286.0ms	556×	body	256	valid
40.0ms	16×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify82.0ms (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))
	5.0b	(*.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 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	0.1b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series335.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

186.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
119.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
29.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite12.0ms (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-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))

simplify98.0ms (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 → 184

Iterations

Useful iterations: 2 (0.0ms)

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

prune170.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	177	7	184
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	179	7	186

Error

Counts

186 → 7

Alt Table

Status	Error	Program
	1.2b	(*.f64 (/.f64 (sin.f64 ky) (exp.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	6.9b	(.f64 (cbrt.f64 (.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	5.8b	(.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)))
	1.1b	(.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)))
	0.8b	(.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))
▶	0.2b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	0.7b	(.f64 (.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))))) (cbrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))

Compiler

Compiled 5248 to 1968 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 (/.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))
✓	0.4b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series364.0ms (2%)

Counts

3 → 84

Calls

3 calls:

193.0ms

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

122.0ms

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

48.0ms

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

rewrite36.0ms (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:

13.0ms

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

4.0ms

(/.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))

simplify163.0ms (0.9%)

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

prune342.0ms (1.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	374	3	377
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	378	6	384

Error

Counts

384 → 6

Alt Table

Status	Error	Program
	5.8b	(.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)))
	0.8b	(.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))
	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
▶	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
	1.2b	(*.f64 (/.f64 (sin.f64 ky) (exp.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	1.1b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th)))

Compiler

Compiled 10689 to 3892 computations (63.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (expm1.f64 (log1p.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))
	0.4b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))
✓	1.1b	(log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

series1.5s (8.2%)

Counts

2 → 60

Calls

2 calls:

1.3s	(log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
185.0ms	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 31

Calls

2 calls:

3.0ms	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
0.0ms	(log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

simplify147.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

875×	`times-frac_binary64`
614×	`fma-def_binary64`
357×	`fma-neg_binary64`
323×	`cancel-sign-sub-inv_binary64`
143×	`sub-neg_binary64`

Counts

91 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	221	3177
1	610	3018
2	2151	2906
3	4989	2904
4	5175	2904

prune276.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	285	6	291

Error

Counts

291 → 6

Alt Table

Status	Error	Program
	5.8b	(.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)))
	0.8b	(.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))
▶	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
	1.2b	(*.f64 (/.f64 (sin.f64 ky) (exp.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	1.1b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th)))

Compiler

Compiled 8590 to 3705 computations (56.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (log1p.f64 (expm1.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))
✓	0.3b	(expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))
	0.4b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky)))

series322.0ms (1.7%)

Counts

2 → 60

Calls

2 calls:

194.0ms	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
127.0ms	(expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 31

Calls

2 calls:

6.0ms	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
0.0ms	(expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

983×	`times-frac_binary64`
607×	`fma-def_binary64`
326×	`cancel-sign-sub-inv_binary64`
163×	`sub-neg_binary64`
145×	`associate-r_binary64`

Counts

91 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	3212
1	628	3061
2	2313	2954
3	4989	2954

prune321.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	286	6	292

Error

Counts

292 → 6

Alt Table

Status	Error	Program
	5.8b	(.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)))
	0.8b	(.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))
✓	0.2b	(*.f64 (log1p.f64 (expm1.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
✓	0.2b	(*.f64 (expm1.f64 (log1p.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))))) (sin.f64 th))
	1.2b	(*.f64 (/.f64 (sin.f64 ky) (exp.f64 (log.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	1.1b	(.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) 1)) (.f64 (/.f64 1 (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 ky))) (sin.f64 th)))

Compiler

Compiled 8525 to 3656 computations (57.1% saved)

regimes3.5s (19.3%)

Accuracy

Total 0.2b remaining (71.6%)

Threshold costs 0.2b (71.6%)

Counts

267 → 1

Compiler

Compiled 51650 to 33674 computations (34.8% saved)

simplify2.0ms (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

end119.0ms (0.6%)

Compiler: Compiled 167 to 103 computations (38.3% saved)

Details

analyze1.9s (10.1%)

sample8.6s (46.5%)

simplify82.0ms (0.4%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series335.0ms (1.8%)

rewrite12.0ms (0.1%)

simplify98.0ms (0.5%)

prune170.0ms (0.9%)

localize10.0ms (0.1%)

series364.0ms (2%)

rewrite36.0ms (0.2%)

simplify163.0ms (0.9%)

prune342.0ms (1.9%)

localize12.0ms (0.1%)

series1.5s (8.2%)

rewrite5.0ms (0%)

simplify147.0ms (0.8%)

prune276.0ms (1.5%)

localize14.0ms (0.1%)

series322.0ms (1.7%)

rewrite8.0ms (0%)

simplify74.0ms (0.4%)

prune321.0ms (1.7%)

regimes3.5s (19.3%)

simplify2.0ms (0%)

end119.0ms (0.6%)

Profiling