Details

analyze1.8s (7.6%)

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 (37%)

Results

6.7s	4752×	body	1024	valid
1.1s	1479×	body	512	valid
348.0ms	1467×	body	128	valid
271.0ms	545×	body	256	valid
36.0ms	13×	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
	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))
▶	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)

localize9.0ms (0%)

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))
✓	0.2b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series379.0ms (1.6%)

Counts

3 → 84

Calls

3 calls:

219.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
132.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
28.0ms	(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))

simplify100.0ms (0.4%)

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

prune183.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	175	9	184
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	9	186

Error

0.0b

Counts

186 → 9

Alt Table

Status	Error	Program
	33.0b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	2.4b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	5.4b	(.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)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	0.3b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)) (sin.f64 ky))) (sin.f64 th))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	31.2b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
▶	0.2b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))))

Compiler

Compiled 5212 to 1992 computations (61.8% saved)

localize12.0ms (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 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
✓	0.1b	(log1p.f64 (*.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)))

series2.5s (10.6%)

Counts

1 → 36

Calls

1 calls:

2.5s	(log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
278×	`cancel-sign-sub-inv_binary64`
244×	`fma-neg_binary64`
202×	`unswap-sqr_binary64`
152×	`times-frac_binary64`

Counts

47 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	2233
1	555	2182
2	2389	2067
3	4889	2063
4	4984	2063
5	4977	2063

prune232.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	228	8	236

Error

0.0b

Counts

236 → 8

Alt Table

Status	Error	Program
	33.0b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	2.4b	(/.f64 (*.f64 (sin.f64 ky) (sin.f64 th)) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
	5.4b	(.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)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	31.2b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
▶	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))

Compiler

Compiled 7473 to 3339 computations (55.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))
✓	0.1b	(log1p.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th)))
✓	0.2b	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
✓	0.2b	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))

series2.9s (12.3%)

Counts

4 → 120

Calls

4 calls:

2.4s	(log1p.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th)))
249.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))
137.0ms	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
55.0ms	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))

rewrite44.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64`
104×	`add-sqr-sqrt_binary64`
92×	`*-un-lft-identity_binary64`
90×	`add-cube-cbrt_binary64`
44×	`associate-l_binary64`

Counts

4 → 192

Calls

4 calls:

11.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))
10.0ms	(/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))
2.0ms	(/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))
0.0ms	(log1p.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th)))

simplify216.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

357×	`associate-r_binary64`
340×	`fma-def_binary64`
323×	`associate-/l*_binary64`
297×	`fma-neg_binary64`
279×	`times-frac_binary64`

Counts

312 → 385

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	495	9994
1	1409	9188
2	4952	9186
3	5191	9186

prune382.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	384	1	385
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	386	7	393

Error

0.0b

Counts

393 → 7

Alt Table

Status	Error	Program
▶	0.2b	(expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	5.4b	(.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)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	31.2b	(.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (.f64 (sqrt.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th)))
✓	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))

Compiler

Compiled 12499 to 5266 computations (57.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.9s (12.3%)

Counts

3 → 108

Calls

3 calls:

2.5s

(log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))

210.0ms

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

210.0ms

(expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
45×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

3 → 94

Calls

3 calls:

5.0ms

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

0.0ms

(log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))))

0.0ms

(expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))

simplify204.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

314×	`fma-neg_binary64`
246×	`times-frac_binary64`
238×	`associate-/l*_binary64`
218×	`associate-r_binary64`
218×	`sub-neg_binary64`

Counts

202 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	408	8194
1	1109	7956
2	4371	7918
3	4849	7916
4	4960	7916

prune222.0ms (1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	237	8	245

Error

Counts

245 → 8

Alt Table

Status	Error	Program
✓	0.2b	(expm1.f64 (log1p.f64 (/.f64 (sin.f64 th) (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky)))))
	0.5b	(*.f64 (/.f64 (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sqrt.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	5.4b	(.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)))
	0.4b	(.f64 (sin.f64 ky) (.f64 (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))
	0.4b	(expm1.f64 (log1p.f64 (/.f64 (/.f64 (sin.f64 th) (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (/.f64 1 (sin.f64 ky)))))
✓	0.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (/.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)) (sin.f64 ky))) (sin.f64 th))))
	0.3b	(.f64 (.f64 (sin.f64 ky) (/.f64 1 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 th))
	1.3b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (/.f64 (sin.f64 th) (/.f64 (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))) (sin.f64 ky))))))

Compiler

Compiled 7840 to 3053 computations (61.1% saved)

regimes2.4s (10.1%)

Accuracy

Total 0.2b remaining (87%)

Threshold costs 0.2b (87%)

Counts

230 → 1

Compiler

Compiled 40840 to 26837 computations (34.3% 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

end128.0ms (0.5%)

Compiler: Compiled 181 to 119 computations (34.3% saved)

Details

analyze1.8s (7.6%)

sample8.6s (37%)

simplify82.0ms (0.4%)

prune4.0ms (0%)

localize9.0ms (0%)

series379.0ms (1.6%)

rewrite12.0ms (0.1%)

simplify100.0ms (0.4%)

prune183.0ms (0.8%)

localize12.0ms (0.1%)

series2.5s (10.6%)

rewrite1.0ms (0%)

simplify96.0ms (0.4%)

prune232.0ms (1%)

localize13.0ms (0.1%)

series2.9s (12.3%)

rewrite44.0ms (0.2%)

simplify216.0ms (0.9%)

prune382.0ms (1.6%)

localize13.0ms (0.1%)

series2.9s (12.3%)

rewrite14.0ms (0.1%)

simplify204.0ms (0.9%)

prune222.0ms (1%)

regimes2.4s (10.1%)

simplify2.0ms (0%)

end128.0ms (0.5%)

Profiling