Details

analyze3.6s (13%)

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)

sample594.0ms (2.1%)

Algorithm

1×

intervals

Results

329.0ms	139×	body	1024	valid
64.0ms	53×	body	512	valid
18.0ms	48×	body	128	valid
12.0ms	16×	body	256	valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify116.0ms (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

prune7.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))

Compiler

Compiled 58 to 35 computations (39.7% saved)

localize21.0ms (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))
✓	0.2b	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

series817.0ms (2.9%)

Counts

3 → 84

Calls

3 calls:

510.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
248.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
58.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

rewrite32.0ms (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:

13.0ms	(*.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th))
6.0ms	(/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
1.0ms	(hypot.f64 (sin.f64 ky) (sin.f64 kx))

simplify218.0ms (0.8%)

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

prune406.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	177	7	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	178	7	185

Error

Counts

185 → 7

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
	31.9b	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	29.1b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	4.8b	(.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)))
	2.3b	(.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)))
	7.7b	(.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))
	1.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 ky)) (cbrt.f64 (sin.f64 ky))) 1) (*.f64 (/.f64 (cbrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sin.f64 th)))

Compiler

Compiled 5196 to 1964 computations (62.2% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.8s (9.9%)

Counts

4 → 108

Calls

4 calls:

2.0s	(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))
424.0ms	(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
243.0ms	(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
58.0ms	(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

rewrite40.0ms (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:

12.0ms	(/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))
11.0ms	(*.f64 (/.f64 (sin.f64 ky) (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))) (sin.f64 th))
1.0ms	(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
1.0ms	(log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))

simplify249.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

295×	`sub-neg_binary64`
278×	`fma-def_binary64`
251×	`times-frac_binary64`
238×	`associate-/r*_binary64`
207×	`associate-/l*_binary64`

Counts

193 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	5770
1	1208	5276
2	4466	5273
3	5032	5273

prune405.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	222	6	228

Error

Counts

228 → 6

Alt Table

Status	Error	Program
	4.8b	(.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)))
▶	0.4b	(*.f64 (/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky))) (sin.f64 th))
	31.9b	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	29.1b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	7.7b	(.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))
	2.3b	(.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 6895 to 2749 computations (60.1% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky))) (sin.f64 th))
✓	0.2b	(/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky))
✓	0.2b	(/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky)))
	0.3b	(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))

series723.0ms (2.6%)

Counts

3 → 84

Calls

3 calls:

403.0ms

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

230.0ms

(/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky)))

90.0ms

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

rewrite89.0ms (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-l_binary64`

Counts

3 → 182

Calls

3 calls:

29.0ms

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

10.0ms

(/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky)))

6.0ms

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

simplify363.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

453×	`cancel-sign-sub-inv_binary64`
248×	`associate-r_binary64`
232×	`fma-def_binary64`
219×	`sub-neg_binary64`
200×	`*-commutative_binary64`

Counts

266 → 346

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	373	7784
1	1005	7027
2	3677	7000
3	4965	7000

prune743.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	381	6	387

Error

Counts

387 → 6

Alt Table

Status	Error	Program
	4.8b	(.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)))
✓	0.4b	(*.f64 (/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky))) (sin.f64 th))
	31.9b	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	29.1b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	7.7b	(.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))
▶	2.3b	(.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 11485 to 3899 computations (66.1% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx))))
✓	0.3b	(*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky)))))
✓	0.4b	(/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))
✓	2.0b	(.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

series1.4s (5.1%)

Counts

3 → 96

Calls

3 calls:

620.0ms

(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

484.0ms

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

309.0ms

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

rewrite90.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
49×	`add-exp-log_binary64`
45×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`

Counts

3 → 141

Calls

3 calls:

27.0ms

(*.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) (*.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

17.0ms

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

8.0ms

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

simplify384.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

534×	`associate-r_binary64`
402×	`fma-neg_binary64`
381×	`associate-l_binary64`
312×	`fma-def_binary64`
309×	`*-commutative_binary64`

Counts

237 → 239

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	445	8893
1	1226	8157
2	4661	8157
3	4990	8157

prune578.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	274	6	280

Error

Counts

280 → 6

Alt Table

Status	Error	Program
	4.8b	(.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)))
✓	0.4b	(*.f64 (/.f64 1 (/.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))) (sin.f64 ky))) (sin.f64 th))
	31.9b	(.f64 (.f64 (sqrt.f64 (sin.f64 ky)) (/.f64 (sqrt.f64 (sin.f64 ky)) (hypot.f64 (sin.f64 kx) (sin.f64 ky)))) (sin.f64 th))
	29.1b	(.f64 (.f64 (/.f64 (sin.f64 ky) (hypot.f64 (sin.f64 ky) (sin.f64 kx))) (sqrt.f64 (sin.f64 th))) (sqrt.f64 (sin.f64 th)))
	7.7b	(.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))
✓	2.3b	(.f64 (/.f64 1 (sqrt.f64 (expm1.f64 (log1p.f64 (hypot.f64 (sin.f64 ky) (sin.f64 kx)))))) (.f64 (sin.f64 th) (/.f64 (sin.f64 ky) (sqrt.f64 (hypot.f64 (sin.f64 kx) (sin.f64 ky))))))

Compiler

Compiled 11190 to 3855 computations (65.5% saved)

regimes6.4s (23%)

Accuracy

Total 0.2b remaining (77.2%)

Threshold costs 0.2b (77.2%)

Counts

277 → 1

Compiler

Compiled 53343 to 34799 computations (34.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	15	18
2	14	18

end1.0ms (0%)

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

sample7.6s (27.4%)

Algorithm

1×

intervals

Results

5.5s	4639×	body	1024	valid
953.0ms	1376×	body	512	valid
259.0ms	1414×	body	128	valid
232.0ms	562×	body	256	valid
22.0ms	9×	body	2048	valid

Compiler

Compiled 173 to 107 computations (38.2% saved)

Details

analyze3.6s (13%)

sample594.0ms (2.1%)

simplify116.0ms (0.4%)

prune7.0ms (0%)

localize21.0ms (0.1%)

series817.0ms (2.9%)

rewrite32.0ms (0.1%)

simplify218.0ms (0.8%)

prune406.0ms (1.5%)

localize31.0ms (0.1%)

series2.8s (9.9%)

rewrite40.0ms (0.1%)

simplify249.0ms (0.9%)

prune405.0ms (1.5%)

localize30.0ms (0.1%)

series723.0ms (2.6%)

rewrite89.0ms (0.3%)

simplify363.0ms (1.3%)

prune743.0ms (2.7%)

localize44.0ms (0.2%)

series1.4s (5.1%)

rewrite90.0ms (0.3%)

simplify384.0ms (1.4%)

prune578.0ms (2.1%)

regimes6.4s (23%)

simplify3.0ms (0%)

end1.0ms (0%)

sample7.6s (27.4%)

Profiling