Details

analyze553.0ms (5.8%)

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
25%	74.9%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
62.4%	31.2%	6.3%	7
62.4%	31.2%	6.3%	8
62.4%	28.1%	9.5%	9
62.4%	28.1%	9.5%	10
62.4%	26.5%	11%	11
62.4%	26.5%	11%	12
62.4%	25.8%	11.8%	13
62.4%	25.8%	11.8%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample110.0ms (1.2%)

Algorithm

1×

intervals

Results

38.0ms	74×	body	1024	valid
22.0ms	53×	body	1024	invalid
11.0ms	135×	body	128	valid
9.0ms	38×	body	512	valid
6.0ms	76×	body	128	invalid
6.0ms	27×	body	512	invalid
2.0ms	2×	body	2048	valid
1.0ms	7×	body	256	valid
1.0ms	6×	body	256	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
491×	`associate-/r*_binary64`
476×	`fabs-mul_binary64`
360×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	27	18
2	65	18
3	104	17
4	137	17
5	196	17
6	329	17
7	736	17
8	2242	17
9	2250	17
10	2619	17
11	4128	17
12	4563	17
13	5391	17

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 51 to 34 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
13×	`fma-udef_binary64`

Counts

3 → 123

Calls

3 calls:

14.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
12.0ms	(/.f64 1/2 (exp.f64 im))
9.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))

series111.0ms (1.2%)

Counts

3 → 40

Calls

3 calls:

85.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
16.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
10.0ms	(/.f64 1/2 (exp.f64 im))

simplify116.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

897×	`fma-def_binary64`
423×	`cancel-sign-sub-inv_binary64`
409×	`fma-neg_binary64`
285×	`times-frac_binary64`
194×	`associate-l_binary64`

Counts

163 → 251

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	2409
1	527	2177
2	2026	2145
3	4644	2139
4	4920	2139

prune134.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	248	3	251
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	3	252

Error

Counts

252 → 3

Alt Table

Status	Error	Program
	0.4b	(fma.f64 1/24 (.f64 (pow.f64 im 4) (sin.f64 re)) (fma.f64 1/2 (.f64 (*.f64 im im) (sin.f64 re)) (sin.f64 re)))
	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
▶	0.0b	(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))

Compiler

Compiled 3191 to 1750 computations (45.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))
✓	0.0b	(exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))
	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1)

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-cube-cbrt_binary64`
20×	`pow1_binary64`
19×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
11×	`add-cbrt-cube_binary64`

Counts

3 → 127

Calls

3 calls:

15.0ms

(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))

15.0ms

(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1)

9.0ms

(exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

series1.8s (19.2%)

Counts

3 → 48

Calls

3 calls:

893.0ms

(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))

478.0ms

(-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1)

461.0ms

(exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

simplify144.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
471×	`distribute-rgt-in_binary64`
435×	`distribute-lft-in_binary64`
385×	`fma-neg_binary64`
228×	`cancel-sign-sub-inv_binary64`

Counts

175 → 302

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	4121
1	529	3443
2	1661	3005
3	4836	3005
4	4887	3005

prune232.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	364	1	365
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	365	3	368

Error

Counts

368 → 3

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (sin.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 (pow.f64 im 4) 1/24))) (sin.f64 re))
▶	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
✓	0.0b	(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))

Compiler

Compiled 7200 to 4782 computations (33.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
	0.0b	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))
✓	3.5b	(log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`pow1_binary64`
21×	`add-cube-cbrt_binary64`
16×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
9×	`log-prod_binary64`

Counts

3 → 102

Calls

3 calls:

13.0ms

(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))

11.0ms

(log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

10.0ms

(exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

series1.6s (16.7%)

Counts

3 → 48

Calls

3 calls:

797.0ms

(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))

400.0ms

(log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

396.0ms

(exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))))

simplify133.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

404×	`fma-def_binary64`
378×	`*-commutative_binary64`
349×	`fma-neg_binary64`
320×	`cancel-sign-sub-inv_binary64`
308×	`distribute-rgt-in_binary64`

Counts

150 → 244

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	2755
1	349	2421
2	1206	2243
3	3509	2209
4	4987	2209
5	4888	2209

prune162.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	370	3	373

Error

Counts

373 → 3

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (.f64 (sin.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 (pow.f64 im 4) 1/24))) (sin.f64 re))
✓	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
✓	0.0b	(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))

Compiler

Compiled 3978 to 2446 computations (38.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 im im) 1/2 (.f64 (pow.f64 im 4) 1/24))
✓	0.1b	(*.f64 (pow.f64 im 4) 1/24)
✓	0.1b	(.f64 (sin.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 (pow.f64 im 4) 1/24)))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
13×	`fma-udef_binary64`

Counts

3 → 112

Calls

3 calls:

14.0ms	(.f64 (sin.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 (pow.f64 im 4) 1/24)))
13.0ms	(*.f64 (pow.f64 im 4) 1/24)
10.0ms	(fma.f64 (.f64 im im) 1/2 (.f64 (pow.f64 im 4) 1/24))

series88.0ms (0.9%)

Counts

3 → 48

Calls

3 calls:

57.0ms	(.f64 (sin.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 (pow.f64 im 4) 1/24)))
18.0ms	(fma.f64 (.f64 im im) 1/2 (.f64 (pow.f64 im 4) 1/24))
14.0ms	(*.f64 (pow.f64 im 4) 1/24)

simplify138.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-neg_binary64`
510×	`cancel-sign-sub-inv_binary64`
276×	`distribute-rgt-neg-in_binary64`
268×	`unswap-sqr_binary64`
257×	`associate-l_binary64`

Counts

160 → 259

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2507
1	461	2285
2	1987	2251
3	4451	2242
4	4972	2242
5	4956	2242

prune144.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	259	3	262

Error

Counts

262 → 3

Alt Table

Status	Error	Program
✓	0.4b	(+.f64 (.f64 (sin.f64 re) (fma.f64 (.f64 im im) 1/2 (*.f64 (pow.f64 im 4) 1/24))) (sin.f64 re))
✓	0.0b	(*.f64 (sin.f64 re) (exp.f64 (log.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))))
✓	0.0b	(*.f64 (sin.f64 re) (-.f64 (exp.f64 (log1p.f64 (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))) 1))

Compiler

Compiled 3882 to 2309 computations (40.5% saved)

regimes322.0ms (3.4%)

Accuracy

Total -0.0b remaining (-54.3%)

Threshold costs -0.0b (-54.3%)

Compiler

Compiled 4980 to 3605 computations (27.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	12	22
2	12	22

end1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

sample3.4s (36%)

Algorithm

1×

intervals

Results

1.0s	1991×	body	1024	valid
737.0ms	1990×	body	1024	invalid
360.0ms	4468×	body	128	valid
245.0ms	1003×	body	512	valid
208.0ms	958×	body	512	invalid
201.0ms	2520×	body	128	invalid
85.0ms	532×	body	256	valid
76.0ms	484×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 83 to 60 computations (27.7% saved)

Details

analyze553.0ms (5.8%)

sample110.0ms (1.2%)

simplify82.0ms (0.9%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite41.0ms (0.4%)

series111.0ms (1.2%)

simplify116.0ms (1.2%)

prune134.0ms (1.4%)

localize11.0ms (0.1%)

rewrite48.0ms (0.5%)

series1.8s (19.2%)

simplify144.0ms (1.5%)

prune232.0ms (2.4%)

localize9.0ms (0.1%)

rewrite39.0ms (0.4%)

series1.6s (16.7%)

simplify133.0ms (1.4%)

prune162.0ms (1.7%)

localize10.0ms (0.1%)

rewrite44.0ms (0.5%)

series88.0ms (0.9%)

simplify138.0ms (1.4%)

prune144.0ms (1.5%)

regimes322.0ms (3.4%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample3.4s (36%)

Profiling