Details

analyze560.0ms (7.2%)

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
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	40.6%	9.5%	7
50%	39%	11%	8
50%	33.6%	16.5%	9
50%	32.4%	17.7%	10
50%	29.5%	20.6%	11
50%	28.8%	21.3%	12
50%	27.3%	22.8%	13
50%	26.9%	23.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample5.6s (71.9%)

Results

1.6s	2066×	body	1024	valid
1.2s	2042×	body	1024	invalid
1.0s	1019×	body	512	valid
749.0ms	4697×	body	128	valid
383.0ms	1018×	body	512	invalid
182.0ms	467×	body	256	valid
153.0ms	532×	body	256	invalid
121.0ms	814×	body	128	invalid
16.0ms	7×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify87.0ms (1.1%)

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)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series37.0ms (0.5%)

Counts

3 → 40

Calls

3 calls:

24.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
7.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
6.0ms	(/.f64 1/2 (exp.f64 im))

rewrite50.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

804×	`log1p-expm1-u_binary64`
804×	`expm1-log1p-u_binary64`
116×	`prod-diff_binary64`
92×	`add-sqr-sqrt_binary64`
86×	`add-log-exp_binary64`

Counts

3 → 63

Calls

3 calls:

49.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
49.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
49.0ms	(/.f64 1/2 (exp.f64 im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	182	35
2	2115	35
3	5120	35
0	0	0
1	0	0

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
601×	`associate--r+_binary64`
447×	`fma-def_binary64`
298×	`sub-neg_binary64`
175×	`associate-l_binary64`

Counts

103 → 96

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	796
1	250	739
2	748	715
3	2524	700
4	5057	700

prune97.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
	0.8b	(+.f64 (sin.f64 re) (.f64 1/2 (.f64 (sin.f64 re) (pow.f64 im 2))))
	32.4b	(-.f64 (+.f64 (.f64 1/2 (.f64 re (exp.f64 im))) (.f64 1/2 (/.f64 re (exp.f64 im)))) (+.f64 (.f64 1/12 (.f64 (pow.f64 re 3) (exp.f64 im))) (.f64 1/12 (/.f64 (pow.f64 re 3) (exp.f64 im)))))
	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (pow.f64 (sqrt.f64 (/.f64 1/2 (exp.f64 im))) 2)))

Compiler

Compiled 1754 to 1023 computations (41.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series56.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

28.0ms	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
18.0ms	(*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re))
10.0ms	(.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re))

rewrite76.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

448×	`fma-def_binary64`
222×	`fma-neg_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
191×	`log-pow_binary64`

Counts

3 → 114

Calls

3 calls:

73.0ms	(+.f64 (.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re)) (*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re)))
73.0ms	(.f64 (.f64 1/2 (exp.f64 im)) (sin.f64 re))
73.0ms	(*.f64 (/.f64 1/2 (exp.f64 im)) (sin.f64 re))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	41
1	239	39
2	3073	36
3	4926	36
0	0	0
1	0	0

simplify105.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
397×	`sub-neg_binary64`
285×	`distribute-lft-out_binary64`
256×	`cancel-sign-sub-inv_binary64`
232×	`distribute-rgt-neg-in_binary64`

Counts

186 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1397
1	326	1308
2	989	1268
3	3283	1204
4	4989	1204
5	4991	1204
6	4948	1204

prune137.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	192	2	194

Error

Counts

194 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 1/2 (/.f64 (sin.f64 re) (exp.f64 im)) (.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im))))
	0.8b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

Compiler

Compiled 4025 to 2184 computations (45.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series58.0ms (0.7%)

Counts

3 → 56

Calls

3 calls:

30.0ms	(fma.f64 1/2 (/.f64 (sin.f64 re) (exp.f64 im)) (.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im))))
14.0ms	(/.f64 (sin.f64 re) (exp.f64 im))
13.0ms	(.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im)))

rewrite65.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

526×	`log-prod_binary64`
263×	`prod-diff_binary64`
186×	`expm1-udef_binary64`
186×	`log1p-udef_binary64`
172×	`pow3_binary64`

Counts

3 → 84

Calls

3 calls:

63.0ms	(fma.f64 1/2 (/.f64 (sin.f64 re) (exp.f64 im)) (.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im))))
63.0ms	(/.f64 (sin.f64 re) (exp.f64 im))
63.0ms	(.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	41
1	203	41
2	2464	41
3	4950	41
0	0	0
1	0	0

simplify97.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
394×	`sub-neg_binary64`
245×	`distribute-rgt-neg-in_binary64`
241×	`associate-r_binary64`
241×	`cancel-sign-sub-inv_binary64`

Counts

140 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1199
1	344	1108
2	1028	1071
3	3396	1010
4	4999	1010
5	4995	1010
6	4947	1010

prune80.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	131	2	133

Error

Counts

133 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (sin.f64 re) (exp.f64 im)) (.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im))))
▶	0.8b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

Compiler

Compiled 2890 to 1389 computations (51.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series28.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
11.0ms	(.f64 (sin.f64 re) (.f64 im im))

rewrite76.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

683×	`log1p-expm1-u_binary64`
683×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
127×	`log-pow_binary64`

Counts

2 → 41

Calls

2 calls:

75.0ms	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))
75.0ms	(.f64 (sin.f64 re) (.f64 im im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	161	24
2	1783	24
3	4958	24
4	4939	24
0	0	0
1	0	0

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

599×	`associate--r+_binary64`
397×	`fma-def_binary64`
338×	`distribute-rgt-neg-in_binary64`
328×	`distribute-lft-neg-in_binary64`
309×	`sub-neg_binary64`

Counts

89 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	780
1	171	718
2	606	648
3	2548	648
4	4963	648
5	5062	648

prune40.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	64	2	66

Error

Counts

66 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 1/2 (/.f64 (sin.f64 re) (exp.f64 im)) (.f64 (sin.f64 re) (.f64 1/2 (exp.f64 im))))
✓	0.8b	(fma.f64 1/2 (.f64 (sin.f64 re) (.f64 im im)) (sin.f64 re))

Compiler

Compiled 1111 to 561 computations (49.5% saved)

regimes327.0ms (4.2%)

Accuracy

Total 0.0b remaining (38.2%)

Threshold costs 0.0b (38.2%)

Counts

58 → 1

Compiler

Compiled 5082 to 3699 computations (27.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24
2	15	24

end50.0ms (0.6%)

Compiler: Compiled 62 to 39 computations (37.1% saved)

Details

analyze560.0ms (7.2%)

sample5.6s (71.9%)

simplify87.0ms (1.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series37.0ms (0.5%)

rewrite50.0ms (0.7%)

simplify45.0ms (0.6%)

prune97.0ms (1.3%)

localize9.0ms (0.1%)

series56.0ms (0.7%)

rewrite76.0ms (1%)

simplify105.0ms (1.4%)

prune137.0ms (1.8%)

localize8.0ms (0.1%)

series58.0ms (0.7%)

rewrite65.0ms (0.8%)

simplify97.0ms (1.2%)

prune80.0ms (1%)

localize6.0ms (0.1%)

series28.0ms (0.4%)

rewrite76.0ms (1%)

simplify68.0ms (0.9%)

prune40.0ms (0.5%)

regimes327.0ms (4.2%)

simplify2.0ms (0%)

end50.0ms (0.6%)

Profiling