Details

analyze560.0ms (8.3%)

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)

sample4.7s (70.5%)

Results

1.5s	2048×	body	1024	valid
1.2s	2026×	body	1024	invalid
771.0ms	4649×	body	128	valid
422.0ms	1055×	body	512	valid
328.0ms	889×	body	512	invalid
145.0ms	807×	body	128	invalid
135.0ms	503×	body	256	valid
131.0ms	492×	body	256	invalid
3.0ms	1×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify77.0ms (1.2%)

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	(*.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)))
✓	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))

rewrite49.0ms (0.7%)

Algorithm

1×	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:

48.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
48.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
48.0ms	(/.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

simplify47.0ms (0.7%)

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

prune89.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	2	97

Error

Counts

97 → 2

Alt Table

Status	Error	Program
	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))
▶	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im)))))))

Compiler

Compiled 1660 to 963 computations (42% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (/.f64 1/2 (exp.f64 im)))
✓	0.0b	(+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im))))
	0.0b	(/.f64 1/2 (exp.f64 im))
✓	0.0b	(log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im)))))

series187.0ms (2.8%)

Counts

3 → 36

Calls

3 calls:

170.0ms	(log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im)))))
9.0ms	(expm1.f64 (/.f64 1/2 (exp.f64 im)))
7.0ms	(+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im))))

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
153×	`prod-diff_binary64`
136×	`expm1-udef_binary64`
135×	`log1p-udef_binary64`

Counts

3 → 96

Calls

3 calls:

44.0ms	(expm1.f64 (/.f64 1/2 (exp.f64 im)))
44.0ms	(+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im))))
44.0ms	(log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	161	22
2	1859	22
3	5020	22

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

748×	`fma-def_binary64`
656×	`distribute-rgt-neg-in_binary64`
630×	`cancel-sign-sub-inv_binary64`
486×	`fma-neg_binary64`
462×	`sub-neg_binary64`

Counts

132 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	399
1	128	384
2	353	363
3	1095	327
4	3685	327
5	4343	327
6	5076	327

prune127.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	148	2	150

Error

Counts

150 → 2

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im)))))))

Compiler

Compiled 2871 to 1886 computations (34.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))
✓	0.0b	(fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im)))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))
	0.0b	(/.f64 1/2 (exp.f64 im))

series37.0ms (0.5%)

Counts

3 → 48

Calls

3 calls:

22.0ms

(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))

9.0ms

(fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im)))))

6.0ms

(expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`expm1-log1p-u_binary64`
878×	`log1p-expm1-u_binary64`
196×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
93×	`add-log-exp_binary64`

Counts

3 → 74

Calls

3 calls:

54.0ms

(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))

54.0ms

(fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im)))))

54.0ms

(expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	201	35
2	2308	35
3	5675	35

simplify50.0ms (0.8%)

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

122 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	844
1	250	787
2	748	763
3	2524	748
4	5057	748

prune90.0ms (1.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	136	2	138

Error

Counts

138 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (expm1.f64 (log1p.f64 (/.f64 1/2 (exp.f64 im))))))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (exp.f64 im)))))))

Compiler

Compiled 2311 to 1359 computations (41.2% saved)

regimes352.0ms (5.2%)

Accuracy

Total 0.2b remaining (83.4%)

Threshold costs 0.2b (83.4%)

Counts

62 → 1

Compiler

Compiled 5490 to 4113 computations (25.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	15	23
2	17	23
3	16	23

end64.0ms (1%)

Compiler: Compiled 64 to 48 computations (25% saved)

Details

analyze560.0ms (8.3%)

sample4.7s (70.5%)

simplify77.0ms (1.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series37.0ms (0.5%)

rewrite49.0ms (0.7%)

simplify47.0ms (0.7%)

prune89.0ms (1.3%)

localize13.0ms (0.2%)

series187.0ms (2.8%)

rewrite46.0ms (0.7%)

simplify78.0ms (1.2%)

prune127.0ms (1.9%)

localize10.0ms (0.2%)

series37.0ms (0.5%)

rewrite55.0ms (0.8%)

simplify50.0ms (0.8%)

prune90.0ms (1.3%)

regimes352.0ms (5.2%)

simplify2.0ms (0%)

end64.0ms (1%)

Profiling