Details

analyze559.0ms (7.7%)

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)

sample4.6s (63.3%)

Results

1.4s	2044×	body	1024	valid
1.2s	2111×	body	1024	invalid
671.0ms	4671×	body	128	valid
434.0ms	1062×	body	512	valid
378.0ms	1032×	body	512	invalid
147.0ms	538×	body	256	invalid
131.0ms	476×	body	256	valid
117.0ms	826×	body	128	invalid
4.0ms	3×	body	2048	valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

778×	`unswap-sqr_binary64`
455×	`associate-/r*_binary64`
357×	`associate-/l*_binary64`
346×	`times-frac_binary64`
315×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	28	18
2	71	18
3	140	17
4	185	17
5	252	17
6	430	17
7	1107	17
8	3311	17
9	3702	17
10	4192	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 79 to 56 computations (29.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

series18.0ms (0.3%)

Counts

2 → 36

Calls

2 calls:

16.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
2.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))

rewrite44.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`prod-diff_binary64`
176×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`
122×	`log1p-expm1-u_binary64`
122×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	257	20
2	3600	20

Stop Event

1×	node limit

Counts

2 → 56

Calls

2 calls:

43.0ms	(+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im))
43.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))

simplify38.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
523×	`fma-def_binary64`
246×	`distribute-rgt-neg-in_binary64`
244×	`sub-neg_binary64`
226×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	735
1	245	670
2	799	646
3	3340	645

Stop Event

1×	node limit

Counts

92 → 83

prune66.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Error

Counts

85 → 5

Alt Table

Status	Error	Program
	18.3b	(cbrt.f64 (pow.f64 (.f64 1/2 (.f64 (sin.f64 re) (*.f64 2 (cosh.f64 im)))) 3))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 (log.f64 (*.f64 2 (cosh.f64 im)))))
	2.4b	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))
▶	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 1631 to 912 computations (44.1% 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))

series40.0ms (0.6%)

Counts

3 → 40

Calls

3 calls:

27.0ms	(*.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))

rewrite44.0ms (0.6%)

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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	182	35
2	2188	35

Stop Event

1×	node limit

Counts

3 → 63

Calls

3 calls:

43.0ms	(fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im)))
43.0ms	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))
43.0ms	(/.f64 1/2 (exp.f64 im))

simplify37.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
443×	`fma-def_binary64`
298×	`sub-neg_binary64`
173×	`associate-r_binary64`
173×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	796
1	251	739
2	791	715
3	3085	700

Stop Event

1×	node limit

Counts

103 → 96

prune83.0ms (1.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Error

Counts

101 → 5

Alt Table

Status	Error	Program
	18.3b	(cbrt.f64 (pow.f64 (.f64 1/2 (.f64 (sin.f64 re) (*.f64 2 (cosh.f64 im)))) 3))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
▶	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 (log.f64 (*.f64 2 (cosh.f64 im)))))
	2.4b	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 1705 to 1007 computations (40.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series255.0ms (3.5%)

Counts

4 → 60

Calls

4 calls:

215.0ms	(log.f64 (*.f64 2 (cosh.f64 im)))
23.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 (log.f64 (*.f64 2 (cosh.f64 im)))))
9.0ms	(exp.f64 (log.f64 (*.f64 2 (cosh.f64 im))))
7.0ms	(cosh.f64 im)

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary64`
276×	`pow2_binary64`
195×	`pow1/3_binary64`
195×	`expm1-udef_binary64`
195×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	227	25
2	2577	25

Stop Event

1×	node limit

Counts

4 → 133

Calls

4 calls:

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

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-neg_binary64`
480×	`fma-def_binary64`
276×	`sub-neg_binary64`
186×	`associate-+l+_binary64`
154×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1032
1	266	971
2	812	943
3	3084	932

Stop Event

1×	node limit

Counts

193 → 176

prune132.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	176	5	181

Error

Counts

181 → 5

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	18.3b	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 (log.f64 (*.f64 2 (cosh.f64 im)))))
▶	2.4b	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 2887 to 1815 computations (37.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(cosh.f64 im)
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))
✓	0.0b	(pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3)
✓	1.0b	(cbrt.f64 (*.f64 2 (cosh.f64 im)))

series599.0ms (8.3%)

Counts

3 → 48

Calls

3 calls:

296.0ms	(cbrt.f64 (*.f64 2 (cosh.f64 im)))
257.0ms	(pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3)
46.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))

rewrite49.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

563×	`log-prod_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
185×	`pow3_binary64`
182×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	266	22
2	2860	22

Stop Event

1×	node limit

Counts

3 → 90

Calls

3 calls:

47.0ms	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))
47.0ms	(pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3)
47.0ms	(cbrt.f64 (*.f64 2 (cosh.f64 im)))

simplify43.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-neg_binary64`
477×	`fma-def_binary64`
281×	`sub-neg_binary64`
209×	`associate-r_binary64`
195×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	1028
1	287	975
2	891	949
3	3401	937

Stop Event

1×	node limit

Counts

138 → 125

prune99.0ms (1.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	161	5	166

Error

Counts

166 → 5

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (+.f64 (exp.f64 (-.f64 0 im)) (exp.f64 im)))
	18.3b	(cbrt.f64 (pow.f64 (*.f64 (cosh.f64 im) (sin.f64 re)) 3))
✓	0.0b	(.f64 (.f64 1/2 (sin.f64 re)) (exp.f64 (log.f64 (*.f64 2 (cosh.f64 im)))))
✓	2.4b	(.f64 (.f64 1/2 (sin.f64 re)) (pow.f64 (cbrt.f64 (*.f64 2 (cosh.f64 im))) 3))
✓	0.0b	(*.f64 (sin.f64 re) (fma.f64 1/2 (exp.f64 im) (/.f64 1/2 (exp.f64 im))))

Compiler

Compiled 2795 to 1786 computations (36.1% saved)

regimes290.0ms (4%)

Accuracy

Total 0.0b remaining (16.9%)

Threshold costs 0.0b (16.9%)

Counts

47 → 1

Compiler

Compiled 3366 to 2670 computations (20.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	18	18
2	20	18
3	21	18

Stop Event

1×

saturated

end91.0ms (1.3%)

Compiler: Compiled 90 to 71 computations (21.1% saved)

Details

analyze559.0ms (7.7%)

sample4.6s (63.3%)

simplify33.0ms (0.4%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series18.0ms (0.3%)

rewrite44.0ms (0.6%)

simplify38.0ms (0.5%)

prune66.0ms (0.9%)

localize7.0ms (0.1%)

series40.0ms (0.6%)

rewrite44.0ms (0.6%)

simplify37.0ms (0.5%)

prune83.0ms (1.2%)

localize10.0ms (0.1%)

series255.0ms (3.5%)

rewrite50.0ms (0.7%)

simplify43.0ms (0.6%)

prune132.0ms (1.8%)

localize10.0ms (0.1%)

series599.0ms (8.3%)

rewrite49.0ms (0.7%)

simplify43.0ms (0.6%)

prune99.0ms (1.4%)

regimes290.0ms (4%)

simplify2.0ms (0%)

end91.0ms (1.3%)

Profiling