Details

analyze60.0ms (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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample788.0ms (26.1%)

Results

678.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify72.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
365×	`times-frac_binary64`
331×	`div-sub_binary64`
156×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	52	10
5	81	10
6	124	10
7	191	10
8	300	10
9	641	10
10	822	10
11	1299	10
12	1328	10
13	1343	10
14	1357	10
15	1377	10
16	1377	10
17	1276	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

series7.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

rewrite101.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

898×	`expm1-log1p-u_binary64`
768×	`prod-diff_binary64`
234×	`egg-rr`
76×	`add-sqr-sqrt_binary64`
73×	`log1p-expm1-u_binary64`

Counts

1 → 234

Calls

1 calls:

90.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	143	10
2	2180	10
3	5409	10
0	0	0
1	0	0

simplify52.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

827×	`associate-/l*_binary64`
533×	`fma-def_binary64`
454×	`cancel-sign-sub-inv_binary64`
411×	`associate-/r/_binary64`
334×	`fma-neg_binary64`

Counts

258 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	414
1	107	408
2	329	366
3	1344	324
4	4841	324
5	5073	324

prune175.0ms (5.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	245	3	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	246	3	249

Error

Counts

249 → 3

Alt Table

Status	Error	Program
	32.5b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))) 1)
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	0.0b	(pow.f64 (/.f64 (+.f64 x y) (-.f64 x y)) -1)

Compiler

Compiled 11929 to 2657 computations (77.7% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(/.f64 y (+.f64 x y))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))

series34.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

18.0ms	(/.f64 y (+.f64 x y))
9.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
7.0ms	(/.f64 x (+.f64 x y))

rewrite83.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

498×	`fma-def_binary64`
256×	`fma-neg_binary64`
239×	`egg-rr`
239×	`log-div_binary64`
172×	`expm1-udef_binary64`

Counts

3 → 239

Calls

3 calls:

77.0ms	(/.f64 x (+.f64 x y))
77.0ms	(/.f64 y (+.f64 x y))
77.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	175	24
2	2847	24
3	5053	24
0	0	0
1	0	0

simplify75.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

610×	`fma-neg_binary64`
453×	`associate-/r/_binary64`
270×	`distribute-neg-frac_binary64`
225×	`distribute-rgt-neg-in_binary64`
221×	`distribute-lft-neg-in_binary64`

Counts

311 → 277

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1290
1	177	1284
2	525	1095
3	2077	1008
4	4888	1008
5	5057	1008

prune163.0ms (5.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	276	1	277
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	278	2	280

Error

Counts

280 → 2

Alt Table

Status	Error	Program
	32.5b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))) 1)
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (log.f64 (exp.f64 (/.f64 y (+.f64 x y)))))

Compiler

Compiled 5789 to 1497 computations (74.1% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (+.f64 x y))
✓	0.0b	(exp.f64 (/.f64 y (+.f64 x y)))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (log.f64 (exp.f64 (/.f64 y (+.f64 x y)))))
✓	2.6b	(log.f64 (exp.f64 (/.f64 y (+.f64 x y))))

series27.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

11.0ms	(exp.f64 (/.f64 y (+.f64 x y)))
8.0ms	(-.f64 (/.f64 x (+.f64 x y)) (log.f64 (exp.f64 (/.f64 y (+.f64 x y)))))
7.0ms	(log.f64 (exp.f64 (/.f64 y (+.f64 x y))))

rewrite88.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

527×	`log-prod_binary64`
448×	`fma-def_binary64`
251×	`fma-neg_binary64`
219×	`egg-rr`
203×	`log-div_binary64`

Counts

3 → 219

Calls

3 calls:

83.0ms	(exp.f64 (/.f64 y (+.f64 x y)))
83.0ms	(-.f64 (/.f64 x (+.f64 x y)) (log.f64 (exp.f64 (/.f64 y (+.f64 x y)))))
83.0ms	(log.f64 (exp.f64 (/.f64 y (+.f64 x y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	186	26
2	2841	26
3	5783	26
0	0	0
1	0	0

simplify59.0ms (2%)

Algorithm

1×	egg-herbie

Rules

734×	`fma-neg_binary64`
404×	`distribute-neg-frac_binary64`
386×	`distribute-rgt-neg-in_binary64`
321×	`times-frac_binary64`
224×	`associate-/l*_binary64`

Counts

291 → 258

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	1338
1	217	1308
2	686	1185
3	3071	1164
4	5046	1164

prune213.0ms (7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	305	2	307

Error

Counts

307 → 2

Alt Table

Status	Error	Program
▶	32.5b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))) 1)
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (log.f64 (exp.f64 (/.f64 y (+.f64 x y)))))

Compiler

Compiled 6279 to 1781 computations (71.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1)))
✓	0.1b	(fma.f64 (/.f64 y x) (/.f64 y x) 1)
✓	4.3b	(-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))

series38.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

15.0ms	(*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1)))
15.0ms	(fma.f64 (/.f64 y x) (/.f64 y x) 1)
8.0ms	(-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))

rewrite116.0ms (3.8%)

Algorithm

2×	batch-egg-rewrite

Rules

833×	`prod-diff_binary64`
448×	`fma-def_binary64`
231×	`fma-neg_binary64`
198×	`egg-rr`
157×	`expm1-udef_binary64`

Counts

3 → 198

Calls

3 calls:

111.0ms	(*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1)))
111.0ms	(fma.f64 (/.f64 y x) (/.f64 y x) 1)
111.0ms	(-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	51
1	171	48
2	2338	48
3	4726	48
4	5011	48
0	0	0
1	0	0

simplify61.0ms (2%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-neg_binary64`
539×	`distribute-neg-frac_binary64`
501×	`associate-/l*_binary64`
280×	`associate-*l/_binary64`
277×	`associate-/r*_binary64`

Counts

270 → 222

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	1107
1	69	1107
2	171	948
3	689	933
4	3363	933
5	5187	933

prune204.0ms (6.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	222	2	224

Error

Counts

224 → 2

Alt Table

Status	Error	Program
✓	32.5b	(fma.f64 2 (*.f64 (/.f64 y x) (-.f64 (/.f64 y x) (fma.f64 (/.f64 y x) (/.f64 y x) 1))) 1)
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (log.f64 (exp.f64 (/.f64 y (+.f64 x y)))))

Compiler

Compiled 6286 to 3469 computations (44.8% saved)

regimes526.0ms (17.4%)

Accuracy

Total 0.0b remaining (46%)

Threshold costs 0.0b (46%)

Counts

171 → 1

Compiler

Compiled 8918 to 5080 computations (43% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	19	27
2	23	27
3	25	27
4	26	27
5	25	27

end55.0ms (1.8%)

Compiler: Compiled 74 to 42 computations (43.2% saved)

Details

analyze60.0ms (2%)

sample788.0ms (26.1%)

simplify72.0ms (2.4%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite101.0ms (3.3%)

simplify52.0ms (1.7%)

prune175.0ms (5.8%)

localize5.0ms (0.2%)

series34.0ms (1.1%)

rewrite83.0ms (2.7%)

simplify75.0ms (2.5%)

prune163.0ms (5.4%)

localize8.0ms (0.3%)

series27.0ms (0.9%)

rewrite88.0ms (2.9%)

simplify59.0ms (2%)

prune213.0ms (7%)

localize8.0ms (0.3%)

series38.0ms (1.2%)

rewrite116.0ms (3.8%)

simplify61.0ms (2%)

prune204.0ms (6.7%)

regimes526.0ms (17.4%)

simplify3.0ms (0.1%)

end55.0ms (1.8%)

Profiling