Details

analyze71.0ms (2.8%)

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
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)

sample720.0ms (28%)

Results

707.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 12 computations (40% saved)

preprocess77.0ms (3%)

Algorithm

2×	egg-herbie

Rules

1022×	`fma-neg_binary64`
485×	`div-sub_binary64`
480×	`times-frac_binary64`
259×	`associate-/l*_binary64`
250×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	22	20
2	34	20
3	54	20
4	104	20
5	192	20
6	319	20
7	676	20
8	1930	20
9	3892	20
10	4645	20
11	4722	20
12	4800	20
13	4830	20
14	4854	20
15	4876	20
16	4902	20
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify54.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
363×	`times-frac_binary64`
334×	`div-sub_binary64`
143×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	57	10
5	93	10
6	154	10
7	244	10
8	437	10
9	990	10
10	2383	10
11	3170	10
12	3927	10
13	3974	10
14	3996	10
15	4016	10
16	4016	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0.1%)

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 (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(/.f64 (-.f64 x y) (+.f64 x y))	x	-inf
1.0ms	(/.f64 (-.f64 x y) (+.f64 x y))	x	0
1.0ms	(/.f64 (-.f64 x y) (+.f64 x y))	x	inf
1.0ms	(/.f64 (-.f64 x y) (+.f64 x y))	y	-inf
1.0ms	(/.f64 (-.f64 x y) (+.f64 x y))	y	0

rewrite114.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	143	10
2	2278	10

Stop Event

1×	node limit

Counts

1 → 233

simplify32.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	414
1	109	408
2	348	366
3	1439	324

Stop Event

1×	node limit

Counts

257 → 247

prune195.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	245	2	247
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)))
	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 11909 to 3092 computations (74% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)
✓	0.0b	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))
	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2))

series130.0ms (5.1%)

Counts

3 → 72

Calls

18 calls:

33.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))	x	-inf
26.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))	y	inf
25.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))	y	-inf
22.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y)))	x	0
2.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2))	x	0

rewrite69.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

768×	`prod-diff_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
107×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	40
1	222	40
2	3039	40

Stop Event

1×	node limit

Counts

3 → 98

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

657×	`associate-/l*_binary64`
525×	`associate-/r*_binary64`
496×	`fma-def_binary64`
365×	`cancel-sign-sub-inv_binary64`
121×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1939
1	441	1915
2	1727	1651

Stop Event

1×	node limit

Counts

170 → 143

prune517.0ms (20.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	637	0	637
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	637	3	640

Error

Counts

640 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)))
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 33604 to 9692 computations (71.2% saved)

localize7.0ms (0.3%)

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)))

series23.0ms (0.9%)

Counts

3 → 72

Calls

18 calls:

3.0ms	(/.f64 x (+.f64 x y))	y	0
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	x	0
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	y	0
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	x	-inf
1.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))	y	-inf

rewrite75.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	175	24
2	3034	24

Stop Event

1×	node limit

Counts

3 → 237

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1290
1	179	1284
2	545	1095
3	2347	1008

Stop Event

1×	node limit

Counts

309 → 275

prune174.0ms (6.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	275	3	278

Error

Counts

278 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (+.f64 x y))) (cbrt.f64 (pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) 2)))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 5738 to 1513 computations (73.6% saved)

regimes135.0ms (5.3%)

Accuracy

Total 0.0b remaining (75.5%)

Threshold costs 0.0b (75.5%)

Counts

55 → 1

Compiler

Compiled 2760 to 1563 computations (43.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	15	29
2	20	29
3	22	29
4	23	29

Stop Event

1×

saturated

end54.0ms (2.1%)

Stop Event

1×

done

Compiler

Compiled 85 to 41 computations (51.8% saved)

Details

analyze71.0ms (2.8%)

sample720.0ms (28%)

preprocess77.0ms (3%)

simplify54.0ms (2.1%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite114.0ms (4.4%)

simplify32.0ms (1.3%)

prune195.0ms (7.6%)

localize9.0ms (0.3%)

series130.0ms (5.1%)

rewrite69.0ms (2.7%)

simplify48.0ms (1.9%)

prune517.0ms (20.1%)

localize7.0ms (0.3%)

series23.0ms (0.9%)

rewrite75.0ms (2.9%)

simplify48.0ms (1.9%)

prune174.0ms (6.8%)

regimes135.0ms (5.3%)

simplify3.0ms (0.1%)

end54.0ms (2.1%)

Profiling