Details

analyze61.0ms (2.5%)

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
37.5%	62.4%	0.1%	5
43.7%	56.2%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample796.0ms (33.4%)

Results

766.0ms	8253×	body	128	valid
1.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	10	10

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 y 1))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (+.f64 y 1))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(/.f64 (+.f64 x y) (+.f64 y 1))

rewrite48.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
565×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
75×	`add-log-exp_binary64`

Counts

1 → 36

Calls

1 calls:

47.0ms

(/.f64 (+.f64 x y) (+.f64 y 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	157	10
2	2144	10
3	6402	10
0	0	0
1	0	0

simplify75.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

580×	`cancel-sign-sub-inv_binary64`
514×	`+-commutative_binary64`
493×	`associate-+l-_binary64`
368×	`associate--r+_binary64`
312×	`sub-neg_binary64`

Counts

60 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	419
1	133	414
2	412	407
3	1581	405
4	3925	405
5	4824	405
6	5046	405

prune45.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Error

Counts

57 → 4

Alt Table

Status	Error	Program
	13.9b	(*.f64 (/.f64 (+.f64 x y) (fma.f64 y y -1)) (-.f64 y 1))
▶	0.0b	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
	0.2b	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)
	0.7b	(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (+.f64 y 1)) 2)) (/.f64 (+.f64 x y) (cbrt.f64 (+.f64 y 1))))

Compiler

Compiled 831 to 486 computations (41.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
✓	0.0b	(/.f64 x (+.f64 1 y))
✓	0.0b	(/.f64 y (+.f64 1 y))

series23.0ms (1%)

Counts

3 → 45

Calls

3 calls:

11.0ms	(/.f64 x (+.f64 1 y))
9.0ms	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
2.0ms	(/.f64 y (+.f64 1 y))

rewrite78.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

503×	`fma-def_binary64`
491×	`log-prod_binary64`
243×	`fma-neg_binary64`
229×	`log-div_binary64`
172×	`egg-rr`

Counts

3 → 172

Calls

3 calls:

75.0ms	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
75.0ms	(/.f64 x (+.f64 1 y))
75.0ms	(/.f64 y (+.f64 1 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	185	27
2	2793	27
3	5705	27
0	0	0
1	0	0

simplify72.0ms (3%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
488×	`fma-neg_binary64`
454×	`sub-neg_binary64`
399×	`associate--r+_binary64`
265×	`associate--l+_binary64`

Counts

217 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	691
1	198	680
2	613	665
3	2140	657
4	4474	657
5	5207	657

prune169.0ms (7.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	214	4	218

Error

Counts

218 → 4

Alt Table

Status	Error	Program
	13.9b	(*.f64 (/.f64 (+.f64 x y) (fma.f64 y y -1)) (-.f64 y 1))
✓	0.0b	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
▶	0.2b	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)
	2.9b	(+.f64 (/.f64 x (+.f64 1 y)) (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y 1)) 3)))

Compiler

Compiled 3824 to 2488 computations (34.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 y 1) (+.f64 x y))
✓	0.2b	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)

series44.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

33.0ms	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)
11.0ms	(/.f64 (+.f64 y 1) (+.f64 x y))

rewrite89.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

820×	`prod-diff_binary64`
251×	`fma-def_binary64`
169×	`log1p-udef_binary64`
168×	`expm1-udef_binary64`
159×	`fma-neg_binary64`

Counts

2 → 82

Calls

2 calls:

87.0ms	(/.f64 (+.f64 y 1) (+.f64 x y))
87.0ms	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	199	20
2	2526	20
3	4873	20
4	5400	20
0	0	0
1	0	0

simplify107.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

321×	`sub-neg_binary64`
317×	`associate-+r+_binary64`
266×	`+-commutative_binary64`
255×	`cancel-sign-sub-inv_binary64`
249×	`associate-+l+_binary64`

Counts

130 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	242	2511
1	748	2502
2	3211	2345
3	4844	2345
4	4985	2345
5	4971	2345

prune151.0ms (6.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	144	4	148

Error

Counts

148 → 4

Alt Table

Status	Error	Program
	13.9b	(*.f64 (/.f64 (+.f64 x y) (fma.f64 y y -1)) (-.f64 y 1))
✓	0.0b	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
✓	0.2b	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)
▶	2.9b	(+.f64 (/.f64 x (+.f64 1 y)) (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y 1)) 3)))

Compiler

Compiled 3979 to 2504 computations (37.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 1 y))
✓	0.0b	(/.f64 y (+.f64 y 1))
✓	0.0b	(pow.f64 (/.f64 y (+.f64 y 1)) 3)
✓	19.5b	(cbrt.f64 (pow.f64 (/.f64 y (+.f64 y 1)) 3))

series10.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(cbrt.f64 (pow.f64 (/.f64 y (+.f64 y 1)) 3))
2.0ms	(pow.f64 (/.f64 y (+.f64 y 1)) 3)
2.0ms	(/.f64 y (+.f64 y 1))

rewrite53.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

740×	`log1p-expm1-u_binary64`
740×	`expm1-log1p-u_binary64`
126×	`egg-rr`
123×	`log1p-udef_binary64`
122×	`expm1-udef_binary64`

Counts

3 → 126

Calls

3 calls:

50.0ms	(/.f64 y (+.f64 y 1))
50.0ms	(pow.f64 (/.f64 y (+.f64 y 1)) 3)
50.0ms	(cbrt.f64 (pow.f64 (/.f64 y (+.f64 y 1)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	157	24
2	1868	24
3	4943	24
0	0	0
1	0	0

simplify76.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
492×	`associate-l_binary64`
453×	`cancel-sign-sub-inv_binary64`
426×	`associate-r_binary64`
383×	`times-frac_binary64`

Counts

162 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	464
1	157	456
2	422	442
3	1160	440
4	3848	440
5	4837	440
6	5005	440

prune140.0ms (5.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
	13.9b	(*.f64 (/.f64 (+.f64 x y) (fma.f64 y y -1)) (-.f64 y 1))
✓	0.0b	(+.f64 (/.f64 x (+.f64 1 y)) (/.f64 y (+.f64 1 y)))
✓	0.2b	(pow.f64 (/.f64 (+.f64 y 1) (+.f64 x y)) -1)
✓	2.9b	(+.f64 (/.f64 x (+.f64 1 y)) (cbrt.f64 (pow.f64 (/.f64 y (+.f64 y 1)) 3)))

Compiler

Compiled 3170 to 2227 computations (29.7% saved)

regimes240.0ms (10.1%)

Accuracy

Total 0.0b remaining (84.2%)

Threshold costs 0.0b (84.2%)

Counts

83 → 1

Compiler

Compiled 3020 to 2182 computations (27.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	12	10
2	11	10

end68.0ms (2.8%)

Compiler: Compiled 72 to 50 computations (30.6% saved)

Details

analyze61.0ms (2.5%)

sample796.0ms (33.4%)

simplify6.0ms (0.2%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite48.0ms (2%)

simplify75.0ms (3.2%)

prune45.0ms (1.9%)

localize5.0ms (0.2%)

series23.0ms (1%)

rewrite78.0ms (3.3%)

simplify72.0ms (3%)

prune169.0ms (7.1%)

localize5.0ms (0.2%)

series44.0ms (1.8%)

rewrite89.0ms (3.7%)

simplify107.0ms (4.5%)

prune151.0ms (6.3%)

localize9.0ms (0.4%)

series10.0ms (0.4%)

rewrite53.0ms (2.2%)

simplify76.0ms (3.2%)

prune140.0ms (5.9%)

regimes240.0ms (10.1%)

simplify2.0ms (0.1%)

end68.0ms (2.8%)

Profiling