Details

analyze713.0ms (10.4%)

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
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample2.1s (30.1%)

Results

724.0ms	6054×	body	128	valid
410.0ms	1043×	body	1024	valid
203.0ms	693×	body	512	valid
173.0ms	522×	body	1024	invalid
147.0ms	1507×	body	128	invalid
95.0ms	354×	body	512	invalid
78.0ms	387×	body	256	valid
45.0ms	79×	body	2048	valid
43.0ms	219×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify203.0ms (3%)

Algorithm

1×	egg-herbie

Rules

2748×	`fma-def_binary64`
1264×	`fma-neg_binary64`
934×	`associate--r-_binary64`
475×	`cancel-sign-sub-inv_binary64`
423×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	17
2	40	17
3	86	15
4	163	15
5	344	15
6	666	15
7	1217	15
8	1463	15
9	1608	15
10	1787	15
11	2322	15
12	2926	15
13	2987	15
14	3089	15
15	3133	15
16	3142	15
17	3142	15
18	3225	15
19	3233	15
20	3237	15
21	4979	15

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

20.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	20.4b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))

Compiler

Compiled 76 to 57 computations (25% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
✓	2.4b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
✓	4.6b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

series101.0ms (1.5%)

Counts

4 → 96

Calls

4 calls:

48.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
37.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
9.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
7.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

rewrite95.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`add-sqr-sqrt_binary64`
308×	`*-un-lft-identity_binary64`
186×	`times-frac_binary64`
125×	`add-cube-cbrt_binary64`
120×	`prod-diff_binary64`

Counts

4 → 330

Calls

4 calls:

17.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
17.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
16.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
6.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

simplify305.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

336×	`fma-def_binary64`
264×	`sub-neg_binary64`
259×	`associate-/r*_binary64`
224×	`+-commutative_binary64`
215×	`associate-/l*_binary64`

Counts

426 → 482

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	720	18151
1	2204	14737
2	4965	14737
3	4971	14737

prune425.0ms (6.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	480	2	482
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	481	3	484

Error

Counts

484 → 3

Alt Table

Status	Error	Program
▶	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
	36.3b	(-.f64 1 (log.f64 (-.f64 (+.f64 (/.f64 x y) (/.f64 x (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 2))))))
	20.4b	(log.f64 (/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))

Compiler

Compiled 19508 to 12326 computations (36.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	2.3b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series89.0ms (1.3%)

Counts

3 → 72

Calls

3 calls:

45.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
37.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
7.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

3 → 97

Calls

3 calls:

7.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))
3.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
0.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify108.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-+l+_binary64`
242×	`associate--r+_binary64`
240×	`associate-/r*_binary64`
221×	`fma-def_binary64`
201×	`+-commutative_binary64`

Counts

169 → 262

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	510	6989
1	1448	6687
2	5068	6687

prune212.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	262	3	265

Error

Counts

265 → 3

Alt Table

Status	Error	Program
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
	36.3b	(-.f64 1 (log.f64 (-.f64 (+.f64 (/.f64 x y) (/.f64 x (pow.f64 y 2))) (+.f64 (/.f64 1 y) (/.f64 1 (pow.f64 y 2))))))
▶	20.4b	(log.f64 (/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))

Compiler

Compiled 9801 to 6615 computations (32.5% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
✓	0.0b	(log.f64 (/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
✓	0.1b	(/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
	2.4b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))

series419.0ms (6.1%)

Counts

2 → 48

Calls

2 calls:

348.0ms	(log.f64 (/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
70.0ms	(/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`add-sqr-sqrt_binary64`
62×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
30×	`log-prod_binary64`
28×	`difference-of-squares_binary64`

Counts

2 → 96

Calls

2 calls:

20.0ms	(log.f64 (/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
13.0ms	(/.f64 (E.f64) (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))

simplify278.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

425×	`+-commutative_binary64`
378×	`associate-+r+_binary64`
271×	`*-commutative_binary64`
245×	`fma-def_binary64`
205×	`associate-/r*_binary64`

Counts

144 → 206

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1172	17352
1	4241	15992
2	4985	15992
3	4972	15992

prune638.0ms (9.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	469	1	470
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	471	2	473

Error

Counts

473 → 2

Alt Table

Status	Error	Program
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 (E.f64) y) (-.f64 1 x))))

Compiler

Compiled 29846 to 19844 computations (33.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 (E.f64) y) (-.f64 1 x))))
✓	0.1b	(/.f64 (*.f64 (E.f64) y) (-.f64 1 x))
✓	0.2b	(/.f64 (E.f64) (-.f64 1 x))
✓	0.3b	(*.f64 (E.f64) y)

series44.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

26.0ms	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 (E.f64) y) (-.f64 1 x))))
13.0ms	(/.f64 (*.f64 (E.f64) y) (-.f64 1 x))
3.0ms	(/.f64 (E.f64) (-.f64 1 x))
2.0ms	(*.f64 (E.f64) y)

rewrite42.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

4 → 121

Calls

4 calls:

25.0ms	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 (E.f64) y) (-.f64 1 x))))
5.0ms	(/.f64 (*.f64 (E.f64) y) (-.f64 1 x))
4.0ms	(/.f64 (E.f64) (-.f64 1 x))
2.0ms	(*.f64 (E.f64) y)

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

446×	`times-frac_binary64`
373×	`associate-/l*_binary64`
273×	`associate-/r*_binary64`
185×	`associate-r_binary64`
181×	`associate-+l+_binary64`

Counts

193 → 246

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	4782
1	1154	4418
2	4908	4418
3	5000	4418

prune168.0ms (2.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	246	2	248

Error

Counts

248 → 2

Alt Table

Status	Error	Program
✓	20.4b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 (E.f64) y) (-.f64 1 x))))

Compiler

Compiled 6600 to 4024 computations (39% saved)

regimes666.0ms (9.7%)

Accuracy

Total 0.0b remaining (67.5%)

Threshold costs 0.0b (67.5%)

Counts

127 → 1

Compiler

Compiled 11224 to 9051 computations (19.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	19	23
2	28	23
3	40	23
4	48	23
5	53	23
6	55	23
7	54	23

end47.0ms (0.7%)

Compiler: Compiled 60 to 45 computations (25% saved)

Details

analyze713.0ms (10.4%)

sample2.1s (30.1%)

simplify203.0ms (3%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series101.0ms (1.5%)

rewrite95.0ms (1.4%)

simplify305.0ms (4.5%)

prune425.0ms (6.2%)

localize6.0ms (0.1%)

series89.0ms (1.3%)

rewrite17.0ms (0.2%)

simplify108.0ms (1.6%)

prune212.0ms (3.1%)

localize7.0ms (0.1%)

series419.0ms (6.1%)

rewrite44.0ms (0.6%)

simplify278.0ms (4.1%)

prune638.0ms (9.3%)

localize11.0ms (0.2%)

series44.0ms (0.6%)

rewrite42.0ms (0.6%)

simplify120.0ms (1.8%)

prune168.0ms (2.5%)

regimes666.0ms (9.7%)

simplify4.0ms (0.1%)

end47.0ms (0.7%)

Profiling