Details

analyze730.0ms (5.1%)

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 (14.8%)

Results

727.0ms	6047×	body	128	valid
437.0ms	1043×	body	1024	valid
206.0ms	697×	body	512	valid
195.0ms	510×	body	1024	invalid
165.0ms	1501×	body	128	invalid
86.0ms	344×	body	512	invalid
83.0ms	385×	body	256	valid
43.0ms	84×	body	2048	valid
40.0ms	184×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify204.0ms (1.4%)

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

1 alts after pruning (1 fresh and 0 done)

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

Error

16.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.8b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	0.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	1.8b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series132.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

75.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
49.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
8.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite16.0ms (0.1%)

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:

6.0ms	(/.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)))

simplify110.0ms (0.8%)

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

prune225.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	259	4	263

Error

0.1b

Counts

263 → 4

Alt Table

Status	Error	Program
▶	16.8b	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
	57.6b	(+.f64 (-.f64 1 (log.f64 x)) (log.f64 (-.f64 y 1)))
	46.6b	(-.f64 1 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))))
✓	16.8b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 9799 to 6617 computations (32.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 y 1))
✓	0.2b	(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
✓	1.8b	(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))

series787.0ms (5.5%)

Counts

4 → 96

Calls

4 calls:

674.0ms	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
94.0ms	(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
11.0ms	(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))
8.0ms	(/.f64 (-.f64 x y) (-.f64 y 1))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
59×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`

Counts

4 → 152

Calls

4 calls:

13.0ms	(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
11.0ms	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
11.0ms	(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))
7.0ms	(/.f64 (-.f64 x y) (-.f64 y 1))

simplify244.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

475×	`+-commutative_binary64`
413×	`associate-+r+_binary64`
279×	`*-commutative_binary64`
271×	`fma-def_binary64`
221×	`sub-neg_binary64`

Counts

248 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1303	18604
1	4583	17764
2	4983	17764

prune448.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	294	2	296

Error

0.0b

Counts

296 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
✓	16.8b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 22087 to 15826 computations (28.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 x) y)
✓	0.0b	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y)))
✓	0.2b	(/.f64 (E.f64) (-.f64 1 x))
✓	0.4b	(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))

series37.0ms (0.3%)

Counts

4 → 76

Calls

4 calls:

17.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y)))
11.0ms	(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))
6.0ms	(/.f64 (-.f64 1 x) y)
3.0ms	(/.f64 (E.f64) (-.f64 1 x))

rewrite683.0ms (4.8%)

Algorithm

1×	rewrite-expression-head

Rules

4491×	`times-frac_binary64`
3542×	`add-sqr-sqrt_binary64`
3538×	`*-un-lft-identity_binary64`
2138×	`add-cube-cbrt_binary64`
1704×	`prod-diff_binary64`

Counts

4 → 2025

Calls

4 calls:

86.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y)))
10.0ms	(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))
5.0ms	(/.f64 (-.f64 1 x) y)
4.0ms	(/.f64 (E.f64) (-.f64 1 x))

simplify4.3s (30.1%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-udef_binary64`
788×	`unsub-neg_binary64`
334×	`times-frac_binary64`
214×	`sub-neg_binary64`
174×	`neg-sub0_binary64`

Counts

2101 → 2405

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1497	211559
1	3522	200060
2	4644	196944
3	5233	196944

prune2.9s (20.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	2404	1	2405
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	2405	2	2407

Error

Counts

2407 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)))
✓	16.8b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 165414 to 92752 computations (43.9% saved)

localize13.0ms (0.1%)

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) (-.f64 1 x)) y)))
✓	0.0b	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y))
	0.2b	(/.f64 (E.f64) (-.f64 1 x))
✓	0.3b	(*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)

series71.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

45.0ms	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)))
15.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y))
10.0ms	(*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
55×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
24×	`fma-neg_binary64`

Counts

3 → 128

Calls

3 calls:

9.0ms	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)))
9.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y))
8.0ms	(*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)

simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

310×	`times-frac_binary64`
254×	`associate-/l*_binary64`
241×	`associate-/r*_binary64`
208×	`associate-+r+_binary64`
191×	`associate-+l+_binary64`

Counts

200 → 300

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	435	6591
1	1204	5667
2	5050	5667

prune316.0ms (2.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	422	2	424

Error

Counts

424 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 (E.f64) (-.f64 1 x)) y)))
✓	16.8b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 11175 to 6739 computations (39.7% saved)

regimes680.0ms (4.8%)

Accuracy

Total 0.0b remaining (45.1%)

Threshold costs 0.0b (45.1%)

Counts

132 → 1

Compiler

Compiled 13712 to 10282 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	24	31
2	36	31
3	45	31
4	50	31
5	51	31
6	50	31

end49.0ms (0.3%)

Compiler: Compiled 68 to 49 computations (27.9% saved)

Details

analyze730.0ms (5.1%)

sample2.1s (14.8%)

simplify204.0ms (1.4%)

prune3.0ms (0%)

localize6.0ms (0%)

series132.0ms (0.9%)

rewrite16.0ms (0.1%)

simplify110.0ms (0.8%)

prune225.0ms (1.6%)

localize8.0ms (0.1%)

series787.0ms (5.5%)

rewrite52.0ms (0.4%)

simplify244.0ms (1.7%)

prune448.0ms (3.1%)

localize8.0ms (0.1%)

series37.0ms (0.3%)

rewrite683.0ms (4.8%)

simplify4.3s (30.1%)

prune2.9s (20.3%)

localize13.0ms (0.1%)

series71.0ms (0.5%)

rewrite36.0ms (0.3%)

simplify109.0ms (0.8%)

prune316.0ms (2.2%)

regimes680.0ms (4.8%)

simplify3.0ms (0%)

end49.0ms (0.3%)

Profiling