Details

analyze700.0ms (11.2%)

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
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)

sample2.0s (31.7%)

Results

689.0ms	6012×	body	128	valid
424.0ms	1100×	body	1024	valid
199.0ms	560×	body	1024	invalid
196.0ms	666×	body	512	valid
171.0ms	1570×	body	128	invalid
94.0ms	353×	body	512	invalid
78.0ms	397×	body	256	valid
46.0ms	81×	body	2048	valid
39.0ms	208×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1074×	`fma-def_binary64`
781×	`fma-neg_binary64`
314×	`div-sub_binary64`
282×	`times-frac_binary64`
194×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	17
2	40	17
3	86	15
4	196	15
5	431	15
6	1016	15
7	2510	15
8	4117	15
9	4867	15

Stop Event

1×	node limit

Counts

1 → 2

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

17.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.2b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize9.0ms (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))
✓	2.7b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series93.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

47.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
39.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
7.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite59.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

338×	`fma-def_binary64`
204×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
174×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	225	37
2	3223	37

Stop Event

1×	node limit

Counts

3 → 113

Calls

3 calls:

57.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
57.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))
57.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify59.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

661×	`associate-+r+_binary64`
407×	`associate-+l+_binary64`
237×	`associate--r+_binary64`
225×	`associate-/r*_binary64`
193×	`associate--l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	366	4967
1	1282	4869

Stop Event

1×	node limit

Counts

185 → 229

prune246.0ms (3.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	224	5	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	5	230

Error

0.1b

Counts

230 → 5

Alt Table

Status	Error	Program
	40.9b	(-.f64 (+.f64 1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 -1 (+.f64 y -1))))
	56.4b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))
	17.2b	(log.f64 (/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)))
▶	17.2b	(-.f64 1 (log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))))
	50.9b	(-.f64 1 (+.f64 (+.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 1/3 (.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3)))) (-.f64 (+.f64 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (/.f64 1 (.f64 y y))) (.f64 (/.f64 x (pow.f64 y 3)) (/.f64 x (pow.f64 (-.f64 1 x) 3)))) (+.f64 (log.f64 (/.f64 -1 y)) (/.f64 x (.f64 y (.f64 y (pow.f64 (-.f64 1 x) 2)))))) (+.f64 (fma.f64 1/2 (.f64 (/.f64 x (.f64 y y)) (/.f64 x (pow.f64 (-.f64 1 x) 2))) (/.f64 (/.f64 1/2 (.f64 y y)) (pow.f64 (-.f64 1 x) 2))) (+.f64 (fma.f64 1/3 (/.f64 (pow.f64 x 3) (.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (/.f64 (/.f64 x (-.f64 1 x)) y)) (/.f64 x (*.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))))))))

Compiler

Compiled 9041 to 6293 computations (30.4% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 y 1))
✓	0.0b	(-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))
✓	0.0b	(/.f64 x (-.f64 y 1))
✓	2.7b	(log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1))))

series55.0ms (0.9%)

Counts

4 → 63

Calls

4 calls:

36.0ms	(log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1))))
9.0ms	(/.f64 x (-.f64 y 1))
9.0ms	(-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))
2.0ms	(/.f64 y (-.f64 y 1))

rewrite72.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

470×	`fma-def_binary64`
283×	`fma-neg_binary64`
256×	`egg-rr`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	209	36
2	3304	36

Stop Event

1×	node limit

Counts

4 → 256

Calls

4 calls:

67.0ms	(/.f64 y (-.f64 y 1))
67.0ms	(-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))
67.0ms	(/.f64 x (-.f64 y 1))
67.0ms	(log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1))))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

489×	`associate-+r+_binary64`
390×	`sub-neg_binary64`
340×	`+-commutative_binary64`
314×	`associate-+l+_binary64`
226×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	2846
1	974	2788
2	4360	2756

Stop Event

1×	node limit

Counts

319 → 351

prune283.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	350	1	351
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	352	4	356

Error

0.1b

Counts

356 → 4

Alt Table

Status	Error	Program
	47.2b	(-.f64 1 (+.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (-.f64 (-.f64 (+.f64 (/.f64 1/3 (.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3))) (+.f64 (+.f64 (/.f64 (/.f64 x (.f64 y y)) (pow.f64 (-.f64 1 x) 2)) (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (/.f64 1 (.f64 y y))) (.f64 (/.f64 x (pow.f64 y 3)) (/.f64 x (pow.f64 (-.f64 1 x) 3))))) (log.f64 (/.f64 -1 y)))) (/.f64 x (.f64 (pow.f64 y 3) (pow.f64 (-.f64 1 x) 3)))) (+.f64 (fma.f64 1/3 (/.f64 (pow.f64 (/.f64 x (-.f64 1 x)) 3) (pow.f64 y 3)) (/.f64 (/.f64 x y) (-.f64 1 x))) (fma.f64 1/2 (.f64 (/.f64 x (.f64 y y)) (/.f64 x (pow.f64 (-.f64 1 x) 2))) (/.f64 (/.f64 1/2 (*.f64 y y)) (pow.f64 (-.f64 1 x) 2)))))))
	56.4b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))
▶	17.2b	(log.f64 (/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)))
✓	17.2b	(-.f64 1 (log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))))

Compiler

Compiled 10263 to 7144 computations (30.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)))
	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	0.2b	(/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1))
✓	2.7b	(+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)

series433.0ms (6.9%)

Counts

3 → 72

Calls

3 calls:

359.0ms	(log.f64 (/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)))
64.0ms	(/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1))
9.0ms	(+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)

rewrite67.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

960×	`prod-diff_binary64`
135×	`add-sqr-sqrt_binary64`
128×	`add-cbrt-cube_binary64`
128×	`log1p-expm1-u_binary64`
128×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	48
1	268	45
2	3880	45

Stop Event

1×	node limit

Counts

3 → 99

Calls

3 calls:

65.0ms	(log.f64 (/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)))
65.0ms	(/.f64 (E.f64) (+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1))
65.0ms	(+.f64 (/.f64 (-.f64 x y) (+.f64 y -1)) 1)

simplify157.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

462×	`+-commutative_binary64`
409×	`associate-+r+_binary64`
269×	`*-commutative_binary64`
269×	`fma-def_binary64`
200×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1106	14786
1	4443	13566

Stop Event

1×	node limit

Counts

171 → 211

prune464.0ms (7.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	283	2	285
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	286	3	289

Error

Counts

289 → 3

Alt Table

Status	Error	Program
	17.2b	(log.f64 (/.f64 (E.f64) (-.f64 (+.f64 (/.f64 x (-.f64 y 1)) 1) (/.f64 y (-.f64 y 1)))))
▶	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 y (E.f64)) (-.f64 1 x))))
✓	17.2b	(-.f64 1 (log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))))

Compiler

Compiled 21195 to 15444 computations (27.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series28.0ms (0.5%)

Counts

4 → 60

Calls

4 calls:

12.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 y (E.f64)) (-.f64 1 x)))
11.0ms	(/.f64 (*.f64 y (E.f64)) (-.f64 1 x))
3.0ms	(/.f64 (E.f64) (-.f64 1 x))
2.0ms	(*.f64 y (E.f64))

rewrite92.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

471×	`fma-def_binary64`
264×	`fma-neg_binary64`
255×	`egg-rr`
210×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	228	38
2	3630	38

Stop Event

1×	node limit

Counts

4 → 255

Calls

4 calls:

86.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (*.f64 y (E.f64)) (-.f64 1 x)))
86.0ms	(/.f64 (*.f64 y (E.f64)) (-.f64 1 x))
86.0ms	(/.f64 (E.f64) (-.f64 1 x))
86.0ms	(*.f64 y (E.f64))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

460×	`fma-def_binary64`
396×	`times-frac_binary64`
382×	`associate--r+_binary64`
299×	`associate--l+_binary64`
253×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1397
1	337	1359
2	986	1206
3	4566	1206

Stop Event

1×	node limit

Counts

315 → 313

prune233.0ms (3.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	314	2	316

Error

Counts

316 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (/.f64 y (-.f64 1 x)) (E.f64))))
✓	17.2b	(-.f64 1 (log1p.f64 (-.f64 (/.f64 x (-.f64 y 1)) (/.f64 y (-.f64 y 1)))))

Compiler

Compiled 7600 to 4809 computations (36.7% saved)

regimes1.0s (16%)

Accuracy

Total 0.0b remaining (46.7%)

Threshold costs 0.0b (46.7%)

Counts

180 → 1

Compiler

Compiled 19010 to 14848 computations (21.9% saved)

simplify3.0ms (0%)

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	22	23
2	38	23
3	48	23
4	55	23
5	57	23

Stop Event

1×

saturated

end49.0ms (0.8%)

Compiler: Compiled 64 to 48 computations (25% saved)

Details

analyze700.0ms (11.2%)

sample2.0s (31.7%)

simplify34.0ms (0.5%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series93.0ms (1.5%)

rewrite59.0ms (0.9%)

simplify59.0ms (0.9%)

prune246.0ms (3.9%)

localize7.0ms (0.1%)

series55.0ms (0.9%)

rewrite72.0ms (1.1%)

simplify64.0ms (1%)

prune283.0ms (4.5%)

localize8.0ms (0.1%)

series433.0ms (6.9%)

rewrite67.0ms (1.1%)

simplify157.0ms (2.5%)

prune464.0ms (7.4%)

localize8.0ms (0.1%)

series28.0ms (0.5%)

rewrite92.0ms (1.5%)

simplify54.0ms (0.9%)

prune233.0ms (3.7%)

regimes1.0s (16%)

simplify3.0ms (0%)

end49.0ms (0.8%)

Profiling