Details

analyze399.0ms (5.8%)

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
0%	99.9%	0.1%	4
0%	87.4%	12.6%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
12.5%	56.2%	31.4%	8
14%	48.4%	37.6%	9
21.1%	41.3%	37.6%	10
26.9%	32.4%	40.7%	11
28.7%	27.5%	43.8%	12
33.4%	22.7%	43.8%	13
37.2%	17.4%	45.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (15.9%)

Results

952.0ms	8256×	body	128	valid
80.0ms	829×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1663×	`fma-def_binary64`
528×	`fma-neg_binary64`
288×	`distribute-rgt-in_binary64`
230×	`unsub-neg_binary64`
193×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	15	12
2	23	12
3	39	12
4	98	12
5	231	12
6	474	12
7	898	12
8	1256	12
9	2133	12
10	3636	12
11	4010	12
12	4136	12
13	4175	12
14	4189	12

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

18.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	18.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))

Compiler

Compiled 41 to 23 computations (43.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
✓	17.5b	(log.f64 (/.f64 x y))

series572.0ms (8.3%)

Counts

2 → 60

Calls

2 calls:

328.0ms	(log.f64 (/.f64 x y))
243.0ms	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))

rewrite62.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

710×	`log1p-expm1-u_binary64`
710×	`expm1-log1p-u_binary64`
191×	`egg-rr`
165×	`prod-diff_binary64`
137×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	165	16
2	2154	16

Stop Event

1×	node limit

Counts

2 → 191

Calls

2 calls:

57.0ms	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
57.0ms	(log.f64 (/.f64 x y))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
410×	`unsub-neg_binary64`
305×	`sub-neg_binary64`
289×	`distribute-rgt-in_binary64`
230×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	558
1	125	540
2	268	540
3	669	540
4	2021	540
5	3640	540
6	4344	540
7	4799	540
8	4924	540
9	4973	540
10	4981	540

Stop Event

1×	node limit

Counts

251 → 209

prune117.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	199	10	209
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	199	11	210

Error

0.0b

Counts

210 → 11

Alt Table

Status	Error	Program
	32.9b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
	32.9b	(fma.f64 x (/.f64 (-.f64 (.f64 (log.f64 x) (log.f64 x)) (.f64 (log.f64 y) (log.f64 y))) (+.f64 (log.f64 x) (log.f64 y))) (neg.f64 z))
	32.9b	(fma.f64 x (/.f64 (-.f64 (pow.f64 (log.f64 x) 3) (pow.f64 (log.f64 y) 3)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (+.f64 (.f64 (log.f64 y) (log.f64 y)) (*.f64 (log.f64 x) (log.f64 y))))) (neg.f64 z))
▶	31.4b	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))
✓	18.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
	51.4b	(+.f64 (fma.f64 (*.f64 x (sqrt.f64 (log.f64 (/.f64 x y)))) (sqrt.f64 (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	44.6b	(+.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 (/.f64 x y))) 2)) (cbrt.f64 (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	50.9b	(fma.f64 x (+.f64 (fma.f64 (sqrt.f64 (log.f64 x)) (sqrt.f64 (log.f64 x)) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (neg.f64 z))
	55.9b	(+.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	54.4b	(pow.f64 (sqrt.f64 (fma.f64 x (log.f64 (/.f64 x y)) z)) 2)
	31.6b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)

Compiler

Compiled 5065 to 1527 computations (69.9% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))
✓	0.3b	(-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))

series702.0ms (10.2%)

Counts

2 → 60

Calls

2 calls:

384.0ms	(-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))
318.0ms	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))

rewrite67.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

903×	`expm1-log1p-u_binary64`
505×	`prod-diff_binary64`
204×	`egg-rr`
117×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	231	16
2	3180	16

Stop Event

1×	node limit

Counts

2 → 204

Calls

2 calls:

62.0ms	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))
62.0ms	(-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

523×	`sub-neg_binary64`
509×	`fma-def_binary64`
415×	`unsub-neg_binary64`
284×	`distribute-rgt-in_binary64`
228×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	1081
1	184	909
2	448	900
3	1158	704
4	3397	704
5	4771	704

Stop Event

1×	node limit

Counts

264 → 228

prune115.0ms (1.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	228	11	239

Error

0.0b

Counts

239 → 11

Alt Table

Status	Error	Program
	50.9b	(fma.f64 x (+.f64 (fma.f64 (sqrt.f64 (log.f64 x)) (sqrt.f64 (log.f64 x)) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (neg.f64 z))
▶	31.6b	(-.f64 (.f64 (log.f64 (neg.f64 x)) x) (+.f64 (.f64 (log.f64 (neg.f64 y)) x) z))
	32.9b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
	33.0b	(fma.f64 x (fma.f64 (pow.f64 (cbrt.f64 (log.f64 x)) 2) (cbrt.f64 (log.f64 x)) (neg.f64 (log.f64 y))) (neg.f64 z))
	32.9b	(fma.f64 x (/.f64 (-.f64 (pow.f64 (log.f64 x) 3) (pow.f64 (log.f64 y) 3)) (+.f64 (.f64 (log.f64 x) (log.f64 x)) (+.f64 (.f64 (log.f64 y) (log.f64 y)) (*.f64 (log.f64 x) (log.f64 y))))) (neg.f64 z))
✓	31.4b	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))
✓	18.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
	51.4b	(+.f64 (fma.f64 (*.f64 x (sqrt.f64 (log.f64 (/.f64 x y)))) (sqrt.f64 (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	44.6b	(+.f64 (fma.f64 (*.f64 x (pow.f64 (cbrt.f64 (log.f64 (/.f64 x y))) 2)) (cbrt.f64 (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	55.9b	(+.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	54.4b	(pow.f64 (sqrt.f64 (fma.f64 x (log.f64 (/.f64 x y)) z)) 2)

Compiler

Compiled 5378 to 1662 computations (69.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (log.f64 (neg.f64 y)) x) z)
✓	0.1b	(*.f64 (log.f64 (neg.f64 y)) x)
✓	0.2b	(*.f64 (log.f64 (neg.f64 x)) x)
✓	0.3b	(-.f64 (.f64 (log.f64 (neg.f64 x)) x) (+.f64 (.f64 (log.f64 (neg.f64 y)) x) z))

series661.0ms (9.6%)

Counts

4 → 69

Calls

4 calls:

317.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x)) x) (+.f64 (.f64 (log.f64 (neg.f64 y)) x) z))
214.0ms	(*.f64 (log.f64 (neg.f64 y)) x)
100.0ms	(+.f64 (*.f64 (log.f64 (neg.f64 y)) x) z)
29.0ms	(*.f64 (log.f64 (neg.f64 x)) x)

rewrite70.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

666×	`fma-def_binary64`
332×	`fma-neg_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
197×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	261	33
2	3732	33

Stop Event

1×	node limit

Counts

4 → 197

Calls

4 calls:

65.0ms	(+.f64 (*.f64 (log.f64 (neg.f64 y)) x) z)
65.0ms	(*.f64 (log.f64 (neg.f64 y)) x)
65.0ms	(*.f64 (log.f64 (neg.f64 x)) x)
65.0ms	(-.f64 (.f64 (log.f64 (neg.f64 x)) x) (+.f64 (.f64 (log.f64 (neg.f64 y)) x) z))

simplify47.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
536×	`sub-neg_binary64`
358×	`fma-neg_binary64`
261×	`associate-+l-_binary64`
246×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	991
1	190	804
2	478	801
3	1378	721
4	4238	721

Stop Event

1×	node limit

Counts

266 → 229

prune117.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	230	10	240

Error

0.0b

Counts

240 → 10

Alt Table

Status	Error	Program
	50.9b	(fma.f64 x (+.f64 (fma.f64 (sqrt.f64 (log.f64 x)) (sqrt.f64 (log.f64 x)) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (neg.f64 z))
✓	31.6b	(-.f64 (.f64 (log.f64 (neg.f64 x)) x) (+.f64 (.f64 (log.f64 (neg.f64 y)) x) z))
▶	32.9b	(fma.f64 x (-.f64 (log.f64 x) (log.f64 y)) (*.f64 -1 z))
	55.9b	(+.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	32.9b	(fma.f64 x (log.f64 x) (neg.f64 (fma.f64 x (log.f64 y) z)))
	54.4b	(pow.f64 (sqrt.f64 (fma.f64 x (log.f64 (/.f64 x y)) z)) 2)
	32.9b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
✓	31.4b	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))
✓	18.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
	51.4b	(+.f64 (fma.f64 (*.f64 x (sqrt.f64 (log.f64 (/.f64 x y)))) (sqrt.f64 (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))

Compiler

Compiled 4789 to 1196 computations (75% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 (log.f64 x) (log.f64 y)) (*.f64 -1 z))
✓	0.3b	(-.f64 (log.f64 x) (log.f64 y))

series581.0ms (8.4%)

Counts

2 → 52

Calls

2 calls:

316.0ms	(-.f64 (log.f64 x) (log.f64 y))
264.0ms	(fma.f64 x (-.f64 (log.f64 x) (log.f64 y)) (*.f64 -1 z))

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

885×	`expm1-log1p-u_binary64`
519×	`prod-diff_binary64`
213×	`egg-rr`
101×	`add-sqr-sqrt_binary64`
95×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	202	16
2	2579	16

Stop Event

1×	node limit

Counts

2 → 213

Calls

2 calls:

68.0ms	(fma.f64 x (-.f64 (log.f64 x) (log.f64 y)) (*.f64 -1 z))
68.0ms	(-.f64 (log.f64 x) (log.f64 y))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

417×	`unsub-neg_binary64`
417×	`fma-def_binary64`
351×	`sub-neg_binary64`
227×	`distribute-rgt-in_binary64`
212×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	666
1	143	590
2	382	590
3	1040	590
4	3072	590
5	3946	590
6	4495	590
7	4734	590
8	4764	590
9	4771	590

Stop Event

1×	node limit

Counts

265 → 230

prune109.0ms (1.6%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	230	10	240

Error

0.0b

Counts

240 → 10

Alt Table

Status	Error	Program
	50.9b	(fma.f64 x (+.f64 (fma.f64 (sqrt.f64 (log.f64 x)) (sqrt.f64 (log.f64 x)) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (neg.f64 z))
✓	31.6b	(-.f64 (.f64 (log.f64 (neg.f64 x)) x) (+.f64 (.f64 (log.f64 (neg.f64 y)) x) z))
✓	32.9b	(fma.f64 x (-.f64 (log.f64 x) (log.f64 y)) (*.f64 -1 z))
	55.9b	(+.f64 (fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))
	32.9b	(fma.f64 x (log.f64 x) (neg.f64 (fma.f64 x (log.f64 y) z)))
	54.4b	(pow.f64 (sqrt.f64 (fma.f64 x (log.f64 (/.f64 x y)) z)) 2)
	32.9b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
✓	31.4b	(fma.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y))) (neg.f64 z))
✓	18.1b	(fma.f64 x (log.f64 (/.f64 x y)) (neg.f64 z))
	51.4b	(+.f64 (fma.f64 (*.f64 x (sqrt.f64 (log.f64 (/.f64 x y)))) (sqrt.f64 (log.f64 (/.f64 x y))) z) (fma.f64 -1 z z))

Compiler

Compiled 5417 to 1699 computations (68.6% saved)

regimes1.6s (23.8%)

Accuracy

Total 0.3b remaining (88.5%)

Threshold costs 0.3b (88.5%)

Counts

119 → 2

Compiler

Compiled 11977 to 7124 computations (40.5% saved)

bsearch39.0ms (0.6%)

Steps

Iters	Range		Point
9	-9.510892274969026e-307	2.7231035217214135e-305	3.50923658615853e-310

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`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	22	38
1	38	38
2	51	38
3	58	38
4	60	38

Stop Event

1×

saturated

end126.0ms (1.8%)

Compiler: Compiled 239 to 137 computations (42.7% saved)

Details

analyze399.0ms (5.8%)

sample1.1s (15.9%)

simplify52.0ms (0.8%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series572.0ms (8.3%)

rewrite62.0ms (0.9%)

simplify84.0ms (1.2%)

prune117.0ms (1.7%)

localize9.0ms (0.1%)

series702.0ms (10.2%)

rewrite67.0ms (1%)

simplify58.0ms (0.8%)

prune115.0ms (1.7%)

localize10.0ms (0.1%)

series661.0ms (9.6%)

rewrite70.0ms (1%)

simplify47.0ms (0.7%)

prune117.0ms (1.7%)

localize7.0ms (0.1%)

series581.0ms (8.4%)

rewrite73.0ms (1.1%)

simplify81.0ms (1.2%)

prune109.0ms (1.6%)

regimes1.6s (23.8%)

bsearch39.0ms (0.6%)

simplify3.0ms (0%)

end126.0ms (1.8%)

Profiling