Details

analyze1.3s (23.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (19.9%)

Results

1.0s	8254×	body	128	valid
96.0ms	752×	body	128	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess44.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

758×	`div-sub_binary64`
354×	`fma-def_binary64`
338×	`fma-neg_binary64`
287×	`distribute-rgt-in_binary64`
252×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	109	176
2	277	154
3	623	154
4	1429	154
5	3919	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

726×	`fma-def_binary64`
585×	`fma-neg_binary64`
512×	`div-sub_binary64`
345×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	84	14
4	185	14
5	371	14
6	871	14
7	2142	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series46.0ms (0.8%)

Counts

2 → 84

Calls

24 calls:

4.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	a	inf
3.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	a	0
3.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	z	0
2.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	z	-inf
2.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	z	inf

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	223	21
2	3231	21

Stop Event

1×	node limit

Counts

2 → 58

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

636×	`times-frac_binary64`
600×	`fma-def_binary64`
499×	`associate-/l*_binary64`
262×	`cancel-sign-sub-inv_binary64`
247×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	374	2438
2	1413	2037

Stop Event

1×	node limit

Counts

142 → 115

prune95.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	114	3	117

Error

0.0b

Counts

117 → 3

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
	11.2b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 2404 to 765 computations (68.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	2.2b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series107.0ms (1.8%)

Counts

4 → 111

Calls

36 calls:

20.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	0
9.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	a	0
5.0ms	(/.f64 y (-.f64 a z))	a	inf
4.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	-inf
4.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))	a	-inf

rewrite91.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

534×	`fma-def_binary64`
283×	`fma-neg_binary64`
254×	`egg-rr`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	234	37
2	3802	37

Stop Event

1×	node limit

Counts

4 → 254

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
757×	`times-frac_binary64`
495×	`cancel-sign-sub-inv_binary64`
330×	`sub-neg_binary64`
170×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	3449
1	582	3422
2	2035	3023

Stop Event

1×	node limit

Counts

365 → 361

prune320.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	359	2	361
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	360	4	364

Error

Counts

364 → 4

Alt Table

Status	Error	Program
	24.5b	(+.f64 x (/.f64 (neg.f64 (-.f64 z y)) (/.f64 a t)))
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	11.2b	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))
✓	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 9490 to 3056 computations (67.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))
✓	0.0b	(*.f64 t (-.f64 y z))
✓	11.5b	(/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z))

series78.0ms (1.4%)

Counts

3 → 120

Calls

36 calls:

4.0ms	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))	x	inf
4.0ms	(/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z))	a	inf
4.0ms	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))	y	-inf
3.0ms	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))	a	0
3.0ms	(/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z))	a	-inf

rewrite86.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

265×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`
130×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	36
2	3940	36

Stop Event

1×	node limit

Counts

3 → 101

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
603×	`times-frac_binary64`
554×	`cancel-sign-sub-inv_binary64`
484×	`associate-/l*_binary64`
264×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	134	3486
1	443	3432
2	1690	2832

Stop Event

1×	node limit

Counts

221 → 182

prune151.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	182	4	186

Error

Counts

186 → 4

Alt Table

Status	Error	Program
▶	2.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1))
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.2b	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))
✓	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 4147 to 1270 computations (69.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) t)
✓	0.0b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1))
✓	0.7b	(pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1)
✓	12.4b	(/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z))

series232.0ms (4%)

Counts

4 → 184

Calls

48 calls:

18.0ms	(/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z))	y	0
18.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1))	y	inf
17.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1))	y	-inf
15.0ms	(pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1)	y	-inf
14.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1))	y	0

rewrite85.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

287×	`log1p-udef_binary64`
168×	`egg-rr`
160×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	305	49
2	4731	49

Stop Event

1×	node limit

Counts

4 → 168

simplify113.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

688×	`times-frac_binary64`
479×	`associate-/l*_binary64`
367×	`associate-/r*_binary64`
203×	`associate-r_binary64`
188×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	8763
1	1671	8531

Stop Event

1×	node limit

Counts

352 → 314

prune268.0ms (4.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	314	0	314
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	314	4	318

Error

Counts

318 → 4

Alt Table

Status	Error	Program
✓	2.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 (-.f64 a z) t) (-.f64 y z)) -1))
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.2b	(+.f64 x (/.f64 (*.f64 t (-.f64 y z)) (-.f64 a z)))
✓	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 10873 to 4179 computations (61.6% saved)

regimes1.1s (19.7%)

Accuracy

Total 0.9b remaining (98.9%)

Threshold costs 0.9b (98.9%)

Counts

131 → 3

Compiler

Compiled 15260 to 10046 computations (34.2% saved)

bsearch53.0ms (0.9%)

Algorithm

2×	binary-search

Calls

2 calls:

28.0ms	t
20.0ms	t

Steps

Iters	Point		Range
1.4771816920899563e-224	∈ [	4.411519880198923e-227	,	2.0967409250077116e-224	]
-1.1923891012664429e+57	∈ [	-2.8169414532548554e+69	,	-1.1766300617178056e+57	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	69
1	40	69
2	49	69
3	53	69
4	55	69

Stop Event

1×

saturated

end70.0ms (1.2%)

Stop Event

1×

done

Compiler

Compiled 173 to 94 computations (45.7% saved)

Details

analyze1.3s (23.1%)

sample1.2s (19.9%)

preprocess44.0ms (0.8%)

simplify22.0ms (0.4%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series46.0ms (0.8%)

rewrite60.0ms (1%)

simplify51.0ms (0.9%)

prune95.0ms (1.6%)

localize8.0ms (0.1%)

series107.0ms (1.8%)

rewrite91.0ms (1.6%)

simplify78.0ms (1.3%)

prune320.0ms (5.5%)

localize11.0ms (0.2%)

series78.0ms (1.4%)

rewrite86.0ms (1.5%)

simplify66.0ms (1.1%)

prune151.0ms (2.6%)

localize9.0ms (0.2%)

series232.0ms (4%)

rewrite85.0ms (1.5%)

simplify113.0ms (1.9%)

prune268.0ms (4.6%)

regimes1.1s (19.7%)

bsearch53.0ms (0.9%)

simplify4.0ms (0.1%)

end70.0ms (1.2%)

Profiling