Details

analyze1.4s (27.6%)

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 (23.6%)

Results

1.1s	8254×	body	128	valid
107.0ms	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)

simplify23.0ms (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)

localize7.0ms (0.1%)

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)

series52.0ms (1%)

Counts

2 → 84

Calls

24 calls:

5.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	a	-inf
4.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	a	0
4.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	z	0
3.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	a	inf
2.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)	z	inf

rewrite53.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
122×	`add-sqr-sqrt_binary64`
121×	`*-un-lft-identity_binary64`
121×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	223	21
2	3254	21

Stop Event

1×	node limit

Counts

2 → 58

simplify50.0ms (1%)

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

prune81.0ms (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)
	11.2b	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)
▶	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))

Compiler

Compiled 2392 to 753 computations (68.5% saved)

localize9.0ms (0.2%)

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))))

series87.0ms (1.7%)

Counts

4 → 111

Calls

36 calls:

6.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	a	inf
5.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	inf
5.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	-inf
4.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	t	0
4.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))	a	-inf

rewrite85.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	234	37
2	3833	37

Stop Event

1×	node limit

Counts

4 → 254

simplify70.0ms (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

prune312.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

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

Error

Counts

364 → 4

Alt Table

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

Compiler

Compiled 9490 to 3054 computations (67.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series83.0ms (1.6%)

Counts

3 → 144

Calls

36 calls:

5.0ms	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)	z	0
4.0ms	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)	y	-inf
4.0ms	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)	t	inf
4.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))	a	-inf
3.0ms	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)	x	0

rewrite72.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

271×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
140×	`add-sqr-sqrt_binary64`
139×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	36
2	3987	36

Stop Event

1×	node limit

Counts

3 → 102

simplify71.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
603×	`times-frac_binary64`
554×	`cancel-sign-sub-inv_binary64`
486×	`associate-/l*_binary64`
265×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	133	3870
1	431	3780
2	1674	2844

Stop Event

1×	node limit

Counts

246 → 185

prune152.0ms (2.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
▶	22.9b	(+.f64 (/.f64 y (/.f64 a t)) x)
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.2b	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)

Compiler

Compiled 4170 to 1284 computations (69.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.3b	(/.f64 y (/.f64 a t))

series13.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(/.f64 y (/.f64 a t))	a	-inf
2.0ms	(/.f64 y (/.f64 a t))	y	-inf
2.0ms	(/.f64 y (/.f64 a t))	t	-inf
1.0ms	(/.f64 y (/.f64 a t))	y	0
1.0ms	(/.f64 y (/.f64 a t))	y	inf

rewrite39.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`pow1_binary64`
724×	`log1p-expm1-u_binary64`
724×	`expm1-log1p-u_binary64`
69×	`*-un-lft-identity_binary64`
69×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	131	7
2	1915	7

Stop Event

1×	node limit

Counts

1 → 43

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	252
1	9	252
2	13	252
3	16	252
4	17	252

Stop Event

1×

saturated

Counts

79 → 44

prune33.0ms (0.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	44	4	48

Error

Counts

48 → 4

Alt Table

Status	Error	Program
✓	1.3b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
✓	22.9b	(+.f64 (/.f64 y (/.f64 a t)) x)
✓	2.5b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.2b	(+.f64 (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) x)

Compiler

Compiled 572 to 243 computations (57.5% saved)

regimes1.1s (20.2%)

Accuracy

Total 0.9b remaining (98.5%)

Threshold costs 0.9b (98.5%)

Counts

128 → 3

Compiler

Compiled 14648 to 9630 computations (34.3% saved)

bsearch52.0ms (1%)

Algorithm

2×	binary-search

Calls

2 calls:

29.0ms	t
19.0ms	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`
6×	`*-commutative_binary64`
5×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	69
1	42	69
2	51	69
3	55	69
4	57	69

Stop Event

1×

saturated

end71.0ms (1.4%)

Stop Event

1×

done

Compiler

Compiled 167 to 90 computations (46.1% saved)

Details

analyze1.4s (27.6%)

sample1.2s (23.6%)

preprocess44.0ms (0.8%)

simplify23.0ms (0.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series52.0ms (1%)

rewrite53.0ms (1%)

simplify50.0ms (1%)

prune81.0ms (1.6%)

localize9.0ms (0.2%)

series87.0ms (1.7%)

rewrite85.0ms (1.6%)

simplify70.0ms (1.3%)

prune312.0ms (6%)

localize8.0ms (0.2%)

series83.0ms (1.6%)

rewrite72.0ms (1.4%)

simplify71.0ms (1.4%)

prune152.0ms (2.9%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite39.0ms (0.7%)

simplify19.0ms (0.4%)

prune33.0ms (0.6%)

regimes1.1s (20.2%)

bsearch52.0ms (1%)

simplify4.0ms (0.1%)

end71.0ms (1.4%)

Profiling