Details

analyze1.3s (27.8%)

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
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (24.9%)

Results

1.0s	8255×	body	128	valid
93.0ms	736×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 34 to 22 computations (35.3% saved)

preprocess44.0ms (1%)

Algorithm

2×	egg-herbie

Rules

956×	`div-sub_binary64`
390×	`fma-def_binary64`
299×	`distribute-rgt-in_binary64`
254×	`distribute-lft-in_binary64`
253×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	176
1	138	154
2	292	154
3	605	154
4	1447	154
5	3922	154
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify27.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
577×	`div-sub_binary64`
529×	`fma-neg_binary64`
259×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	41	14
3	82	14
4	188	14
5	381	14
6	902	14
7	2369	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
	2.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
▶	1.4b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 88 to 52 computations (40.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.8b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series96.0ms (2.1%)

Counts

3 → 144

Calls

36 calls:

6.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	y	-inf
5.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))	z	-inf
4.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	t	-inf
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))	x	inf
3.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))	a	-inf

rewrite72.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`fma-neg_binary64`
252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	257	37
2	4024	37

Stop Event

1×	node limit

Counts

3 → 110

simplify84.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
520×	`sub-neg_binary64`
290×	`associate--l+_binary64`
214×	`associate--r+_binary64`
206×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4417
1	767	4078
2	2702	3496

Stop Event

1×	node limit

Counts

254 → 222

prune168.0ms (3.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	220	4	224

Error

Counts

224 → 4

Alt Table

Status	Error	Program
	1.5b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
	2.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
▶	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	12.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 5394 to 1910 computations (64.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	2.8b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

series91.0ms (2%)

Counts

3 → 144

Calls

36 calls:

6.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))	t	0
5.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	a	0
4.0ms	(/.f64 (-.f64 a t) (-.f64 z t))	z	-inf
4.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	z	inf
3.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))	a	-inf

rewrite73.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	263	37
2	4303	37

Stop Event

1×	node limit

Counts

3 → 118

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

805×	`times-frac_binary64`
532×	`sub-neg_binary64`
296×	`associate--l+_binary64`
215×	`associate--r+_binary64`
209×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4417
1	793	4081
2	2853	3769

Stop Event

1×	node limit

Counts

262 → 230

prune149.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	230	4	234

Error

Counts

234 → 4

Alt Table

Status	Error	Program
▶	1.5b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
	2.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
✓	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	12.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 5582 to 1929 computations (65.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	2.8b	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))

series91.0ms (2%)

Counts

3 → 144

Calls

36 calls:

7.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))	t	0
5.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))	a	inf
4.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))	x	inf
3.0ms	(.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))))	a	-inf
3.0ms	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))	a	0

rewrite75.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`expm1-udef_binary64`
266×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
142×	`add-cbrt-cube_binary64`
142×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	290	37
2	4211	37

Stop Event

1×	node limit

Counts

3 → 95

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
520×	`sub-neg_binary64`
290×	`associate--l+_binary64`
214×	`associate--r+_binary64`
206×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4417
1	767	4078
2	2702	3496

Stop Event

1×	node limit

Counts

239 → 207

prune126.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	207	4	211

Error

Counts

211 → 4

Alt Table

Status	Error	Program
✓	1.5b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
▶	2.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
✓	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	12.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 5042 to 1837 computations (63.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 t a))
✓	2.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)

series49.0ms (1.1%)

Counts

2 → 84

Calls

24 calls:

6.0ms	(/.f64 y (-.f64 t a))	y	0
4.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	t	-inf
3.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	t	0
3.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	a	0
2.0ms	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)	t	inf

rewrite50.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
220×	`log1p-udef_binary64`
120×	`add-sqr-sqrt_binary64`
114×	`log1p-expm1-u_binary64`
114×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	224	21
2	3274	21

Stop Event

1×	node limit

Counts

2 → 58

simplify47.0ms (1%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
651×	`times-frac_binary64`
590×	`cancel-sign-sub-inv_binary64`
189×	`sub-neg_binary64`
132×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	165	2442
1	541	2442
2	1822	1825

Stop Event

1×	node limit

Counts

142 → 123

prune79.0ms (1.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	123	4	127

Error

Counts

127 → 4

Alt Table

Status	Error	Program
✓	1.5b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
✓	2.0b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)
✓	1.3b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	12.8b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 2603 to 852 computations (67.3% saved)

regimes567.0ms (12.2%)

Accuracy

Total 1.0b remaining (99.1%)

Threshold costs 0b (0%)

Counts

67 → 3

Compiler

Compiled 8129 to 5349 computations (34.2% saved)

bsearch35.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

22.0ms	y
12.0ms	y

Steps

Iters	Point		Range
1.0514448438020326e-28	∈ [	9.981666015011039e-29	,	2.720785482535562e-28	]
-3.9258428577443835e+52	∈ [	-2.7763211234545303e+53	,	-3.8728654451901895e+52	]

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	59
1	37	59
2	48	59
3	54	59
4	57	59

Stop Event

1×

saturated

end73.0ms (1.6%)

Stop Event

1×

fuel

Compiler

Compiled 157 to 89 computations (43.3% saved)

Details

analyze1.3s (27.8%)

sample1.2s (24.9%)

preprocess44.0ms (1%)

simplify27.0ms (0.6%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series96.0ms (2.1%)

rewrite72.0ms (1.5%)

simplify84.0ms (1.8%)

prune168.0ms (3.6%)

localize7.0ms (0.2%)

series91.0ms (2%)

rewrite73.0ms (1.6%)

simplify76.0ms (1.6%)

prune149.0ms (3.2%)

localize8.0ms (0.2%)

series91.0ms (2%)

rewrite75.0ms (1.6%)

simplify79.0ms (1.7%)

prune126.0ms (2.7%)

localize7.0ms (0.1%)

series49.0ms (1.1%)

rewrite50.0ms (1.1%)

simplify47.0ms (1%)

prune79.0ms (1.7%)

regimes567.0ms (12.2%)

bsearch35.0ms (0.8%)

simplify4.0ms (0.1%)

end73.0ms (1.6%)

Profiling