Details

analyze1.3s (27.1%)

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
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (28.6%)

Results

1.0s	8256×	body	128	valid
335.0ms	2678×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

preprocess49.0ms (1%)

Algorithm

2×	egg-herbie

Rules

504×	`fma-def_binary64`
380×	`distribute-rgt-in_binary64`
345×	`div-sub_binary64`
302×	`unsub-neg_binary64`
282×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	143
1	101	143
2	207	121
3	512	121
4	1221	121
5	3304	121
0	5	5

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
165×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	65	11
4	151	11
5	315	11
6	546	11
7	973	11
8	1854	11
9	2736	11
10	3572	11
11	3748	11
12	3793	11
13	3838	11
14	3838	11

Stop Event

1×

saturated

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
▶	5.8b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	6.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	5.5b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series33.0ms (0.7%)

Counts

2 → 88

Calls

24 calls:

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

rewrite83.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`prod-diff_binary64`
214×	`fma-def_binary64`
192×	`egg-rr`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	197	18
2	2825	18

Stop Event

1×	node limit

Counts

2 → 192

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-def_binary64`
643×	`fma-neg_binary64`
174×	`cancel-sign-sub-inv_binary64`
155×	`distribute-rgt-in_binary64`
155×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	1214
1	72	944
2	169	908
3	395	774
4	838	774
5	1606	774
6	2684	774
7	3466	774
8	3687	774
9	3744	774
10	3744	774

Stop Event

1×

saturated

Counts

280 → 213

prune143.0ms (3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	208	5	213
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	209	6	215

Error

0.0b

Counts

215 → 6

Alt Table

Status	Error	Program
	37.8b	(fma.f64 y (.f64 (sqrt.f64 (-.f64 z t)) (.f64 (sqrt.f64 (-.f64 z t)) (/.f64 1 a))) x)
	5.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 a)) x)
	6.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	5.8b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)
	7.0b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) 2))
	49.6b	(*.f64 t (/.f64 (neg.f64 y) a))

Compiler

Compiled 7154 to 2025 computations (71.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.2b	(pow.f64 (/.f64 a (-.f64 z t)) -1)
✓	5.5b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

series207.0ms (4.3%)

Counts

3 → 120

Calls

33 calls:

41.0ms	(pow.f64 (/.f64 a (-.f64 z t)) -1)	z	0
21.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)	t	inf
12.0ms	(pow.f64 (/.f64 a (-.f64 z t)) -1)	z	-inf
12.0ms	(pow.f64 (/.f64 a (-.f64 z t)) -1)	t	inf
11.0ms	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)	z	-inf

rewrite61.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

441×	`prod-diff_binary64`
215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
204×	`fma-def_binary64`
122×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	236	25
2	3151	25

Stop Event

1×	node limit

Counts

3 → 104

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

606×	`fma-neg_binary64`
568×	`cancel-sign-sub-inv_binary64`
192×	`times-frac_binary64`
176×	`associate-/l*_binary64`
169×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1798
1	175	1528
2	513	1418
3	2281	1376

Stop Event

1×	node limit

Counts

224 → 137

prune99.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	137	6	143

Error

0.0b

Counts

143 → 6

Alt Table

Status	Error	Program
	6.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	5.9b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)
	17.0b	(fma.f64 (/.f64 y a) z x)
✓	5.8b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)
	7.0b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) 2))
	49.6b	(*.f64 t (/.f64 (neg.f64 y) a))

Compiler

Compiled 2125 to 810 computations (61.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.3b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t)))
✓	5.5b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)

series40.0ms (0.8%)

Counts

3 → 120

Calls

30 calls:

4.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)	t	inf
2.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)	z	-inf
2.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)	z	inf
2.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)	x	0
2.0ms	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)	t	0

rewrite78.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`prod-diff_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	37
1	261	25
2	3549	25

Stop Event

1×	node limit

Counts

3 → 86

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
483×	`associate-/l*_binary64`
409×	`associate-/r*_binary64`
259×	`associate-*l/_binary64`
198×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1684
1	167	1396
2	441	1358
3	1445	1247

Stop Event

1×	node limit

Counts

206 → 122

prune68.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	123	5	128

Error

0.0b

Counts

128 → 5

Alt Table

Status	Error	Program
	6.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	5.9b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)
▶	4.0b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	7.0b	(*.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (pow.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) 2))
✓	5.8b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)

Compiler

Compiled 1880 to 831 computations (55.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.9b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series20.0ms (0.4%)

Counts

1 → 60

Calls

15 calls:

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

rewrite42.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
446×	`prod-diff_binary64`
202×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	194	11
2	2698	11

Stop Event

1×	node limit

Counts

1 → 29

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
690×	`fma-neg_binary64`
199×	`cancel-sign-sub-inv_binary64`
102×	`div-sub_binary64`
93×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	964
1	58	694
2	135	680
3	311	590
4	620	590
5	1070	590
6	1844	590
7	2933	590
8	3274	590
9	3310	590
10	3340	590
11	3345	590
12	3345	590

Stop Event

1×

saturated

Counts

89 → 45

prune29.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	44	6	50

Error

Counts

50 → 6

Alt Table

Status	Error	Program
	6.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	5.9b	(fma.f64 y (/.f64 (/.f64 1 a) (/.f64 1 (-.f64 z t))) x)
✓	5.8b	(fma.f64 y (pow.f64 (/.f64 a (-.f64 z t)) -1) x)
✓	4.0b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	45.0b	(cbrt.f64 (pow.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x) 3))
	5.1b	(*.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) (pow.f64 (cbrt.f64 (fma.f64 (/.f64 y a) (-.f64 z t) x)) 2))

Compiler

Compiled 655 to 188 computations (71.3% saved)

regimes758.0ms (15.9%)

Accuracy

Total 0.3b remaining (93.7%)

Threshold costs 0.3b (93.7%)

Counts

44 → 3

Compiler

Compiled 6487 to 4164 computations (35.8% saved)

bsearch1.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(*.f64 y (-.f64 z t))
0.0ms	(*.f64 y (-.f64 z t))

Steps

Iters	Point		Range
7.464711217148032e+252	∈ [	7.464711217148032e+252	,	7.31373714863341e+273	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-1.3273183236345312e+302	]

Compiler

Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	65
1	32	65
2	35	65
3	37	65
4	38	65

Stop Event

1×

saturated

end84.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 201 to 108 computations (46.3% saved)

Details

analyze1.3s (27.1%)

sample1.4s (28.6%)

preprocess49.0ms (1%)

simplify46.0ms (1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series33.0ms (0.7%)

rewrite83.0ms (1.7%)

simplify78.0ms (1.6%)

prune143.0ms (3%)

localize7.0ms (0.1%)

series207.0ms (4.3%)

rewrite61.0ms (1.3%)

simplify49.0ms (1%)

prune99.0ms (2.1%)

localize8.0ms (0.2%)

series40.0ms (0.8%)

rewrite78.0ms (1.6%)

simplify44.0ms (0.9%)

prune68.0ms (1.4%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite42.0ms (0.9%)

simplify75.0ms (1.6%)

prune29.0ms (0.6%)

regimes758.0ms (15.9%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end84.0ms (1.7%)

Profiling