Details

analyze517.0ms (24%)

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%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
48.4%	45.8%	5.8%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample894.0ms (41.5%)

Results

807.0ms	8256×	body	128	valid
71.0ms	766×	body	128	invalid

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess130.0ms (6%)

Algorithm

2×	egg-herbie

Rules

2118×	`associate-/l/_binary64`
1625×	`fma-def_binary64`
405×	`*-commutative_binary64`
364×	`distribute-rgt-out_binary64`
238×	`swap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	46	40
2	82	40
3	130	40
4	168	40
5	189	40
6	201	32
7	262	32
8	1429	32
9	2330	32
10	2895	32
11	2944	32
12	2947	32
13	2947	32
14	4118	32
15	4231	32
16	4315	32
17	4330	32
18	4374	32
19	4379	32
20	4379	32
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 10 to 6 computations (40% saved)

simplify29.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-/l*_binary64`
731×	`associate-/l/_binary64`
589×	`associate-/r/_binary64`
532×	`associate-*l/_binary64`
346×	`associate-/r*_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	10
2	28	10
3	41	10
4	50	10
5	56	10
6	60	8
7	75	8
8	257	8
9	1190	8
10	1448	8
11	1585	8
12	1598	8
13	1603	8
14	1608	8

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
▶	4.1b	(fma.f64 x (/.f64 y z) x)
	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.5%)

Counts

1 → 36

Calls

9 calls:

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

rewrite36.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
323×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1638	8

Stop Event

1×	node limit

Counts

1 → 29

simplify17.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

20×	`fma-def_binary64`
10×	`associate-r_binary64`
9×	`associate-/r/_binary64`
8×	`associate-/l*_binary64`
6×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	324
1	19	324
2	31	264
3	42	264
4	72	264
5	86	264
6	106	264
7	115	264
8	117	264

Stop Event

1×

saturated

Counts

65 → 35

prune18.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	33	4	37

Error

Counts

37 → 4

Alt Table

Status	Error	Program
	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
	34.0b	(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) 2)
	4.1b	(+.f64 x (*.f64 x (/.f64 y z)))
▶	4.0b	(fma.f64 y (/.f64 x z) x)

Compiler

Compiled 466 to 153 computations (67.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.6%)

Counts

1 → 36

Calls

9 calls:

3.0ms	(fma.f64 y (/.f64 x z) x)	x	inf
2.0ms	(fma.f64 y (/.f64 x z) x)	x	-inf
1.0ms	(fma.f64 y (/.f64 x z) x)	x	0
1.0ms	(fma.f64 y (/.f64 x z) x)	y	-inf
1.0ms	(fma.f64 y (/.f64 x z) x)	y	inf

rewrite34.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

616×	`log1p-expm1-u_binary64`
616×	`expm1-log1p-u_binary64`
323×	`log-prod_binary64`
119×	`expm1-udef_binary64`
119×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	124	8
2	1638	8

Stop Event

1×	node limit

Counts

1 → 29

simplify17.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

20×	`fma-def_binary64`
10×	`associate-r_binary64`
9×	`associate-/r/_binary64`
8×	`associate-/l*_binary64`
6×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	324
1	19	324
2	31	264
3	42	264
4	72	264
5	86	264
6	106	264
7	115	264
8	117	264

Stop Event

1×

saturated

Counts

65 → 35

prune14.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

Counts

39 → 4

Alt Table

Status	Error	Program
	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
	34.0b	(pow.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) 2)
▶	4.1b	(+.f64 x (*.f64 x (/.f64 y z)))
✓	4.0b	(fma.f64 y (/.f64 x z) x)

Compiler

Compiled 457 to 146 computations (68.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 x (/.f64 y z)))
✓	5.1b	(*.f64 x (/.f64 y z))

series22.0ms (1%)

Counts

2 → 72

Calls

18 calls:

2.0ms	(*.f64 x (/.f64 y z))	z	0
2.0ms	(+.f64 x (*.f64 x (/.f64 y z)))	x	-inf
2.0ms	(*.f64 x (/.f64 y z))	x	-inf
2.0ms	(*.f64 x (/.f64 y z))	y	-inf
2.0ms	(+.f64 x (*.f64 x (/.f64 y z)))	x	inf

rewrite43.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

873×	`expm1-log1p-u_binary64`
839×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
78×	`log1p-expm1-u_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	156	15
2	2301	15

Stop Event

1×	node limit

Counts

2 → 62

simplify26.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

20×	`fma-def_binary64`
10×	`associate-r_binary64`
9×	`associate-/r/_binary64`
8×	`associate-/l*_binary64`
6×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	576
1	19	576
2	31	516
3	42	516
4	72	516
5	86	516
6	106	516
7	115	516
8	117	516

Stop Event

1×

saturated

Counts

134 → 68

prune31.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	68	4	72

Error

Counts

72 → 4

Alt Table

Status	Error	Program
	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
▶	4.1b	(+.f64 x (/.f64 x (/.f64 z y)))
✓	4.1b	(+.f64 x (*.f64 x (/.f64 y z)))
✓	4.0b	(fma.f64 y (/.f64 x z) x)

Compiler

Compiled 868 to 284 computations (67.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 x (/.f64 z y)))
✓	5.1b	(/.f64 x (/.f64 z y))

series23.0ms (1.1%)

Counts

2 → 72

Calls

18 calls:

4.0ms	(/.f64 x (/.f64 z y))	x	inf
2.0ms	(/.f64 x (/.f64 z y))	x	-inf
2.0ms	(/.f64 x (/.f64 z y))	y	-inf
2.0ms	(+.f64 x (/.f64 x (/.f64 z y)))	x	-inf
2.0ms	(+.f64 x (/.f64 x (/.f64 z y)))	x	inf

rewrite48.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
156×	`expm1-udef_binary64`
156×	`log1p-udef_binary64`
138×	`fma-neg_binary64`
86×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	162	15
2	2569	15

Stop Event

1×	node limit

Counts

2 → 79

simplify26.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

20×	`fma-def_binary64`
10×	`associate-r_binary64`
9×	`associate-/r/_binary64`
8×	`associate-/l*_binary64`
6×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	576
1	19	576
2	31	516
3	42	516
4	72	516
5	86	516
6	106	516
7	115	516
8	117	516

Stop Event

1×

saturated

Counts

151 → 84

prune38.0ms (1.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	84	4	88

Error

Counts

88 → 4

Alt Table

Status	Error	Program
	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)
✓	4.1b	(+.f64 x (/.f64 x (/.f64 z y)))
✓	4.1b	(+.f64 x (*.f64 x (/.f64 y z)))
✓	4.0b	(fma.f64 y (/.f64 x z) x)

Compiler

Compiled 1093 to 359 computations (67.2% saved)

regimes88.0ms (4.1%)

Accuracy

Total 2.7b remaining (99.6%)

Threshold costs 0b (0%)

Counts

11 → 4

Compiler

Compiled 472 to 274 computations (41.9% saved)

bsearch1.0ms (0%)

Algorithm

3×	left-value

Calls

3 calls:

0.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)
0.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)
0.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)

Steps

Iters

Point

Range

2.325475704519075e+238

∈ [

2.325475704519075e+238

5.450062167632807e+240

]

1.9816485472502953e+98

∈ [

1.9816485472502953e+98

3.595494272488288e+99

]

-6.582729939135484e-168

∈ [

-6.582729939135484e-168

-2.4130908965204265e-169

]

Compiler

Compiled 10 to 6 computations (40% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	81
1	27	81

Stop Event

1×

saturated

end55.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 157 to 65 computations (58.6% saved)

Details

analyze517.0ms (24%)

sample894.0ms (41.5%)

preprocess130.0ms (6%)

simplify29.0ms (1.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series11.0ms (0.5%)

rewrite36.0ms (1.7%)

simplify17.0ms (0.8%)

prune18.0ms (0.8%)

localize4.0ms (0.2%)

series12.0ms (0.6%)

rewrite34.0ms (1.6%)

simplify17.0ms (0.8%)

prune14.0ms (0.7%)

localize4.0ms (0.2%)

series22.0ms (1%)

rewrite43.0ms (2%)

simplify26.0ms (1.2%)

prune31.0ms (1.4%)

localize4.0ms (0.2%)

series23.0ms (1.1%)

rewrite48.0ms (2.2%)

simplify26.0ms (1.2%)

prune38.0ms (1.7%)

regimes88.0ms (4.1%)

bsearch1.0ms (0%)

simplify4.0ms (0.2%)

end55.0ms (2.5%)

Profiling