Details

analyze390.0ms (12.4%)

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
6.2%	93.6%	0.1%	6
20.3%	79.6%	0.1%	7
28.9%	71%	0.1%	8
39.8%	60.1%	0.1%	9
57.5%	42.3%	0.1%	10
63.9%	36%	0.1%	11
68.6%	31.3%	0.1%	12
79.5%	20.3%	0.1%	13
82.9%	17%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample890.0ms (28.4%)

Results

876.0ms	8254×	body	128	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess38.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

600×	`fma-neg_binary64`
488×	`div-sub_binary64`
280×	`times-frac_binary64`
258×	`associate-/r*_binary64`
237×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	34	52
2	54	52
3	81	52
4	130	52
5	185	52
6	248	52
7	314	52
8	371	52
9	546	52
10	980	52
11	2530	52
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify30.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1370×	`fma-neg_binary64`
645×	`fma-def_binary64`
388×	`div-sub_binary64`
183×	`times-frac_binary64`
154×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	28	13
4	43	13
5	59	13
6	79	13
7	100	13
8	117	13
9	164	13
10	227	13
11	312	13
12	542	13
13	1354	13
14	2772	13
15	4570	13

Stop Event

1×	node limit

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

8.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series22.0ms (0.7%)

Counts

1 → 36

Calls

9 calls:

3.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))	y	inf
3.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))	x	inf
3.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))	x	-inf
3.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))	x	0
2.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))	z	0

rewrite56.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
189×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
100×	`add-cbrt-cube_binary64`
100×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	204	13
2	2992	13

Stop Event

1×	node limit

Counts

1 → 35

simplify45.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

338×	`fma-def_binary64`
312×	`+-commutative_binary64`
289×	`sub-neg_binary64`
246×	`times-frac_binary64`
213×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1140
1	268	1140
2	1007	1004
3	4045	983

Stop Event

1×	node limit

Counts

71 → 69

prune53.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	64	5	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	5	70

Error

Counts

70 → 5

Alt Table

Status	Error	Program
▶	8.5b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	33.1b	(-.f64 (neg.f64 z) (fma.f64 (/.f64 z y) x (*.f64 (/.f64 z y) z)))
	34.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	8.6b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	33.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (/.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z))))

Compiler

Compiled 1514 to 752 computations (50.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.0b	(/.f64 x (-.f64 1 (/.f64 y z)))
✓	8.5b	(/.f64 y (-.f64 1 (/.f64 y z)))

series33.0ms (1.1%)

Counts

2 → 48

Calls

15 calls:

6.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))	x	inf
4.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))	x	-inf
4.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))	x	0
2.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))	y	inf
2.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))	z	-inf

rewrite51.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
379×	`prod-diff_binary64`
183×	`log-div_binary64`
180×	`expm1-udef_binary64`
179×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	197	20
2	2782	20

Stop Event

1×	node limit

Counts

2 → 76

simplify42.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

711×	`cancel-sign-sub-inv_binary64`
504×	`fma-neg_binary64`
244×	`times-frac_binary64`
209×	`distribute-rgt-neg-in_binary64`
208×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	1032
1	176	1032
2	572	891
3	2634	849

Stop Event

1×	node limit

Counts

124 → 106

prune75.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	106	5	111

Error

Counts

111 → 5

Alt Table

Status	Error	Program
✓	8.5b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	33.1b	(-.f64 (neg.f64 z) (fma.f64 (/.f64 z y) x (*.f64 (/.f64 z y) z)))
	34.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
▶	8.6b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	33.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 x y)) 1) (/.f64 (sqrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z))))

Compiler

Compiled 2454 to 1326 computations (46% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
✓	8.5b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series67.0ms (2.1%)

Counts

2 → 72

Calls

18 calls:

12.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)	x	-inf
10.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)	x	inf
10.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)	x	0
4.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)	y	inf
3.0ms	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)	y	-inf

rewrite91.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`prod-diff_binary64`
169×	`egg-rr`
125×	`add-sqr-sqrt_binary64`
119×	`add-cbrt-cube_binary64`
119×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	248	26
2	3544	26

Stop Event

1×	node limit

Counts

2 → 169

simplify83.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

435×	`associate-+r+_binary64`
355×	`sub-neg_binary64`
306×	`+-commutative_binary64`
295×	`associate-+l+_binary64`
291×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	324	3973
1	1068	3940
2	4639	3931

Stop Event

1×	node limit

Counts

241 → 251

prune196.0ms (6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	251	5	256

Error

Counts

256 → 5

Alt Table

Status	Error	Program
✓	8.5b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
▶	8.5b	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))
	34.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
✓	8.6b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	33.2b	(/.f64 (sqrt.f64 (+.f64 y x)) (/.f64 (-.f64 1 (/.f64 y z)) (sqrt.f64 (+.f64 y x))))

Compiler

Compiled 11395 to 4908 computations (56.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	8.0b	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))

series32.0ms (1%)

Counts

2 → 60

Calls

15 calls:

4.0ms	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))	z	0
3.0ms	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))	y	inf
3.0ms	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))	x	-inf
3.0ms	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))	x	inf
3.0ms	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))	x	0

rewrite56.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

807×	`prod-diff_binary64`
202×	`log1p-udef_binary64`
115×	`add-sqr-sqrt_binary64`
109×	`add-cbrt-cube_binary64`
109×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	227	23
2	3257	23

Stop Event

1×	node limit

Counts

2 → 67

simplify129.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

455×	`fma-def_binary64`
353×	`+-commutative_binary64`
266×	`times-frac_binary64`
233×	`associate-/l*_binary64`
190×	`associate--r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1602
1	322	1602
2	1212	1355
3	4847	1343

Stop Event

1×	node limit

Counts

127 → 116

prune88.0ms (2.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	116	5	121

Error

Counts

121 → 5

Alt Table

Status	Error	Program
✓	8.5b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	8.5b	(*.f64 (+.f64 y x) (/.f64 1 (-.f64 1 (/.f64 y z))))
	34.9b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
✓	8.6b	(pow.f64 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)) -1)
	33.2b	(/.f64 (sqrt.f64 (+.f64 y x)) (/.f64 (-.f64 1 (/.f64 y z)) (sqrt.f64 (+.f64 y x))))

Compiler

Compiled 2176 to 1072 computations (50.7% saved)

regimes548.0ms (17.5%)

Accuracy

Total 0.1b remaining (87.3%)

Threshold costs 0.1b (87.3%)

Counts

75 → 3

Compiler

Compiled 4320 to 2958 computations (31.5% saved)

bsearch3.0ms (0.1%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
0.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Steps

Iters	Point		Range
-0.0	∈ [	-0.0	,	4.9526729375962424e-297	]
-1.3138219577186698e-278	∈ [	-1.3138219577186698e-278	,	-6.205806913430948e-283	]

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
11×	`*-commutative_binary64`
11×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	101
1	41	101
2	60	101
3	85	101
4	100	101
5	108	101
6	110	101

Stop Event

1×

saturated

end85.0ms (2.7%)

Stop Event

1×

fuel

Compiler

Compiled 223 to 130 computations (41.7% saved)

Details

analyze390.0ms (12.4%)

sample890.0ms (28.4%)

preprocess38.0ms (1.2%)

simplify30.0ms (1%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series22.0ms (0.7%)

rewrite56.0ms (1.8%)

simplify45.0ms (1.4%)

prune53.0ms (1.7%)

localize6.0ms (0.2%)

series33.0ms (1.1%)

rewrite51.0ms (1.6%)

simplify42.0ms (1.3%)

prune75.0ms (2.4%)

localize7.0ms (0.2%)

series67.0ms (2.1%)

rewrite91.0ms (2.9%)

simplify83.0ms (2.7%)

prune196.0ms (6.3%)

localize6.0ms (0.2%)

series32.0ms (1%)

rewrite56.0ms (1.8%)

simplify129.0ms (4.1%)

prune88.0ms (2.8%)

regimes548.0ms (17.5%)

bsearch3.0ms (0.1%)

simplify6.0ms (0.2%)

end85.0ms (2.7%)

Profiling