Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (45.8%)

Results

447.0ms	2100×	body	512	valid
415.0ms	4714×	body	128	valid
153.0ms	1023×	body	256	valid
113.0ms	419×	body	1024	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

preprocess19.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

16.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 47 to 39 computations (17% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	2.9b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series7.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))	x	inf
1.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))	x	-inf
1.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))	x	0
1.0ms	(/.f64 1 (-.f64 x 1))	x	-inf
1.0ms	(/.f64 1 (+.f64 x 1))	x	-inf

rewrite71.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

867×	`prod-diff_binary64`
162×	`expm1-udef_binary64`
162×	`log1p-udef_binary64`
130×	`egg-rr`
101×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	192	30
2	2968	30

Stop Event

1×	node limit

Counts

3 → 180

simplify33.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

423×	`associate-l_binary64`
355×	`fma-neg_binary64`
347×	`associate-/r*_binary64`
286×	`cancel-sign-sub-inv_binary64`
218×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	575
1	198	543
2	594	540
3	1924	537

Stop Event

1×	node limit

Counts

216 → 221

prune187.0ms (7.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	219	3	222

Error

0.4b

Counts

222 → 3

Alt Table

Status	Error	Program
	32.6b	(+.f64 (/.f64 -2 (*.f64 x x)) (-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4))))
✓	16.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
▶	29.7b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1))) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))

Compiler

Compiled 5798 to 4685 computations (19.2% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x -1))
✓	0.0b	(fma.f64 x x (-.f64 1 x))
✓	0.3b	(/.f64 1 (+.f64 1 (pow.f64 x 3)))
✓	29.6b	(fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1)))

series12.0ms (0.5%)

Counts

4 → 48

Calls

12 calls:

2.0ms	(/.f64 1 (+.f64 x -1))	x	0
1.0ms	(fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1)))	x	-inf
1.0ms	(fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1)))	x	inf
1.0ms	(/.f64 1 (+.f64 1 (pow.f64 x 3)))	x	-inf
1.0ms	(/.f64 1 (+.f64 1 (pow.f64 x 3)))	x	inf

rewrite60.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

767×	`prod-diff_binary64`
152×	`add-sqr-sqrt_binary64`
147×	`pow1_binary64`
146×	`*-un-lft-identity_binary64`
142×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	315	51
2	4047	51

Stop Event

1×	node limit

Counts

4 → 105

simplify35.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

488×	`fma-neg_binary64`
306×	`cancel-sign-sub-inv_binary64`
272×	`fma-def_binary64`
208×	`times-frac_binary64`
199×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	695
1	224	655
2	674	652
3	2250	649

Stop Event

1×	node limit

Counts

153 → 154

prune150.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	4	157

Error

0.0b

Counts

157 → 4

Alt Table

Status	Error	Program
	32.6b	(+.f64 (/.f64 -2 (*.f64 x x)) (-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4))))
▶	32.5b	(+.f64 (/.f64 (/.f64 -2 x) x) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))
✓	16.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
✓	29.7b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1))) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))

Compiler

Compiled 5610 to 4408 computations (21.4% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -1 (+.f64 x -1))
	0.0b	(/.f64 1 (+.f64 x -1))
✓	0.1b	(/.f64 (/.f64 -2 x) x)

series5.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(/.f64 (/.f64 -2 x) x)	x	0
1.0ms	(/.f64 (/.f64 -2 x) x)	x	-inf
1.0ms	(/.f64 -1 (+.f64 x -1))	x	-inf
1.0ms	(/.f64 -1 (+.f64 x -1))	x	inf
1.0ms	(/.f64 (/.f64 -2 x) x)	x	inf

rewrite45.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`log1p-expm1-u_binary64`
910×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
87×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	184	14
2	2484	14

Stop Event

1×	node limit

Counts

2 → 63

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
474×	`fma-neg_binary64`
450×	`associate-/r*_binary64`
264×	`cancel-sign-sub-inv_binary64`
239×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	267
1	76	251
2	211	250
3	592	248
4	1686	248

Stop Event

1×	node limit

Counts

87 → 79

prune85.0ms (3.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	122	7	129

Error

0.0b

Counts

129 → 7

Alt Table

Status	Error	Program
▶	32.6b	(+.f64 (/.f64 -2 (*.f64 x x)) (-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4))))
✓	32.5b	(+.f64 (/.f64 (/.f64 -2 x) x) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))
✓	16.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
	44.3b	(+.f64 (cbrt.f64 (pow.f64 (/.f64 -2 (*.f64 x x)) 3)) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))
	33.1b	(+.f64 (pow.f64 (cbrt.f64 (/.f64 -2 (*.f64 x x))) 3) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))
	48.7b	(+.f64 (*.f64 (/.f64 -2 (sqrt.f64 x)) (/.f64 (/.f64 1 x) (sqrt.f64 x))) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))
✓	29.7b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1))) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))

Compiler

Compiled 3031 to 2354 computations (22.3% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4)))
✓	0.2b	(/.f64 2 (pow.f64 x 4))
✓	0.2b	(/.f64 -2 (pow.f64 x 6))
✓	0.4b	(/.f64 -2 (*.f64 x x))

series13.0ms (0.5%)

Counts

4 → 24

Calls

12 calls:

2.0ms	(/.f64 -2 (pow.f64 x 6))	x	-inf
1.0ms	(-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4)))	x	0
1.0ms	(-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4)))	x	-inf
1.0ms	(-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4)))	x	inf
1.0ms	(/.f64 -2 (pow.f64 x 6))	x	0

rewrite66.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

735×	`prod-diff_binary64`
146×	`add-sqr-sqrt_binary64`
141×	`pow1_binary64`
140×	`add-log-exp_binary64`
140×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	302	35
2	3869	35

Stop Event

1×	node limit

Counts

4 → 158

simplify24.0ms (1%)

Algorithm

1×	egg-herbie

Rules

513×	`associate-l_binary64`
463×	`associate-*l/_binary64`
373×	`associate-/l*_binary64`
345×	`associate-*r/_binary64`
285×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	267
1	46	249
2	109	249
3	285	249
4	1224	249

Stop Event

1×	node limit

Counts

182 → 164

prune129.0ms (5.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	3	0	3
Picked	0	1	1
Done	0	3	3
Total	166	5	171

Error

Counts

171 → 5

Alt Table

Status	Error	Program
✓	32.6b	(+.f64 (/.f64 -2 (*.f64 x x)) (-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4))))
✓	32.5b	(+.f64 (/.f64 (/.f64 -2 x) x) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))
	32.3b	(+.f64 (*.f64 -2 (pow.f64 x -2)) (-.f64 (/.f64 -2 (pow.f64 x 6)) (/.f64 2 (pow.f64 x 4))))
✓	16.2b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
✓	29.7b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 x 3))) (fma.f64 x x (-.f64 1 x)) (/.f64 -1 (+.f64 x -1))) (fma.f64 (/.f64 -1 (+.f64 x -1)) 1 (/.f64 1 (+.f64 x -1))))

Compiler

Compiled 4287 to 3259 computations (24% saved)

regimes173.0ms (7%)

Accuracy

Total 0.0b remaining (57.8%)

Threshold costs 0.0b (57.8%)

Counts

63 → 3

Compiler

Compiled 2414 to 1922 computations (20.4% saved)

bsearch34.0ms (1.4%)

Algorithm

2×	binary-search

Calls

2 calls:

16.0ms	x
16.0ms	x

Steps

Iters	Point		Range
218.49470597842105	∈ [	43.18887148678363	,	276420.7550463244	]
-220.90960044263244	∈ [	-9979.600912883168	,	-0.0035811007973851052	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	91
1	47	91
2	64	91
3	72	91
4	77	91
5	78	91

Stop Event

1×

saturated

end118.0ms (4.7%)

Stop Event

1×

fuel

Compiler

Compiled 226 to 180 computations (20.4% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16
0	1	1

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16
0	1	1

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16

Details

analyze4.0ms (0.2%)

sample1.1s (45.8%)

preprocess19.0ms (0.8%)

simplify10.0ms (0.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite71.0ms (2.8%)

simplify33.0ms (1.3%)

prune187.0ms (7.5%)

localize15.0ms (0.6%)

series12.0ms (0.5%)

rewrite60.0ms (2.4%)

simplify35.0ms (1.4%)

prune150.0ms (6%)

localize9.0ms (0.4%)

series5.0ms (0.2%)

rewrite45.0ms (1.8%)

simplify24.0ms (1%)

prune85.0ms (3.4%)

localize9.0ms (0.4%)

series13.0ms (0.5%)

rewrite66.0ms (2.6%)

simplify24.0ms (1%)

prune129.0ms (5.2%)

regimes173.0ms (7%)

bsearch34.0ms (1.4%)

simplify4.0ms (0.2%)

end118.0ms (4.7%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16
0	1	1

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	39	16
5	57	16
6	94	16
7	127	16
8	170	16
9	206	16
10	232	16
11	234	16