Details

analyze7.0ms (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 7 to 6 computations (14.3% saved)

sample1.1s (38.1%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 20 to 17 computations (15% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	12	4
2	13	4
3	10	4

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x 1/3)

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x 1/3)

series2.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

2.0ms

(-.f64 x 1/3)

rewrite91.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

821×	`log1p-udef_binary64`
452×	`log1p-expm1-u_binary64`
452×	`expm1-log1p-u_binary64`
389×	`pow1_binary64`
218×	`unpow-prod-down_binary64`

Counts

1 → 48

Calls

1 calls:

89.0ms

(-.f64 x 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	93	4
2	1121	4
3	4749	4
4	6108	4
0	0	0
1	0	0

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

51 → 50

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3
1	2	3

prune50.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	3	51

Error

0.0b

Counts

51 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x 1/3)
	22.3b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
▶	17.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))

Compiler

Compiled 486 to 378 computations (22.2% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(+.f64 x 1/3)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))
✓	16.1b	(/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9))

series15.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9))
4.0ms	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))
4.0ms	(fma.f64 x x -1/9)
2.0ms	(+.f64 x 1/3)

rewrite109.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

408×	`log-prod_binary64`
235×	`pow2_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`
163×	`egg-rr`

Counts

4 → 163

Calls

4 calls:

104.0ms	(fma.f64 x x -1/9)
104.0ms	(+.f64 x 1/3)
104.0ms	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))
104.0ms	(/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	199	20
2	2362	20
3	4992	20
0	0	0
1	0	0

simplify122.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/r*_binary64`
414×	`fma-def_binary64`
274×	`distribute-rgt-neg-in_binary64`
256×	`associate-/l/_binary64`
242×	`distribute-lft-neg-in_binary64`

Counts

211 → 187

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	339
1	112	315
2	280	311
3	708	306
4	1934	306
5	4518	306
6	4755	306
7	4955	306
8	4884	306

prune224.0ms (7.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	186	4	190

Error

Counts

190 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x 1/3)
▶	0.1b	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3)))))
	22.3b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
✓	17.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))

Compiler

Compiled 2520 to 1922 computations (23.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x 1/3)
✓	0.0b	(/.f64 1 (-.f64 x 1/3))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3))))
✓	0.1b	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3)))))

series15.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3))))
5.0ms	(/.f64 1 (-.f64 x 1/3))
3.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3)))))

rewrite101.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

699×	`expm1-log1p-u_binary64`
698×	`log1p-expm1-u_binary64`
129×	`expm1-udef_binary64`
129×	`log1p-udef_binary64`
111×	`log-pow_binary64`

Counts

3 → 92

Calls

3 calls:

98.0ms	(/.f64 1 (-.f64 x 1/3))
98.0ms	(log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3))))
98.0ms	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	175	18
2	1776	18
3	4963	18
4	4859	18
0	0	0
1	0	0

simplify147.0ms (5%)

Algorithm

1×	egg-herbie

Rules

601×	`associate-/r*_binary64`
413×	`fma-def_binary64`
274×	`distribute-rgt-neg-in_binary64`
256×	`associate-/l/_binary64`
242×	`distribute-lft-neg-in_binary64`

Counts

128 → 85

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	417
1	106	405
2	272	397
3	699	387
4	1923	387
5	4507	387
6	4742	387
7	4942	387
8	4986	387
9	4878	387

prune143.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	135	4	139

Error

Counts

139 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x 1/3)
✓	0.1b	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3)))))
▶	22.3b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
✓	17.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))

Compiler

Compiled 1608 to 1351 computations (16% saved)

localize16.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 x 3) -1/27)
✓	0.1b	(fma.f64 x 1/3 1/9)
✓	21.4b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))

series16.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(+.f64 (pow.f64 x 3) -1/27)
6.0ms	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
3.0ms	(fma.f64 x 1/3 1/9)

rewrite94.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
197×	`expm1-udef_binary64`
197×	`log1p-udef_binary64`
179×	`prod-diff_binary64`
162×	`log-pow_binary64`

Counts

3 → 103

Calls

3 calls:

90.0ms	(+.f64 (pow.f64 x 3) -1/27)
90.0ms	(fma.f64 x 1/3 1/9)
90.0ms	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	241	30
2	2723	30
3	4882	30
0	0	0
1	0	0

simplify181.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

139 → 116

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	183
1	27	165
2	39	165
3	48	165
4	70	165
5	126	165
6	307	165
7	623	165
8	633	165
9	763	165
10	917	165
11	1080	165
12	1308	165
13	1609	165
14	1957	165
15	2432	165
16	3050	165
17	3246	165
18	3420	165
19	3534	165
20	3581	165
21	3633	165
22	4511	165
23	4814	165

prune150.0ms (5.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	116	4	120

Error

Counts

120 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x 1/3)
✓	0.1b	(/.f64 1 (log1p.f64 (expm1.f64 (/.f64 1 (-.f64 x 1/3)))))
✓	22.3b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
✓	17.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))

Compiler

Compiled 2147 to 1575 computations (26.6% saved)

regimes159.0ms (5.4%)

Accuracy

Total 0.0b remaining (86.6%)

Threshold costs 0.0b (86.6%)

Counts

26 → 1

Compiler

Compiled 548 to 447 computations (18.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	7	4
2	8	4
3	7	4

end106.0ms (3.6%)

Compiler: Compiled 47 to 36 computations (23.4% saved)

Details

analyze7.0ms (0.2%)

sample1.1s (38.1%)

simplify12.0ms (0.4%)

prune4.0ms (0.1%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite91.0ms (3.1%)

simplify11.0ms (0.4%)

prune50.0ms (1.7%)

localize12.0ms (0.4%)

series15.0ms (0.5%)

rewrite109.0ms (3.7%)

simplify122.0ms (4.2%)

prune224.0ms (7.7%)

localize13.0ms (0.4%)

series15.0ms (0.5%)

rewrite101.0ms (3.5%)

simplify147.0ms (5%)

prune143.0ms (4.9%)

localize16.0ms (0.5%)

series16.0ms (0.5%)

rewrite94.0ms (3.2%)

simplify181.0ms (6.2%)

prune150.0ms (5.1%)

regimes159.0ms (5.4%)

simplify6.0ms (0.2%)

end106.0ms (3.6%)

Profiling