Details

analyze5.0ms (0.4%)

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)

sample629.0ms (46.6%)

Results

600.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 17 computations (15% saved)

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	9	4
2	7	4

prune2.0ms (0.2%)

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)

localize5.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series1.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

1.0ms

(-.f64 x 1/3)

rewrite82.0ms (6.1%)

Algorithm

2×	batch-egg-rewrite

Rules

772×	`log1p-udef_binary64`
420×	`log1p-expm1-u_binary64`
420×	`expm1-log1p-u_binary64`
271×	`fma-neg_binary64`
203×	`unpow-prod-down_binary64`

Counts

1 → 49

Calls

1 calls:

81.0ms

(-.f64 x 1/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	100	4
2	1216	4
3	4760	4
4	6000	4
0	0	0
1	0	0

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

52 → 51

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3
1	2	3

prune26.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	49	3	52

Error

Counts

52 → 3

Alt Table

Status	Error	Program
	34.0b	(log.f64 (exp.f64 (-.f64 x 1/3)))
▶	23.0b	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
✓	0.0b	(-.f64 x 1/3)

Compiler

Compiled 482 to 388 computations (19.5% saved)

localize8.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (fma.f64 x 1/3 1/9))
✓	0.0b	(-.f64 (pow.f64 x 3) 1/27)
✓	0.2b	(fma.f64 x 1/3 1/9)
✓	22.2b	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))

series9.0ms (0.7%)

Counts

4 → 39

Calls

4 calls:

3.0ms	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
3.0ms	(-.f64 (pow.f64 x 3) 1/27)
2.0ms	(fma.f64 x x (fma.f64 x 1/3 1/9))
1.0ms	(fma.f64 x 1/3 1/9)

rewrite70.0ms (5.2%)

Algorithm

2×	batch-egg-rewrite

Rules

645×	`fma-neg_binary64`
371×	`fma-def_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
161×	`prod-diff_binary64`

Counts

4 → 142

Calls

4 calls:

68.0ms	(fma.f64 x x (fma.f64 x 1/3 1/9))
68.0ms	(-.f64 (pow.f64 x 3) 1/27)
68.0ms	(fma.f64 x 1/3 1/9)
68.0ms	(/.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	39
1	255	39
2	2762	39
3	4863	39
0	0	0
1	0	0

simplify66.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

592×	`rules-20_binary64`
535×	`rules-13_binary64`
443×	`rules-14-rev_binary64`
421×	`fma-neg_binary64`
262×	`rules-4_binary64`

Counts

181 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	234
1	31	184
2	72	178
3	178	178
4	416	178
5	1810	178
6	4626	178
7	4917	178

prune111.0ms (8.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	159	3	162

Error

Counts

162 → 3

Alt Table

Status	Error	Program
▶	34.0b	(log.f64 (exp.f64 (-.f64 x 1/3)))
✓	23.0b	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
✓	0.0b	(-.f64 x 1/3)

Compiler

Compiled 2824 to 2064 computations (26.9% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 x 1/3))
	0.0b	(-.f64 x 1/3)
✓	0.3b	(log.f64 (exp.f64 (-.f64 x 1/3)))

series3.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

1.0ms	(exp.f64 (-.f64 x 1/3))
1.0ms	(log.f64 (exp.f64 (-.f64 x 1/3)))

rewrite76.0ms (5.6%)

Algorithm

2×	batch-egg-rewrite

Rules

498×	`log1p-expm1-u_binary64`
498×	`expm1-log1p-u_binary64`
337×	`fma-neg_binary64`
212×	`log-prod_binary64`
188×	`fma-def_binary64`

Counts

2 → 82

Calls

2 calls:

75.0ms	(exp.f64 (-.f64 x 1/3))
75.0ms	(log.f64 (exp.f64 (-.f64 x 1/3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	120	10
2	1450	10
3	4899	10
0	0	0
1	0	0

simplify68.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

904×	`fma-def_binary64`
741×	`rules-5_binary64`
650×	`rules-21_binary64`
560×	`rules-13_binary64`
443×	`fma-neg_binary64`

Counts

98 → 91

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	105
1	58	103
2	204	90
3	912	90
4	3660	90
5	4964	86
6	5310	86

prune86.0ms (6.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	142	3	145

Error

Counts

145 → 3

Alt Table

Status	Error	Program
✓	34.0b	(log.f64 (exp.f64 (-.f64 x 1/3)))
✓	23.0b	(/.f64 (-.f64 (pow.f64 x 3) 1/27) (fma.f64 x x (fma.f64 x 1/3 1/9)))
✓	0.0b	(-.f64 x 1/3)

Compiler

Compiled 1421 to 1183 computations (16.7% saved)

regimes36.0ms (2.7%)

Accuracy

Total 0.0b remaining (75.6%)

Threshold costs 0.0b (75.6%)

Counts

14 → 1

Compiler

Compiled 288 to 235 computations (18.4% saved)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	4	4

end45.0ms (3.3%)

Compiler: Compiled 32 to 24 computations (25% saved)

Details

analyze5.0ms (0.4%)

sample629.0ms (46.6%)

simplify7.0ms (0.5%)

prune2.0ms (0.2%)

localize5.0ms (0.4%)

series1.0ms (0.1%)

rewrite82.0ms (6.1%)

simplify7.0ms (0.5%)

prune26.0ms (1.9%)

localize8.0ms (0.6%)

series9.0ms (0.7%)

rewrite70.0ms (5.2%)

simplify66.0ms (4.9%)

prune111.0ms (8.3%)

localize5.0ms (0.3%)

series3.0ms (0.2%)

rewrite76.0ms (5.6%)

simplify68.0ms (5.1%)

prune86.0ms (6.4%)

regimes36.0ms (2.7%)

simplify1.0ms (0.1%)

end45.0ms (3.3%)

Profiling