Details

analyze96.0ms (5%)

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
25%	74.9%	0.1%	5
50%	50%	0.1%	6
56.2%	37.5%	6.3%	7
68.7%	25%	6.3%	8
71.8%	18.7%	9.5%	9
78%	12.5%	9.5%	10
79.6%	9.4%	11%	11
82.7%	6.2%	11%	12
83.5%	4.7%	11.8%	13
85.1%	3.1%	11.8%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample933.0ms (48.2%)

Results

817.0ms	8256×	body	128	valid
8.0ms	87×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify43.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
586×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
115×	`sub-neg_binary64`
82×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	58	12
3	109	12
4	229	11
5	450	11
6	661	11
7	940	11
8	1194	11
9	1320	11
10	1347	11
11	1268	11

prune6.0ms (0.3%)

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
	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
▶	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 67 to 49 computations (26.9% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y 1))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

series9.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

5.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
4.0ms	(*.f64 x (-.f64 y 1))

rewrite71.0ms (3.7%)

Algorithm

2×	batch-egg-rewrite

Rules

614×	`fma-def_binary64`
402×	`fma-neg_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
128×	`add-sqr-sqrt_binary64`

Counts

2 → 108

Calls

2 calls:

69.0ms	(*.f64 x (-.f64 y 1))
69.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	257	21
2	3200	19
3	4860	19
0	0	0
1	0	0

simplify63.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
433×	`fma-def_binary64`
126×	`sub-neg_binary64`
98×	`cancel-sign-sub-inv_binary64`
82×	`distribute-rgt-in_binary64`

Counts

156 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	413
1	69	413
2	144	411
3	283	393
4	524	393
5	913	393
6	1151	393
7	1254	393
8	1326	393
9	1347	393
10	1268	393

prune93.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
	48.0b	(log.f64 (exp.f64 (fma.f64 x (-.f64 y 1) (fma.f64 y -1/2 918938533204673/1000000000000000))))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 2186 to 1585 computations (27.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
✓	0.0b	(fma.f64 y (-.f64 1/2 x) x)

series9.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

5.0ms	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
4.0ms	(fma.f64 y (-.f64 1/2 x) x)

rewrite62.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

484×	`unpow-prod-down_binary64`
383×	`log-prod_binary64`
245×	`pow2_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

2 → 89

Calls

2 calls:

60.0ms	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
60.0ms	(fma.f64 y (-.f64 1/2 x) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	184	19
2	2298	19
3	5569	19
0	0	0
1	0	0

simplify70.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

588×	`fma-neg_binary64`
527×	`fma-def_binary64`
110×	`sub-neg_binary64`
103×	`cancel-sign-sub-inv_binary64`
101×	`distribute-rgt-in_binary64`

Counts

137 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	486
1	81	468
2	179	466
3	359	412
4	665	412
5	1059	412
6	1170	412
7	1264	412
8	1326	412
9	1347	412
10	1268	412

prune63.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
▶	48.0b	(log.f64 (exp.f64 (-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))))
✓	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 1700 to 1207 computations (29% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
	0.0b	(fma.f64 y (-.f64 1/2 x) x)
✓	0.7b	(log.f64 (exp.f64 (-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))))

series5.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(log.f64 (exp.f64 (-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))))

rewrite80.0ms (4.1%)

Algorithm

2×	batch-egg-rewrite

Rules

421×	`log-prod_binary64`
186×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
182×	`pow1/3_binary64`

Counts

1 → 54

Calls

1 calls:

78.0ms

(log.f64 (exp.f64 (-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	201	11
2	2484	11
3	4927	11
4	4904	11
0	0	0
1	0	0

simplify57.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-neg_binary64`
436×	`fma-def_binary64`
120×	`sub-neg_binary64`
95×	`cancel-sign-sub-inv_binary64`
83×	`distribute-rgt-in_binary64`

Counts

78 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	255
1	64	255
2	142	253
3	278	235
4	521	235
5	909	235
6	1151	235
7	1254	235
8	1326	235
9	1347	235
10	1268	235

prune92.0ms (4.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
✓	48.0b	(log.f64 (exp.f64 (-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))))
✓	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y (-.f64 1/2 x) x))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 2892 to 2100 computations (27.4% saved)

regimes111.0ms (5.7%)

Accuracy

Total 0.0b remaining (81.5%)

Threshold costs 0.0b (81.5%)

Counts

31 → 1

Compiler

Compiled 1260 to 952 computations (24.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	14	12
2	15	12
3	13	12

end50.0ms (2.6%)

Compiler: Compiled 57 to 42 computations (26.3% saved)

Details

analyze96.0ms (5%)

sample933.0ms (48.2%)

simplify43.0ms (2.2%)

prune6.0ms (0.3%)

localize7.0ms (0.4%)

series9.0ms (0.5%)

rewrite71.0ms (3.7%)

simplify63.0ms (3.3%)

prune93.0ms (4.8%)

localize5.0ms (0.2%)

series9.0ms (0.5%)

rewrite62.0ms (3.2%)

simplify70.0ms (3.6%)

prune63.0ms (3.2%)

localize7.0ms (0.4%)

series5.0ms (0.3%)

rewrite80.0ms (4.1%)

simplify57.0ms (2.9%)

prune92.0ms (4.8%)

regimes111.0ms (5.7%)

simplify2.0ms (0.1%)

end50.0ms (2.6%)

Profiling