Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50%	0.4%	49.6%	10
50.2%	0.2%	49.6%	11
50.2%	0.1%	49.7%	12
50.2%	0%	49.8%	13
50.2%	0%	49.8%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample879.0ms (24.4%)

Results

833.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

437×	`fma-neg_binary64`
249×	`rules-42_binary64`
239×	`rules-40_binary64`
215×	`rules-41_binary64`
215×	`rules-43_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	43	11
2	122	11
3	422	7
4	801	7
5	7	7

prune2.0ms (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	(exp.f64 (fma.f64 x x -1))

Compiler

Compiled 25 to 17 computations (32% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 x x -1))

series2.0ms (0.1%)

Counts

1 → 4

Calls

1 calls:

2.0ms

(exp.f64 (fma.f64 x x -1))

rewrite82.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

726×	`log1p-udef_binary64`
392×	`log1p-expm1-u_binary64`
392×	`expm1-log1p-u_binary64`
294×	`fma-neg_binary64`
211×	`unpow-prod-down_binary64`

Counts

1 → 53

Calls

1 calls:

81.0ms

(exp.f64 (fma.f64 x x -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	107	7
2	1185	7
3	4817	7
4	6022	7
0	0	0
1	0	0

simplify64.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

913×	`rules-42_binary64`
913×	`rules-43_binary64`
770×	`rules-41_binary64`
435×	`fma-def_binary64`
337×	`rules-13_binary64`

Counts

57 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	81
1	149	63
2	626	56
3	3561	55
4	4601	55
5	5072	55

prune48.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	3	61

Error

0.0b

Counts

61 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))
▶	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
	0.5b	(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))

Compiler

Compiled 857 to 644 computations (24.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 x) x)
✓	0.0b	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))

series9.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))
3.0ms	(pow.f64 (exp.f64 x) x)

rewrite64.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

557×	`log1p-expm1-u_binary64`
557×	`expm1-log1p-u_binary64`
475×	`fma-neg_binary64`
277×	`fma-def_binary64`
165×	`egg-rr`

Counts

2 → 165

Calls

2 calls:

57.0ms	(pow.f64 (exp.f64 x) x)
57.0ms	(*.f64 (pow.f64 (exp.f64 x) x) (exp.f64 -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	149	15
2	1696	13
3	5015	13
0	0	0
1	0	0

simplify139.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-def_binary64`
542×	`rules-22-rev_binary64`
451×	`rules-13_binary64`
443×	`fma-neg_binary64`
232×	`rules-23-rev_binary64`

Counts

189 → 178

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	32	210
1	220	166
2	899	156
3	4781	154
4	4381	154
5	4674	90
6	3126	90
7	3735	90
8	4942	90

prune147.0ms (4.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))
	0.5b	(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
▶	0.0b	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 -1))

Compiler

Compiled 3003 to 1822 computations (39.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (exp.f64 x) x)
✓	0.0b	(log1p.f64 (pow.f64 (exp.f64 x) x))
✓	0.0b	(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))
✓	0.0b	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 -1))

series297.0ms (8.2%)

Counts

3 → 36

Calls

3 calls:

287.0ms	(log1p.f64 (pow.f64 (exp.f64 x) x))
7.0ms	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 -1))
2.0ms	(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))

rewrite65.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

642×	`expm1-log1p-u_binary64`
641×	`log1p-expm1-u_binary64`
242×	`prod-diff_binary64`
130×	`egg-rr`
124×	`expm1-udef_binary64`

Counts

3 → 130

Calls

3 calls:

63.0ms	(log1p.f64 (pow.f64 (exp.f64 x) x))
63.0ms	(expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x)))
63.0ms	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	171	23
2	1946	23
3	5077	23
0	0	0
1	0	0

simplify117.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
613×	`fma-neg_binary64`
523×	`rules-13_binary64`
289×	`rules-40_binary64`
289×	`rules-42_binary64`

Counts

166 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	370
1	305	320
2	1211	315
3	4748	314
4	4569	314
5	4731	314
6	4807	314

prune161.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	192	3	195

Error

Counts

195 → 3

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))
	0.5b	(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
✓	0.0b	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 -1))

Compiler

Compiled 3085 to 1877 computations (39.2% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))
	0.0b	(exp.f64 (fma.f64 x x -1))
✓	0.0b	(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3))
✓	1.0b	(pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3)

series503.0ms (13.9%)

Counts

3 → 36

Calls

3 calls:

286.0ms

(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3))

215.0ms

(pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3)

2.0ms

(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))

rewrite106.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

760×	`fma-neg_binary64`
427×	`fma-def_binary64`
251×	`egg-rr`
203×	`prod-diff_binary64`
197×	`expm1-udef_binary64`

Counts

3 → 251

Calls

3 calls:

99.0ms

(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))

98.0ms

(cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3))

98.0ms

(pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	293	42
2	3062	41
3	5078	41
0	0	0
1	0	0

simplify71.0ms (2%)

Algorithm

1×	egg-herbie

Rules

967×	`fma-neg_binary64`
711×	`rules-43_binary64`
454×	`rules-40_binary64`
454×	`rules-42_binary64`
453×	`rules-41_binary64`

Counts

287 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	557
1	438	485
2	1917	470
3	4889	468
4	5068	468

prune450.0ms (12.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	396	0	396
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	396	3	399

Error

Counts

399 → 3

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 (cbrt.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 2/3)) (pow.f64 (pow.f64 (exp.f64 (fma.f64 x x -1)) 7/3) 1/3))
	0.5b	(*.f64 (exp.f64 -1) (fma.f64 1/2 (pow.f64 x 4) (fma.f64 x x 1)))
✓	0.0b	(*.f64 (expm1.f64 (log1p.f64 (pow.f64 (exp.f64 x) x))) (exp.f64 -1))

Compiler

Compiled 11875 to 9325 computations (21.5% saved)

regimes271.0ms (7.5%)

Accuracy

Total 0.0b remaining (22.1%)

Threshold costs 0.0b (22.1%)

Counts

79 → 1

Compiler

Compiled 4340 to 3426 computations (21.1% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	9	15

end69.0ms (1.9%)

Compiler: Compiled 62 to 49 computations (21% saved)

Details

analyze5.0ms (0.1%)

sample879.0ms (24.4%)

simplify24.0ms (0.7%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite82.0ms (2.3%)

simplify64.0ms (1.8%)

prune48.0ms (1.3%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite64.0ms (1.8%)

simplify139.0ms (3.9%)

prune147.0ms (4.1%)

localize9.0ms (0.2%)

series297.0ms (8.2%)

rewrite65.0ms (1.8%)

simplify117.0ms (3.3%)

prune161.0ms (4.5%)

localize13.0ms (0.4%)

series503.0ms (13.9%)

rewrite106.0ms (2.9%)

simplify71.0ms (2%)

prune450.0ms (12.5%)

regimes271.0ms (7.5%)

simplify1.0ms (0%)

end69.0ms (1.9%)

Profiling