Details

analyze415.0ms (1.8%)

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
43.7%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.1s (17.8%)

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Results

2.6s	2566×	body	8192	exit
1.0s	7664×	body	128	valid
127.0ms	196×	body	1024	valid
104.0ms	262×	body	512	valid
35.0ms	133×	body	256	valid
10.0ms	78×	body	128	invalid
2.0ms	1×	body	2048	valid

Compiler

Compiled 57 to 42 computations (26.3% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
✓	0.2b	(log.f64 (+.f64 1 (exp.f64 x)))

series292.0ms (1.3%)

Counts

3 → 32

Calls

3 calls:

206.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
84.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite143.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

804×	`prod-diff_binary64`
319×	`fma-def_binary64`
238×	`egg-rr`
166×	`expm1-udef_binary64`
165×	`log1p-udef_binary64`

Counts

3 → 238

Calls

3 calls:

99.0ms	(+.f64 1 (exp.f64 x))
99.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
99.0ms	(log.f64 (+.f64 1 (exp.f64 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	185	22
2	2316	22
3	4831	22
4	5020	22
0	0	0
1	0	0

prune206.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	267	4	271

Error

0.2b

Counts

271 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	10.9b	(-.f64 (+.f64 (log.f64 2) (.f64 1/2 x)) (.f64 x y))
	26.5b	(log.f64 (.f64 (exp.f64 (neg.f64 (.f64 x y))) (+.f64 1 (exp.f64 x))))
	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

Compiler

Compiled 5612 to 1530 computations (72.7% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.1%)

Counts

2 → 27

Calls

2 calls:

12.0ms	(-.f64 (+.f64 (log.f64 2) (.f64 1/2 x)) (.f64 x y))
5.0ms	(+.f64 (log.f64 2) (*.f64 1/2 x))

rewrite71.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

540×	`fma-def_binary64`
529×	`log-prod_binary64`
248×	`fma-neg_binary64`
201×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`

Counts

2 → 182

Calls

2 calls:

65.0ms	(+.f64 (log.f64 2) (*.f64 1/2 x))
65.0ms	(-.f64 (+.f64 (log.f64 2) (.f64 1/2 x)) (.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	223	19
2	2870	17
3	5618	17
0	0	0
1	0	0

prune163.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	209	4	213

Error

0.2b

Counts

213 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	26.5b	(log.f64 (.f64 (exp.f64 (neg.f64 (.f64 x y))) (+.f64 1 (exp.f64 x))))
▶	12.4b	(pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 3)
	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

Compiler

Compiled 3576 to 2283 computations (36.2% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.8b	(pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 3)
✓	1.1b	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

series15.5s (67.5%)

Counts

3 → 72

Calls

3 calls:

15.5s	(pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 3)
53.0ms	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))
15.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

rewrite62.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

570×	`unpow-prod-down_binary64`
404×	`log-prod_binary64`
251×	`pow2_binary64`
177×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`

Counts

3 → 143

Calls

3 calls:

57.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
57.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2))) 3)
57.0ms	(cbrt.f64 (fma.f64 x (-.f64 1/2 y) (log.f64 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	215	32
2	2317	32
3	5467	32
0	0	0
1	0	0

prune206.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	215	4	219

Error

0.2b

Counts

219 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	26.5b	(log.f64 (.f64 (exp.f64 (neg.f64 (.f64 x y))) (+.f64 1 (exp.f64 x))))
	61.0b	(pow.f64 (+.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (-.f64 1/2 y)) (log.f64 (/.f64 1 x))))) (.f64 1/3 (/.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (-.f64 1/2 y)) (log.f64 (/.f64 1 x))))) (log.f64 2)) (*.f64 (-.f64 1/2 y) x)))) 3)
▶	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

Compiler

Compiled 5486 to 4397 computations (19.9% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(log1p.f64 (exp.f64 x))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
✓	15.5b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

series878.0ms (3.8%)

Counts

4 → 60

Calls

4 calls:

233.0ms	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))
217.0ms	(log1p.f64 (exp.f64 x))
215.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
213.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 2)

rewrite90.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

295×	`fma-neg_binary64`
267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`
155×	`add-sqr-sqrt_binary64`
155×	`expm1-log1p-u_binary64`

Counts

4 → 132

Calls

4 calls:

86.0ms	(log1p.f64 (exp.f64 x))
86.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
86.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 2)
86.0ms	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	330	32
2	3970	32
3	4981	32
0	0	0
1	0	0

prune229.0ms (1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	254	0	254
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	254	4	258

Error

0.2b

Counts

258 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	26.5b	(log.f64 (.f64 (exp.f64 (neg.f64 (.f64 x y))) (+.f64 1 (exp.f64 x))))
	61.0b	(pow.f64 (+.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (-.f64 1/2 y)) (log.f64 (/.f64 1 x))))) (.f64 1/3 (/.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (-.f64 1/2 y)) (log.f64 (/.f64 1 x))))) (log.f64 2)) (*.f64 (-.f64 1/2 y) x)))) 3)
✓	16.3b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) 2)))

Compiler

Compiled 7493 to 2939 computations (60.8% saved)

regimes473.0ms (2.1%)

Accuracy

Total 0.1b remaining (28.3%)

Threshold costs 0.1b (28.3%)

Counts

126 → 1

Compiler

Compiled 6629 to 4147 computations (37.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	11	11
2	13	11
3	14	11
4	14	11

end93.0ms (0.4%)

Compiler: Compiled 111 to 79 computations (28.8% saved)

Details

analyze415.0ms (1.8%)

sample4.1s (17.8%)

localize7.0ms (0%)

series292.0ms (1.3%)

rewrite143.0ms (0.6%)

prune206.0ms (0.9%)

localize7.0ms (0%)

series16.0ms (0.1%)

rewrite71.0ms (0.3%)

prune163.0ms (0.7%)

localize8.0ms (0%)

series15.5s (67.5%)

rewrite62.0ms (0.3%)

prune206.0ms (0.9%)

localize25.0ms (0.1%)

series878.0ms (3.8%)

rewrite90.0ms (0.4%)

prune229.0ms (1%)

regimes473.0ms (2.1%)

simplify2.0ms (0%)

end93.0ms (0.4%)

Profiling