Details

analyze56.0ms (2.6%)

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
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample871.0ms (41.3%)

Results

858.0ms

8256×

body

128

valid

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess62.0ms (2.9%)

Algorithm

2×	egg-herbie

Rules

762×	`fma-neg_binary64`
504×	`fma-def_binary64`
425×	`times-frac_binary64`
376×	`div-sub_binary64`
206×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	29	24
2	55	24
3	116	24
4	271	24
5	568	20
6	1384	20
7	3080	20
8	4110	20
9	4417	20
10	4558	20
11	4596	20
12	4606	20
13	4606	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 6 computations (40% saved)

simplify53.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
621×	`fma-neg_binary64`
448×	`times-frac_binary64`
307×	`div-sub_binary64`
143×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	18	12
2	38	12
3	82	12
4	182	12
5	331	12
6	818	10
7	2221	10
8	3129	10
9	3837	10
10	3958	10
11	4001	10
12	4011	10
13	4011	10

Stop Event

1×

saturated

Counts

1 → 2

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	(/.f64 (+.f64 f n) (-.f64 n f))

Compiler

Compiled 35 to 18 computations (48.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

series7.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(/.f64 (+.f64 f n) (-.f64 n f))	n	-inf
1.0ms	(/.f64 (+.f64 f n) (-.f64 n f))	f	0
1.0ms	(/.f64 (+.f64 f n) (-.f64 n f))	f	inf
1.0ms	(/.f64 (+.f64 f n) (-.f64 n f))	n	0
1.0ms	(/.f64 (+.f64 f n) (-.f64 n f))	f	-inf

rewrite41.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`log1p-expm1-u_binary64`
884×	`expm1-log1p-u_binary64`
79×	`add-sqr-sqrt_binary64`
78×	`*-un-lft-identity_binary64`
78×	`pow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	144	10
2	2307	10

Stop Event

1×	node limit

Counts

1 → 35

simplify25.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

822×	`associate-/l*_binary64`
504×	`associate-/r*_binary64`
384×	`associate-/r/_binary64`
251×	`cancel-sign-sub-inv_binary64`
194×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	426
1	112	393
2	383	342
3	1549	324

Stop Event

1×	node limit

Counts

59 → 49

prune35.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

Counts

50 → 3

Alt Table

Status	Error	Program
▶	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	33.5b	(+.f64 1 (.f64 2 (+.f64 (pow.f64 (/.f64 f n) 3) (.f64 (+.f64 (/.f64 f n) 1) (/.f64 f n)))))
	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)

Compiler

Compiled 725 to 310 computations (57.2% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	0.5b	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))

series21.0ms (1%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))	n	0
2.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))	f	inf
2.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))	f	-inf
2.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))	n	-inf
2.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))	f	0

rewrite47.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`prod-diff_binary64`
317×	`fma-def_binary64`
155×	`expm1-udef_binary64`
155×	`log1p-udef_binary64`
145×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	166	22
2	2514	22

Stop Event

1×	node limit

Counts

2 → 73

simplify45.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

446×	`cancel-sign-sub-inv_binary64`
423×	`times-frac_binary64`
419×	`fma-neg_binary64`
307×	`associate-/l*_binary64`
253×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1089
1	236	1017
2	834	933
3	3835	918

Stop Event

1×	node limit

Counts

121 → 103

prune87.0ms (4.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	152	3	155

Error

Counts

155 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
▶	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
	33.7b	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))

Compiler

Compiled 2332 to 974 computations (58.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
✓	0.0b	(/.f64 (-.f64 n f) (+.f64 f n))

series15.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

1.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)	n	-inf
1.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)	n	0
1.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)	f	inf
1.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)	f	-inf
1.0ms	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)	f	0

rewrite114.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

974×	`prod-diff_binary64`
233×	`egg-rr`
171×	`log1p-udef_binary64`
100×	`add-sqr-sqrt_binary64`
97×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	189	20
2	2892	20

Stop Event

1×	node limit

Counts

2 → 280

simplify39.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

759×	`cancel-sign-sub-inv_binary64`
468×	`fma-neg_binary64`
269×	`distribute-neg-frac_binary64`
247×	`distribute-rgt-neg-in_binary64`
243×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	852
1	154	792
2	522	702
3	2042	651

Stop Event

1×	node limit

Counts

328 → 306

prune193.0ms (9.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	306	3	309

Error

Counts

309 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
▶	33.7b	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))

Compiler

Compiled 13209 to 3870 computations (70.7% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 f (/.f64 n f))
✓	5.4b	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))

series23.0ms (1.1%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(/.f64 f (/.f64 n f))	f	inf
2.0ms	(/.f64 f (/.f64 n f))	n	-inf
2.0ms	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))	f	inf
2.0ms	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))	n	-inf
2.0ms	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))	f	-inf

rewrite62.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

573×	`log-prod_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
196×	`log-div_binary64`
169×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	232	28
2	3002	28

Stop Event

1×	node limit

Counts

2 → 80

simplify28.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

767×	`associate-/l*_binary64`
522×	`associate-/l/_binary64`
453×	`associate-/r*_binary64`
405×	`associate-*l/_binary64`
345×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	16	567
1	41	543
2	79	486
3	182	486
4	882	456

Stop Event

1×	node limit

Counts

128 → 90

prune50.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	90	3	93

Error

Counts

93 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(pow.f64 (/.f64 (-.f64 n f) (+.f64 f n)) -1)
✓	33.7b	(fma.f64 (/.f64 2 n) (/.f64 f (/.f64 n f)) (fma.f64 2 (/.f64 f n) 1))

Compiler

Compiled 1873 to 927 computations (50.5% saved)

regimes153.0ms (7.2%)

Accuracy

Total 0.0b remaining (41.1%)

Threshold costs 0.0b (41.1%)

Counts

64 → 1

Compiler

Compiled 2420 to 1664 computations (31.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	12	19
2	18	19
3	22	19
4	25	19
5	26	19

Stop Event

1×

saturated

end51.0ms (2.4%)

Stop Event

1×

done

Compiler

Compiled 69 to 41 computations (40.6% saved)

Details

analyze56.0ms (2.6%)

sample871.0ms (41.3%)

preprocess62.0ms (2.9%)

simplify53.0ms (2.5%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite41.0ms (2%)

simplify25.0ms (1.2%)

prune35.0ms (1.7%)

localize9.0ms (0.4%)

series21.0ms (1%)

rewrite47.0ms (2.2%)

simplify45.0ms (2.1%)

prune87.0ms (4.1%)

localize7.0ms (0.3%)

series15.0ms (0.7%)

rewrite114.0ms (5.4%)

simplify39.0ms (1.8%)

prune193.0ms (9.1%)

localize9.0ms (0.4%)

series23.0ms (1.1%)

rewrite62.0ms (3%)

simplify28.0ms (1.3%)

prune50.0ms (2.4%)

regimes153.0ms (7.2%)

simplify2.0ms (0.1%)

end51.0ms (2.4%)

Profiling