Details

analyze38.0ms (1.6%)

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 10 to 6 computations (40% saved)

sample747.0ms (32.4%)

Results

736.0ms

8256×

body

128

valid

Compiler

Compiled 20 to 12 computations (40% saved)

preprocess61.0ms (2.6%)

Algorithm

2×	egg-herbie

Rules

660×	`fma-neg_binary64`
445×	`div-sub_binary64`
433×	`times-frac_binary64`
346×	`fma-def_binary64`
238×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	14	20
2	22	20
3	34	20
4	56	20
5	107	20
6	153	20
7	275	20
8	690	20
9	1931	20
10	3137	20
11	3592	20
12	3802	20
13	3910	20
14	3964	20
15	3964	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify53.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
362×	`div-sub_binary64`
361×	`times-frac_binary64`
137×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	31	10
5	54	10
6	91	10
7	134	10
8	214	10
9	439	10
10	1099	10
11	1804	10
12	2674	10
13	3121	10
14	3277	10
15	3299	10
16	3319	10
17	3319	10

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series7.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(/.f64 (+.f64 x y) (-.f64 x y))	x	0
1.0ms	(/.f64 (+.f64 x y) (-.f64 x y))	x	-inf
1.0ms	(/.f64 (+.f64 x y) (-.f64 x y))	y	inf
1.0ms	(/.f64 (+.f64 x y) (-.f64 x y))	y	-inf
1.0ms	(/.f64 (+.f64 x y) (-.f64 x y))	x	inf

rewrite42.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`log1p-expm1-u_binary64`
828×	`expm1-log1p-u_binary64`
552×	`prod-diff_binary64`
74×	`add-sqr-sqrt_binary64`
70×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	140	10
2	2143	10

Stop Event

1×	node limit

Counts

1 → 35

simplify27.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

823×	`associate-/l*_binary64`
492×	`associate-/r*_binary64`
361×	`associate-/r/_binary64`
338×	`cancel-sign-sub-inv_binary64`
194×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	417
1	121	399
2	382	339
3	1513	327

Stop Event

1×	node limit

Counts

59 → 49

prune38.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	4	50

Error

Counts

50 → 4

Alt Table

Status	Error	Program
	1.3b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	33.5b	(-.f64 -1 (.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x)))))
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
▶	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)

Compiler

Compiled 735 to 316 computations (57% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series16.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)	x	-inf
2.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)	y	-inf
1.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)	y	inf
1.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)	x	0
1.0ms	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)	y	0

rewrite130.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

768×	`prod-diff_binary64`
268×	`egg-rr`
250×	`fma-def_binary64`
167×	`expm1-udef_binary64`
167×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	185	20
2	2742	20

Stop Event

1×	node limit

Counts

2 → 268

simplify41.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

757×	`cancel-sign-sub-inv_binary64`
496×	`fma-neg_binary64`
198×	`distribute-rgt-neg-in_binary64`
198×	`distribute-neg-frac_binary64`
194×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	831
1	161	807
2	521	705
3	2021	666

Stop Event

1×	node limit

Counts

316 → 294

prune222.0ms (9.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	294	4	298

Error

Counts

298 → 4

Alt Table

Status	Error	Program
▶	1.3b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	33.5b	(-.f64 -1 (.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x)))))
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)

Compiler

Compiled 12400 to 3795 computations (69.4% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	2.1b	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

series21.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))	x	-inf
3.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))	x	0
2.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))	y	inf
2.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))	y	-inf
2.0ms	(log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y)))	y	0

rewrite57.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

903×	`expm1-log1p-u_binary64`
742×	`prod-diff_binary64`
82×	`add-sqr-sqrt_binary64`
80×	`log1p-expm1-u_binary64`
77×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	161	22
2	2349	22

Stop Event

1×	node limit

Counts

2 → 69

simplify48.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

540×	`cancel-sign-sub-inv_binary64`
427×	`associate-+l+_binary64`
323×	`fma-neg_binary64`
296×	`associate-+r+_binary64`
262×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	969
1	272	915
2	871	831
3	3596	825

Stop Event

1×	node limit

Counts

117 → 106

prune115.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
✓	1.3b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
▶	33.5b	(-.f64 -1 (.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x)))))
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)

Compiler

Compiled 2388 to 1046 computations (56.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (.f64 (/.f64 x y) x)))
✓	0.1b	(.f64 (+.f64 (/.f64 x y) 1) (.f64 (/.f64 x y) x))
✓	0.2b	(*.f64 (/.f64 x y) x)
✓	2.3b	(.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x))))

series81.0ms (3.5%)

Counts

4 → 96

Calls

24 calls:

16.0ms	(.f64 (+.f64 (/.f64 x y) 1) (.f64 (/.f64 x y) x))	y	inf
6.0ms	(.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x))))	x	inf
5.0ms	(.f64 (+.f64 (/.f64 x y) 1) (.f64 (/.f64 x y) x))	y	-inf
5.0ms	(.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x))))	x	-inf
4.0ms	(.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x))))	y	inf

rewrite77.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`fma-neg_binary64`
238×	`log1p-udef_binary64`
237×	`expm1-udef_binary64`
140×	`egg-rr`
136×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	67
1	275	63
2	4077	63

Stop Event

1×	node limit

Counts

4 → 140

simplify56.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
538×	`associate-/l*_binary64`
296×	`associate-*l/_binary64`
293×	`associate-/r*_binary64`
267×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	1521
1	67	1509
2	188	1305
3	695	1203
4	3841	1155

Stop Event

1×	node limit

Counts

236 → 161

prune119.0ms (5.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
✓	1.3b	(expm1.f64 (log1p.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
✓	33.5b	(-.f64 -1 (.f64 (/.f64 2 y) (+.f64 x (.f64 (+.f64 (/.f64 x y) 1) (*.f64 (/.f64 x y) x)))))
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	0.0b	(pow.f64 (/.f64 (-.f64 x y) (+.f64 x y)) -1)

Compiler

Compiled 4249 to 2216 computations (47.8% saved)

regimes210.0ms (9.1%)

Accuracy

Total 0.0b remaining (51%)

Threshold costs 0.0b (51%)

Counts

80 → 1

Compiler

Compiled 3541 to 2418 computations (31.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	18	22
2	22	22
3	25	22
4	26	22

Stop Event

1×

saturated

end68.0ms (3%)

Stop Event

1×

done

Compiler

Compiled 86 to 52 computations (39.5% saved)

Details

analyze38.0ms (1.6%)

sample747.0ms (32.4%)

preprocess61.0ms (2.6%)

simplify53.0ms (2.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite42.0ms (1.8%)

simplify27.0ms (1.2%)

prune38.0ms (1.6%)

localize6.0ms (0.3%)

series16.0ms (0.7%)

rewrite130.0ms (5.6%)

simplify41.0ms (1.8%)

prune222.0ms (9.6%)

localize7.0ms (0.3%)

series21.0ms (0.9%)

rewrite57.0ms (2.5%)

simplify48.0ms (2.1%)

prune115.0ms (5%)

localize10.0ms (0.4%)

series81.0ms (3.5%)

rewrite77.0ms (3.3%)

simplify56.0ms (2.4%)

prune119.0ms (5.2%)

regimes210.0ms (9.1%)

simplify2.0ms (0.1%)

end68.0ms (3%)

Profiling