Details

analyze109.0ms (2.7%)

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
37.5%	62.4%	0.1%	6
37.5%	40.6%	22%	7
43.7%	32.8%	23.5%	8
43.7%	21.1%	35.2%	9
46.8%	16.8%	36.4%	10
46.8%	10.7%	42.4%	11
48.4%	8.5%	43.1%	12
48.4%	5.4%	46.2%	13
49.2%	4.3%	46.6%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample812.0ms (19.9%)

Results

744.0ms	8256×	body	128	valid
54.0ms	536×	body	128	invalid

Compiler

Compiled 18 to 12 computations (33.3% saved)

preprocess53.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

428×	`unswap-sqr_binary64`
334×	`associate-/l/_binary64`
292×	`sqr-pow_binary64`
271×	`associate-*r/_binary64`
263×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	15	18
2	22	18
3	40	18
4	95	18
5	271	18
6	854	18
7	1424	18
8	3749	18
9	4019	18
10	4459	18
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

445×	`associate-l_binary64`
407×	`associate-*l/_binary64`
368×	`unswap-sqr_binary64`
264×	`associate-r_binary64`
252×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	13	9
3	22	9
4	51	9
5	140	9
6	425	9
7	1429	9
8	2660	9
9	4022	9
10	4406	9
11	4981	9

Stop Event

1×	node limit

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 x (pow.f64 (exp.f64 y) y))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series243.0ms (6%)

Counts

2 → 36

Calls

9 calls:

103.0ms	(*.f64 x (pow.f64 (exp.f64 y) y))	x	0
64.0ms	(*.f64 x (pow.f64 (exp.f64 y) y))	x	-inf
62.0ms	(*.f64 x (pow.f64 (exp.f64 y) y))	x	inf
6.0ms	(*.f64 x (pow.f64 (exp.f64 y) y))	y	inf
2.0ms	(*.f64 x (pow.f64 (exp.f64 y) y))	y	-inf

rewrite48.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`log1p-expm1-u_binary64`
505×	`expm1-log1p-u_binary64`
428×	`unpow-prod-down_binary64`
289×	`log-prod_binary64`
155×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	120	15
2	1421	15

Stop Event

1×	node limit

Counts

2 → 65

simplify48.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

521×	`fma-def_binary64`
436×	`distribute-rgt-out_binary64`
393×	`associate-l_binary64`
376×	`*-commutative_binary64`
320×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	330
1	77	322
2	192	315
3	585	311
4	2229	311
5	4304	311
6	4795	311

Stop Event

1×	node limit

Counts

101 → 83

prune61.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

0.0b

Counts

84 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))
	0.5b	(+.f64 (.f64 1/6 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
✓	0.0b	(*.f64 x (pow.f64 (exp.f64 y) y))

Compiler

Compiled 1203 to 576 computations (52.1% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (sqrt.f64 (exp.f64 y)) (*.f64 y 1/2))
✓	0.0b	(sqrt.f64 (exp.f64 y))
✓	0.0b	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))
✓	0.0b	(*.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y))

series650.0ms (15.9%)

Counts

4 → 52

Calls

15 calls:

246.0ms	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))	x	0
190.0ms	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))	x	inf
190.0ms	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))	x	-inf
6.0ms	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))	y	inf
4.0ms	(.f64 x (.f64 (pow.f64 (sqrt.f64 (exp.f64 y)) (.f64 y 1/2)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2))))	y	-inf

rewrite49.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`log-prod_binary64`
227×	`log-pow_binary64`
187×	`expm1-udef_binary64`
187×	`log1p-udef_binary64`
174×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	52
1	253	29
2	2968	29

Stop Event

1×	node limit

Counts

4 → 86

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

445×	`*-commutative_binary64`
420×	`unswap-sqr_binary64`
329×	`distribute-lft-out_binary64`
280×	`fma-def_binary64`
223×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	74	1137
1	180	1091
2	455	821
3	1485	818
4	2456	690
5	4246	570

Stop Event

1×	node limit

Counts

138 → 117

prune182.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	150	4	154

Error

0.0b

Counts

154 → 4

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 1/6 (.f64 (pow.f64 y 6) x)) (+.f64 (.f64 (pow.f64 y 2) x) (+.f64 (.f64 1/2 (*.f64 (pow.f64 y 4) x)) x)))
▶	0.0b	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))
✓	0.0b	(*.f64 x (pow.f64 (exp.f64 y) y))
	0.0b	(.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3))) y))) (.f64 x (exp.f64 (.f64 1/2 (.f64 y (log.f64 (sqrt.f64 (exp.f64 y))))))))

Compiler

Compiled 3440 to 1803 computations (47.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (*.f64 y 1/2)))
	0.0b	(sqrt.f64 (exp.f64 y))
✓	0.0b	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))
	0.0b	(*.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y))

series616.0ms (15.1%)

Counts

2 → 36

Calls

9 calls:

241.0ms	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))	x	0
177.0ms	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))	x	-inf
173.0ms	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))	x	inf
8.0ms	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))	y	inf
5.0ms	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))	y	-inf

rewrite54.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`log-prod_binary64`
236×	`log-pow_binary64`
221×	`expm1-udef_binary64`
221×	`log1p-udef_binary64`
168×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	57
1	300	25
2	3606	25

Stop Event

1×	node limit

Counts

2 → 35

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Rules

546×	`fma-def_binary64`
525×	`unswap-sqr_binary64`
502×	`associate-l_binary64`
393×	`distribute-rgt-out_binary64`
364×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	45	918
1	114	854
2	261	763
3	780	703
4	2923	591

Stop Event

1×	node limit

Counts

71 → 54

prune133.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	112	4	116

Error

0.0b

Counts

116 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))
✓	0.0b	(*.f64 x (pow.f64 (exp.f64 y) y))
	0.5b	(fma.f64 x (fma.f64 1/2 (pow.f64 y 4) (fma.f64 1/6 (pow.f64 y 6) (*.f64 y y))) x)
▶	0.0b	(.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3))) y))) (.f64 (exp.f64 (*.f64 1/4 (pow.f64 y 2))) x))

Compiler

Compiled 2150 to 1277 computations (40.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (exp.f64 (.f64 1/4 (pow.f64 y 2))) x)
✓	0.0b	(sqrt.f64 (pow.f64 (exp.f64 y) 3))
✓	0.1b	(pow.f64 (exp.f64 y) 3)
✓	6.8b	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3)))

series278.0ms (6.8%)

Counts

4 → 16

Calls

15 calls:

120.0ms	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3)))	y	inf
117.0ms	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3)))	y	-inf
12.0ms	(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3)))	y	0
5.0ms	(.f64 (exp.f64 (.f64 1/4 (pow.f64 y 2))) x)	x	0
4.0ms	(.f64 (exp.f64 (.f64 1/4 (pow.f64 y 2))) x)	x	-inf

rewrite50.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

542×	`log-prod_binary64`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`
204×	`log-pow_binary64`
189×	`pow3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	277	28
2	2924	28

Stop Event

1×	node limit

Counts

4 → 114

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1926×	`fma-def_binary64`
420×	`*-commutative_binary64`
269×	`distribute-lft-out_binary64`
228×	`unswap-sqr_binary64`
170×	`associate-+l+_binary64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	47	165
1	121	161
2	334	146
3	1088	133
4	2722	133
5	3547	133
6	3755	133
7	3915	133
8	4086	133
9	4307	127

Stop Event

1×	node limit

Counts

130 → 134

prune180.0ms (4.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	134	4	138

Error

0.0b

Counts

138 → 4

Alt Table

Status	Error	Program
✓	0.0b	(.f64 x (.f64 (pow.f64 (exp.f64 y) (/.f64 y 4)) (pow.f64 (.f64 (sqrt.f64 (exp.f64 y)) (exp.f64 y)) (.f64 y 1/2))))
✓	0.0b	(*.f64 x (pow.f64 (exp.f64 y) y))
	0.5b	(fma.f64 x (fma.f64 1/2 (pow.f64 y 4) (fma.f64 1/6 (pow.f64 y 6) (*.f64 y y))) x)
✓	0.0b	(.f64 (exp.f64 (.f64 1/2 (.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) 3))) y))) (.f64 (exp.f64 (*.f64 1/4 (pow.f64 y 2))) x))

Compiler

Compiled 3193 to 2366 computations (25.9% saved)

regimes188.0ms (4.6%)

Accuracy

Total 0.0b remaining (71.9%)

Threshold costs 0.0b (71.9%)

Counts

41 → 1

Compiler

Compiled 3749 to 2808 computations (25.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	7	9

Stop Event

1×

saturated

end77.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 85 to 58 computations (31.8% saved)

Details

analyze109.0ms (2.7%)

sample812.0ms (19.9%)

preprocess53.0ms (1.3%)

simplify42.0ms (1%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series243.0ms (6%)

rewrite48.0ms (1.2%)

simplify48.0ms (1.2%)

prune61.0ms (1.5%)

localize11.0ms (0.3%)

series650.0ms (15.9%)

rewrite49.0ms (1.2%)

simplify63.0ms (1.5%)

prune182.0ms (4.5%)

localize12.0ms (0.3%)

series616.0ms (15.1%)

rewrite54.0ms (1.3%)

simplify41.0ms (1%)

prune133.0ms (3.3%)

localize14.0ms (0.3%)

series278.0ms (6.8%)

rewrite50.0ms (1.2%)

simplify57.0ms (1.4%)

prune180.0ms (4.4%)

regimes188.0ms (4.6%)

simplify2.0ms (0%)

end77.0ms (1.9%)

Profiling