Details

analyze87.0ms (5.3%)

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
50%	37.5%	12.6%	7
56.2%	31.2%	12.6%	8
62.4%	18.7%	18.8%	9
65.6%	15.6%	18.8%	10
68.7%	9.4%	22%	11
70.2%	7.8%	22%	12
71.8%	4.7%	23.5%	13
72.6%	3.9%	23.5%	14

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample712.0ms (43.8%)

Results

686.0ms	8256×	body	128	valid
12.0ms	155×	body	128	invalid

Compiler

Compiled 16 to 10 computations (37.5% saved)

preprocess14.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	16	14
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	9	7
2	10	7

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.7b	(.f64 x (.f64 y y))
▶	0.1b	(.f64 (.f64 x y) y)

Compiler

Compiled 40 to 22 computations (45% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 x y) y)

series7.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(.f64 (.f64 x y) y)	x	-inf
1.0ms	(.f64 (.f64 x y) y)	x	0
1.0ms	(.f64 (.f64 x y) y)	x	inf
1.0ms	(.f64 (.f64 x y) y)	y	-inf
1.0ms	(.f64 (.f64 x y) y)	y	inf

rewrite29.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

431×	`log1p-expm1-u_binary64`
431×	`expm1-log1p-u_binary64`
371×	`unpow-prod-down_binary64`
273×	`log-prod_binary64`
180×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	99	7
2	1204	7

Stop Event

1×	node limit

Counts

1 → 17

simplify65.0ms (4%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
448×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
277×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	12	168
2	23	168
3	44	168
4	105	168
5	314	168
6	1257	168
7	2131	168
8	2295	168
9	2479	168
10	2687	168
11	2979	168
12	3372	168
13	3852	168
14	4415	168

Stop Event

1×	node limit

Counts

41 → 19

prune11.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	17	4	21

Error

0.1b

Counts

21 → 4

Alt Table

Status	Error	Program
	31.4b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
✓	0.1b	(.f64 (.f64 x y) y)
▶	9.7b	(.f64 x (.f64 y y))
	10.2b	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)

Compiler

Compiled 218 to 100 computations (54.1% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.4b	(.f64 x (.f64 y y))

series8.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(.f64 x (.f64 y y))	x	-inf
1.0ms	(.f64 x (.f64 y y))	x	0
1.0ms	(.f64 x (.f64 y y))	x	inf
1.0ms	(.f64 x (.f64 y y))	y	-inf
1.0ms	(.f64 x (.f64 y y))	y	inf

rewrite31.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

421×	`log1p-expm1-u_binary64`
421×	`expm1-log1p-u_binary64`
326×	`unpow-prod-down_binary64`
252×	`log-prod_binary64`
175×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	100	7
2	1212	7

Stop Event

1×	node limit

Counts

1 → 20

simplify77.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
448×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
277×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	12	168
2	23	168
3	44	168
4	105	168
5	314	168
6	1257	168
7	2131	168
8	2295	168
9	2479	168
10	2687	168
11	2979	168
12	3372	168
13	3852	168
14	4415	168

Stop Event

1×	node limit

Counts

44 → 22

prune13.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	22	4	26

Error

0.1b

Counts

26 → 4

Alt Table

Status	Error	Program
	31.4b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
✓	0.1b	(.f64 (.f64 x y) y)
✓	9.7b	(.f64 x (.f64 y y))
▶	10.2b	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)

Compiler

Compiled 239 to 110 computations (54% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)
	9.4b	(.f64 x (.f64 y y))
✓	21.6b	(cbrt.f64 (.f64 x (.f64 y y)))

series76.0ms (4.7%)

Counts

2 → 0

Calls

12 calls:

24.0ms	(cbrt.f64 (.f64 x (.f64 y y)))	x	-inf
18.0ms	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)	x	-inf
10.0ms	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)	x	0
5.0ms	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)	y	0
3.0ms	(pow.f64 (cbrt.f64 (.f64 x (.f64 y y))) 3)	x	inf

rewrite42.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`log1p-expm1-u_binary64`
588×	`expm1-log1p-u_binary64`
330×	`log-prod_binary64`
117×	`expm1-udef_binary64`
117×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	161	16
2	1712	16

Stop Event

1×	node limit

Counts

2 → 64

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

64 → 64

prune52.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	83	7	90

Error

0.0b

Counts

90 → 7

Alt Table

Status	Error	Program
	34.2b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 y)) (sqrt.f64 y))
✓	9.7b	(.f64 x (.f64 y y))
	9.9b	(.f64 (.f64 (.f64 x y) (cbrt.f64 (.f64 y y))) (cbrt.f64 y))
	31.4b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
✓	0.1b	(.f64 (.f64 x y) y)
	38.6b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 y y) 3)))
▶	0.8b	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)

Compiler

Compiled 1128 to 495 computations (56.1% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 y (.f64 y x))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)
✓	21.6b	(cbrt.f64 (.f64 y (.f64 y x)))

series64.0ms (4%)

Counts

3 → 24

Calls

18 calls:

20.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)	x	-inf
11.0ms	(cbrt.f64 (.f64 y (.f64 y x)))	x	-inf
4.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)	x	inf
4.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)	x	0
3.0ms	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)	y	-inf

rewrite44.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
352×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	161	23
2	1726	23

Stop Event

1×	node limit

Counts

3 → 89

simplify61.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
448×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
277×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	12	168
2	23	168
3	44	168
4	105	168
5	314	168
6	1257	168
7	2131	168
8	2295	168
9	2479	168
10	2687	168
11	2979	168
12	3372	168
13	3852	168
14	4415	168

Stop Event

1×	node limit

Counts

113 → 76

prune45.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	75	8	83

Error

0.0b

Counts

83 → 8

Alt Table

Status	Error	Program
	34.2b	(.f64 (.f64 (*.f64 x y) (sqrt.f64 y)) (sqrt.f64 y))
✓	9.7b	(.f64 x (.f64 y y))
	31.4b	(pow.f64 (*.f64 y (sqrt.f64 x)) 2)
✓	0.1b	(.f64 (.f64 x y) y)
✓	0.8b	(pow.f64 (cbrt.f64 (.f64 y (.f64 y x))) 3)
	0.8b	(.f64 (.f64 (*.f64 y x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
	0.8b	(.f64 (cbrt.f64 y) (.f64 (cbrt.f64 (.f64 y x)) (pow.f64 (cbrt.f64 (.f64 y (*.f64 y x))) 2)))
	38.6b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 y y) 3)))

Compiler

Compiled 996 to 370 computations (62.9% saved)

regimes71.0ms (4.4%)

Accuracy

Total 0.1b remaining (78.8%)

Threshold costs 0.1b (78.8%)

Counts

18 → 1

Compiler

Compiled 629 to 421 computations (33.1% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	7	7

Stop Event

1×

saturated

end79.0ms (4.9%)

Stop Event

1×

fuel

Compiler

Compiled 100 to 63 computations (37% saved)

Details

analyze87.0ms (5.3%)

sample712.0ms (43.8%)

preprocess14.0ms (0.9%)

simplify9.0ms (0.5%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series7.0ms (0.5%)

rewrite29.0ms (1.8%)

simplify65.0ms (4%)

prune11.0ms (0.7%)

localize3.0ms (0.2%)

series8.0ms (0.5%)

rewrite31.0ms (1.9%)

simplify77.0ms (4.8%)

prune13.0ms (0.8%)

localize5.0ms (0.3%)

series76.0ms (4.7%)

rewrite42.0ms (2.6%)

simplify6.0ms (0.4%)

prune52.0ms (3.2%)

localize7.0ms (0.4%)

series64.0ms (4%)

rewrite44.0ms (2.7%)

simplify61.0ms (3.7%)

prune45.0ms (2.8%)

regimes71.0ms (4.4%)

simplify3.0ms (0.2%)

end79.0ms (4.9%)

Profiling