Details

analyze773.0ms (20.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
18.7%	81.1%	0.2%	9
21.8%	78%	0.2%	10
25%	74.9%	0.2%	11
34.7%	64.9%	0.4%	12
47.2%	51.9%	0.9%	13
49%	49.2%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (28.9%)

Results

858.0ms	8256×	body	128	valid
203.0ms	1801×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess26.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

55×	`associate-/l*_binary64`
32×	`associate-/r/_binary64`
31×	`associate-/r*_binary64`
30×	`associate-*r/_binary64`
23×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	70
1	73	70
2	158	70
3	262	70
4	289	70
0	4	4
1	4	4

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort a1 a2)

(sort b1 b2)

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	38	10
3	67	10
4	79	10
5	79	10

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

7.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.0b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
▶	11.6b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 62 to 37 computations (40.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	11.3b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series26.0ms (0.7%)

Counts

1 → 48

Calls

12 calls:

3.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))	a1	-inf
3.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))	b1	-inf
3.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))	a2	-inf
2.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))	a1	inf
2.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))	a2	0

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
237×	`pow2_binary64`
170×	`pow1/3_binary64`
161×	`expm1-udef_binary64`
161×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	169	10
2	2523	10

Stop Event

1×	node limit

Counts

1 → 59

simplify17.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	480
1	17	480
2	38	480
3	67	480
4	79	480
5	79	480

Stop Event

1×

saturated

Counts

107 → 61

prune48.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	52	9	61
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	53	10	63

Error

0.0b

Counts

63 → 10

Alt Table

Status	Error	Program
	30.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 b2))) 2)
	11.8b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	12.1b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
	11.8b	(.f64 (/.f64 a1 (pow.f64 (cbrt.f64 (.f64 b1 b2)) 2)) (/.f64 a2 (cbrt.f64 (*.f64 b1 b2))))
	12.8b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	10.4b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	11.6b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
▶	9.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	13.7b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))
	12.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 982 to 384 computations (60.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.6b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))

series31.0ms (0.8%)

Counts

1 → 48

Calls

12 calls:

5.0ms	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))	a2	inf
4.0ms	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))	b2	0
3.0ms	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))	a1	-inf
3.0ms	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))	a2	-inf
2.0ms	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))	a2	0

rewrite42.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
178×	`pow1/3_binary64`
169×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`
165×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	175	10
2	2603	10

Stop Event

1×	node limit

Counts

1 → 64

simplify18.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`associate-*r/_binary64`
9×	`associate-/r/_binary64`
7×	`*-commutative_binary64`
6×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	480
1	17	480
2	38	480
3	67	480
4	79	480
5	79	480

Stop Event

1×

saturated

Counts

112 → 66

prune53.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	5	3	8
Picked	0	1	1
Done	1	0	1
Total	68	8	76

Error

Counts

76 → 8

Alt Table

Status	Error	Program
	30.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 b2))) 2)
	11.8b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
▶	8.8b	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)
	10.5b	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))
	11.6b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	11.6b	(/.f64 (.f64 a2 a1) (.f64 b1 b2))
✓	9.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	12.8b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))

Compiler

Compiled 827 to 318 computations (61.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.6b	(*.f64 a2 (/.f64 a1 b2))
✓	5.2b	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)

series42.0ms (1.1%)

Counts

2 → 84

Calls

21 calls:

4.0ms	(*.f64 a2 (/.f64 a1 b2))	a2	0
4.0ms	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)	a1	0
3.0ms	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)	a2	-inf
3.0ms	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)	a1	-inf
2.0ms	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)	a2	0

rewrite45.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
242×	`pow2_binary64`
172×	`pow1/3_binary64`
165×	`expm1-udef_binary64`
165×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	172	17
2	2521	17

Stop Event

1×	node limit

Counts

2 → 78

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

13×	`associate-/l*_binary64`
9×	`associate-/r/_binary64`
8×	`associate-*r/_binary64`
7×	`*-commutative_binary64`
7×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	19	732
2	39	732
3	67	732
4	78	732
5	78	732

Stop Event

1×

saturated

Counts

162 → 82

prune53.0ms (1.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	82	8	90

Error

Counts

90 → 8

Alt Table

Status	Error	Program
	30.3b	(pow.f64 (sqrt.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 b2))) 2)
	11.8b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
✓	8.8b	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)
	10.8b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
▶	10.5b	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))
	11.6b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	11.6b	(/.f64 (.f64 a2 a1) (.f64 b1 b2))
✓	9.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))

Compiler

Compiled 1118 to 430 computations (61.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.8b	(*.f64 b1 (/.f64 b2 a1))
✓	7.2b	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))

series40.0ms (1.1%)

Counts

2 → 84

Calls

21 calls:

3.0ms	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))	b2	0
3.0ms	(*.f64 b1 (/.f64 b2 a1))	b2	-inf
3.0ms	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))	a1	-inf
3.0ms	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))	a2	-inf
2.0ms	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))	a1	inf

rewrite47.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
242×	`pow2_binary64`
172×	`pow1/3_binary64`
165×	`expm1-udef_binary64`
165×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	172	17
2	2509	17

Stop Event

1×	node limit

Counts

2 → 79

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

14×	`associate-/l*_binary64`
9×	`*-commutative_binary64`
9×	`associate-/r/_binary64`
7×	`associate-*r/_binary64`
6×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	20	732
2	41	732
3	69	732
4	79	732

Stop Event

1×

saturated

Counts

163 → 83

prune45.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	84	7	91

Error

Counts

91 → 7

Alt Table

Status	Error	Program
	11.5b	(/.f64 a2 (*.f64 b2 (/.f64 b1 a1)))
✓	10.5b	(/.f64 a2 (*.f64 b1 (/.f64 b2 a1)))
	11.8b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
✓	8.8b	(/.f64 (*.f64 a2 (/.f64 a1 b2)) b1)
	10.8b	(/.f64 (*.f64 a1 (/.f64 a2 b2)) b1)
	11.6b	(/.f64 (.f64 a2 a1) (.f64 b1 b2))
✓	9.8b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))

Compiler

Compiled 1020 to 360 computations (64.7% saved)

regimes845.0ms (22.7%)

Accuracy

Total 2.4b remaining (99.1%)

Threshold costs 0b (0%)

Counts

47 → 5

Compiler

Compiled 4835 to 3042 computations (37.1% saved)

bsearch1.0ms (0%)

Algorithm

4×	left-value

Calls

4 calls:

0.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
0.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
0.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
0.0ms	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Steps

Iters	Point		Range
8.987345384745695e+305	∈ [	8.987345384745695e+305	,	#hash((type . real) (value . +inf))	]
-0.0	∈ [	-0.0	,	2.1309043613517e-310	]
-1.393023e-318	∈ [	-1.393023e-318	,	0.0	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-8.749313114363235e+295	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	110
1	38	110

Stop Event

1×

saturated

end370.0ms (9.9%)

Stop Event

1×

fuel

Compiler

Compiled 553 to 219 computations (60.4% saved)

Details

analyze773.0ms (20.8%)

sample1.1s (28.9%)

preprocess26.0ms (0.7%)

simplify7.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series26.0ms (0.7%)

rewrite42.0ms (1.1%)

simplify17.0ms (0.5%)

prune48.0ms (1.3%)

localize5.0ms (0.1%)

series31.0ms (0.8%)

rewrite42.0ms (1.1%)

simplify18.0ms (0.5%)

prune53.0ms (1.4%)

localize5.0ms (0.1%)

series42.0ms (1.1%)

rewrite45.0ms (1.2%)

simplify25.0ms (0.7%)

prune53.0ms (1.4%)

localize5.0ms (0.1%)

series40.0ms (1.1%)

rewrite47.0ms (1.3%)

simplify22.0ms (0.6%)

prune45.0ms (1.2%)

regimes845.0ms (22.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end370.0ms (9.9%)

Profiling