Details

analyze930.0ms (27.9%)

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
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
18.7%	81.1%	0.2%	11
25.3%	74.3%	0.4%	12
33.5%	65.6%	0.9%	13
38.5%	59.7%	1.8%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.1s (31.6%)

Results

845.0ms	8256×	body	128	valid
188.0ms	1847×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess22.0ms (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)

simplify8.0ms (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

4.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	8.1b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	10.2b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 62 to 37 computations (40.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.1b	(/.f64 a2 (*.f64 b1 b2))
✓	4.7b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))

series42.0ms (1.3%)

Counts

2 → 84

Calls

21 calls:

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

rewrite52.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`
78×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	17
2	2305	17

Stop Event

1×	node limit

Counts

2 → 68

simplify24.0ms (0.7%)

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	9	732
1	20	732
2	41	732
3	69	732
4	79	732
5	79	732

Stop Event

1×

saturated

Counts

152 → 71

prune46.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	63	8	71
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	64	9	73

Error

0.0b

Counts

73 → 9

Alt Table

Status	Error	Program
	9.7b	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))
	26.4b	(pow.f64 (sqrt.f64 (/.f64 (.f64 a1 a2) (.f64 b1 b2))) 2)
	12.5b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	10.9b	(/.f64 (/.f64 (*.f64 a1 a2) b2) b1)
	12.4b	(/.f64 (/.f64 (*.f64 a1 a2) b1) b2)
	10.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
▶	9.4b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	8.1b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	9.5b	(.f64 a1 (.f64 (/.f64 1 b1) (/.f64 a2 b2)))

Compiler

Compiled 974 to 407 computations (58.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.8b	(/.f64 a1 (/.f64 b1 (/.f64 a2 b2)))
✓	5.1b	(/.f64 b1 (/.f64 a2 b2))

series37.0ms (1.1%)

Counts

2 → 84

Calls

21 calls:

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

rewrite51.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

574×	`log-prod_binary64`
180×	`log-div_binary64`
169×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`
154×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	178	17
2	2772	17

Stop Event

1×	node limit

Counts

2 → 96

simplify25.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	18	732
2	39	732
3	67	732
4	79	732
5	79	732

Stop Event

1×

saturated

Counts

180 → 99

prune59.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	4	3	7
Picked	1	0	1
Done	1	0	1
Total	100	8	108

Error

Counts

108 → 8

Alt Table

Status	Error	Program
▶	7.4b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	9.7b	(.f64 a1 (.f64 (/.f64 a2 b1) (/.f64 1 b2)))
	8.1b	(/.f64 a1 (/.f64 (*.f64 b2 b1) a2))
	12.5b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
	10.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	9.6b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
	10.3b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))
	11.1b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))

Compiler

Compiled 1383 to 512 computations (63% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.2b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
✓	5.7b	(/.f64 a1 (*.f64 b2 b1))

series41.0ms (1.2%)

Counts

2 → 48

Calls

21 calls:

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

rewrite44.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`
78×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	17
2	2305	17

Stop Event

1×	node limit

Counts

2 → 68

simplify19.0ms (0.6%)

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

116 → 69

prune44.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	69	8	77

Error

Counts

77 → 8

Alt Table

Status	Error	Program
	8.1b	(/.f64 a1 (/.f64 (*.f64 b2 b1) a2))
	12.5b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
✓	7.4b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	10.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	9.6b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
	10.3b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))
▶	8.1b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.1b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))

Compiler

Compiled 932 to 390 computations (58.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.1b	(/.f64 a2 (*.f64 b2 b1))
✓	4.7b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))

series42.0ms (1.3%)

Counts

2 → 48

Calls

21 calls:

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

rewrite52.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`log1p-expm1-u_binary64`
866×	`expm1-log1p-u_binary64`
86×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`
78×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	166	17
2	2305	17

Stop Event

1×	node limit

Counts

2 → 68

simplify19.0ms (0.6%)

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

116 → 69

prune44.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	8	77

Error

Counts

77 → 8

Alt Table

Status	Error	Program
	8.1b	(/.f64 a1 (/.f64 (*.f64 b2 b1) a2))
	12.5b	(/.f64 (*.f64 (/.f64 a2 b1) a1) b2)
✓	7.4b	(.f64 a2 (/.f64 a1 (.f64 b2 b1)))
	10.4b	(/.f64 1 (/.f64 (.f64 b1 b2) (.f64 a1 a2)))
	9.6b	(*.f64 (/.f64 1 (/.f64 b1 a2)) (/.f64 a1 b2))
	10.3b	(*.f64 (/.f64 1 b1) (/.f64 a1 (/.f64 b2 a2)))
✓	8.1b	(.f64 a1 (/.f64 a2 (.f64 b2 b1)))
	11.1b	(*.f64 (/.f64 a2 b2) (/.f64 a1 b1))

Compiler

Compiled 849 to 329 computations (61.2% saved)

regimes513.0ms (15.4%)

Accuracy

Total 2.0b remaining (97.9%)

Threshold costs 0b (0%)

Counts

32 → 5

Compiler

Compiled 3087 to 2009 computations (34.9% 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
6.474204089623792e+306	∈ [	6.474204089623792e+306	,	#hash((type . real) (value . +inf))	]
-0.0	∈ [	-0.0	,	4.5744264e-316	]
-7.4e-323	∈ [	-7.4e-323	,	0.0	]
-1.040164306635014e+306	∈ [	-1.040164306635014e+306	,	-4.8170980774799135e+299	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	119
1	33	119

Stop Event

1×

saturated

end131.0ms (3.9%)

Stop Event

1×

fuel

Compiler

Compiled 604 to 242 computations (59.9% saved)

Details

analyze930.0ms (27.9%)

sample1.1s (31.6%)

preprocess22.0ms (0.7%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series42.0ms (1.3%)

rewrite52.0ms (1.6%)

simplify24.0ms (0.7%)

prune46.0ms (1.4%)

localize7.0ms (0.2%)

series37.0ms (1.1%)

rewrite51.0ms (1.5%)

simplify25.0ms (0.7%)

prune59.0ms (1.8%)

localize5.0ms (0.2%)

series41.0ms (1.2%)

rewrite44.0ms (1.3%)

simplify19.0ms (0.6%)

prune44.0ms (1.3%)

localize5.0ms (0.2%)

series42.0ms (1.3%)

rewrite52.0ms (1.5%)

simplify19.0ms (0.6%)

prune44.0ms (1.3%)

regimes513.0ms (15.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end131.0ms (3.9%)

Profiling