Details

analyze825.0ms (20.5%)

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 (26.9%)

Results

868.0ms	8256×	body	128	valid
200.0ms	1867×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess26.0ms (0.6%)

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)

simplify6.0ms (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

prune5.0ms (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

6.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
▶	11.0b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

Compiler

Compiled 62 to 37 computations (40.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	10.7b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))

series27.0ms (0.7%)

Counts

1 → 48

Calls

12 calls:

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

rewrite43.0ms (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 (0.4%)

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

prune44.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	54	7	61
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Error

0.0b

Counts

63 → 8

Alt Table

Status	Error	Program
▶	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	11.0b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.8b	(.f64 (cbrt.f64 (.f64 (/.f64 a1 b1) (/.f64 a2 b2))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 b2))) 2))
	12.3b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
	13.1b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	11.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
	11.6b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 940 to 350 computations (62.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.2b	(/.f64 (*.f64 a1 a2) b2)
✓	6.9b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))

series41.0ms (1%)

Counts

2 → 48

Calls

21 calls:

4.0ms	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))	a1	-inf
3.0ms	(/.f64 (*.f64 a1 a2) b2)	a2	inf
3.0ms	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))	a2	-inf
2.0ms	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))	a1	inf
2.0ms	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))	a1	0

rewrite50.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

579×	`log-prod_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
169×	`log-div_binary64`
169×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	209	17
2	2913	17

Stop Event

1×	node limit

Counts

2 → 108

simplify21.0ms (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

156 → 110

prune79.0ms (2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	109	9	118

Error

Counts

118 → 9

Alt Table

Status	Error	Program
	11.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
▶	9.7b	(/.f64 (*.f64 (/.f64 a1 b2) a2) b1)
✓	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	11.0b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.8b	(.f64 (cbrt.f64 (.f64 (/.f64 a1 b1) (/.f64 a2 b2))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 b2))) 2))
	12.3b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
	13.1b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	11.6b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 1542 to 645 computations (58.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.8b	(*.f64 (/.f64 a1 b2) a2)
✓	6.9b	(/.f64 (*.f64 (/.f64 a1 b2) a2) b1)

series41.0ms (1%)

Counts

2 → 84

Calls

21 calls:

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

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`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	2519	17

Stop Event

1×	node limit

Counts

2 → 80

simplify25.0ms (0.6%)

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

164 → 83

prune58.0ms (1.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	83	9	92

Error

Counts

92 → 9

Alt Table

Status	Error	Program
▶	11.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
✓	9.7b	(/.f64 (*.f64 (/.f64 a1 b2) a2) b1)
✓	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	11.0b	(/.f64 (.f64 a1 a2) (.f64 b1 b2))
	12.2b	(*.f64 (/.f64 a1 b1) (/.f64 a2 b2))
	12.8b	(.f64 (cbrt.f64 (.f64 (/.f64 a1 b1) (/.f64 a2 b2))) (pow.f64 (cbrt.f64 (*.f64 (/.f64 a1 b1) (/.f64 a2 b2))) 2))
	12.3b	(.f64 a1 (.f64 a2 (/.f64 1 (*.f64 b1 b2))))
	13.1b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
	11.6b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 1166 to 452 computations (61.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.6b	(/.f64 a1 (*.f64 b1 b2))
✓	7.7b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)

series44.0ms (1.1%)

Counts

2 → 84

Calls

21 calls:

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

rewrite44.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

867×	`log1p-expm1-u_binary64`
867×	`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	2308	17

Stop Event

1×	node limit

Counts

2 → 69

simplify24.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	19	732
2	40	732
3	67	732
4	79	732
5	79	732

Stop Event

1×

saturated

Counts

153 → 72

prune39.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	3	2	5
Picked	0	1	1
Done	1	2	3
Total	74	7	81

Error

Counts

81 → 7

Alt Table

Status	Error	Program
✓	11.3b	(.f64 (/.f64 a1 (.f64 b1 b2)) a2)
✓	9.7b	(/.f64 (*.f64 (/.f64 a1 b2) a2) b1)
	11.0b	(/.f64 (*.f64 (/.f64 a1 b1) a2) b2)
	10.5b	(/.f64 a2 (/.f64 b2 (/.f64 a1 b1)))
	13.1b	(*.f64 a1 (/.f64 1 (/.f64 b1 (/.f64 a2 b2))))
✓	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
	11.6b	(.f64 (/.f64 (.f64 a1 a2) b1) (/.f64 1 b2))

Compiler

Compiled 859 to 334 computations (61.1% saved)

regimes1.0s (25.8%)

Accuracy

Total 3.0b remaining (99.5%)

Threshold costs 0b (0%)

Counts

50 → 5

Compiler

Compiled 5169 to 3397 computations (34.3% saved)

bsearch2.0ms (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
1.0497743534829688e+287	∈ [	1.0497743534829688e+287	,	2.5311788560258127e+294	]
0.0	∈ [	0.0	,	3.609189646773505e-300	]
-3.689148761672353e-240	∈ [	-3.689148761672353e-240	,	-1.3635296466761632e-243	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-5.006095713757291e+286	]

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	29	110
1	34	110

Stop Event

1×

saturated

end373.0ms (9.3%)

Stop Event

1×

fuel

Compiler

Compiled 557 to 217 computations (61% saved)

Details

analyze825.0ms (20.5%)

sample1.1s (26.9%)

preprocess26.0ms (0.6%)

simplify6.0ms (0.2%)

prune5.0ms (0.1%)

localize5.0ms (0.1%)

series27.0ms (0.7%)

rewrite43.0ms (1.1%)

simplify17.0ms (0.4%)

prune44.0ms (1.1%)

localize6.0ms (0.1%)

series41.0ms (1%)

rewrite50.0ms (1.2%)

simplify21.0ms (0.5%)

prune79.0ms (2%)

localize5.0ms (0.1%)

series41.0ms (1%)

rewrite44.0ms (1.1%)

simplify25.0ms (0.6%)

prune58.0ms (1.4%)

localize5.0ms (0.1%)

series44.0ms (1.1%)

rewrite44.0ms (1.1%)

simplify24.0ms (0.6%)

prune39.0ms (1%)

regimes1.0s (25.8%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end373.0ms (9.3%)

Profiling