Details

analyze741.0ms (12.6%)

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)

sample1.0s (17.6%)

Results

832.0ms	8256×	body	128	valid
185.0ms	1867×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

preprocess28.0ms (0.5%)

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 (0.1%)

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

prune6.0ms (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))

series29.0ms (0.5%)

Counts

1 → 48

Calls

12 calls:

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

rewrite51.0ms (0.9%)

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	2503	10

Stop Event

1×	node limit

Counts

1 → 59

simplify20.0ms (0.3%)

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

prune52.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	57	6	63

Error

Counts

63 → 6

Alt Table

Status	Error	Program
	12.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
▶	8.4b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
	10.5b	(*.f64 (/.f64 a2 (/.f64 b1 a1)) (/.f64 1 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))

Compiler

Compiled 899 to 322 computations (64.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	8.1b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))

series30.0ms (0.5%)

Counts

1 → 48

Calls

12 calls:

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

rewrite44.0ms (0.7%)

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	2581	10

Stop Event

1×	node limit

Counts

1 → 64

simplify23.0ms (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

112 → 66

prune63.0ms (1.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	66	6	72

Error

Counts

72 → 6

Alt Table

Status	Error	Program
	12.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	8.4b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
▶	10.5b	(*.f64 (/.f64 a2 (/.f64 b1 a1)) (/.f64 1 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))

Compiler

Compiled 805 to 296 computations (63.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	5.1b	(/.f64 a2 (/.f64 b1 a1))
✓	6.0b	(*.f64 (/.f64 a2 (/.f64 b1 a1)) (/.f64 1 b2))

series44.0ms (0.7%)

Counts

2 → 84

Calls

21 calls:

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

rewrite53.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

619×	`log-prod_binary64`
202×	`log-div_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
165×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	217	17
2	3161	17

Stop Event

1×	node limit

Counts

2 → 104

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	732
1	20	732
2	43	732
3	70	732
4	77	732

Stop Event

1×

saturated

Counts

188 → 107

prune124.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	107	6	113

Error

Counts

113 → 6

Alt Table

Status	Error	Program
	12.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
▶	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	8.4b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
✓	10.5b	(*.f64 (/.f64 a2 (/.f64 b1 a1)) (/.f64 1 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))

Compiler

Compiled 1455 to 593 computations (59.2% saved)

localize7.0ms (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))

series43.0ms (0.7%)

Counts

2 → 48

Calls

21 calls:

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

rewrite56.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	208	17
2	2891	17

Stop Event

1×	node limit

Counts

2 → 108

simplify21.0ms (0.3%)

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

prune89.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	110	6	116

Error

Counts

116 → 6

Alt Table

Status	Error	Program
	12.3b	(.f64 a1 (/.f64 a2 (.f64 b1 b2)))
✓	11.3b	(.f64 (/.f64 1 b1) (/.f64 (.f64 a1 a2) b2))
✓	8.4b	(*.f64 (/.f64 a2 b1) (/.f64 a1 b2))
✓	10.5b	(*.f64 (/.f64 a2 (/.f64 b1 a1)) (/.f64 1 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))

Compiler

Compiled 1410 to 563 computations (60.1% saved)

regimes2.9s (49.3%)

Accuracy

Total 2.9b remaining (98.8%)

Threshold costs 0b (0%)

Counts

142 → 5

Compiler

Compiled 14708 to 9961 computations (32.3% saved)

bsearch4.0ms (0.1%)

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
2.5311788560258127e+294	∈ [	2.5311788560258127e+294	,	#hash((type . real) (value . +inf))	]
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)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

62×	`distribute-rgt-neg-in_binary64`
48×	`distribute-lft-neg-out_binary64`
46×	`cancel-sign-sub-inv_binary64`
44×	`neg-sub0_binary64`
43×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	131
1	62	129
2	90	113
3	134	113
4	182	113
5	219	113
6	281	113
7	348	113
8	418	113
9	470	113
10	491	113
11	495	113

Stop Event

1×

saturated

end360.0ms (6.1%)

Stop Event

1×

fuel

Compiler

Compiled 568 to 224 computations (60.6% saved)

Iter	Nodes	Cost
0	40	131
1	62	129
2	90	113
3	134	113
4	182	113
5	219	113
6	281	113
7	348	113
8	418	113
9	470	113
10	491	113
11	495	113

Iter	Nodes	Cost
0	40	131
1	62	129
2	90	113
3	134	113
4	182	113
5	219	113
6	281	113
7	348	113
8	418	113
9	470	113
10	491	113
11	495	113

Details

analyze741.0ms (12.6%)

sample1.0s (17.6%)

preprocess28.0ms (0.5%)

simplify7.0ms (0.1%)

prune6.0ms (0.1%)

localize5.0ms (0.1%)

series29.0ms (0.5%)

rewrite51.0ms (0.9%)

simplify20.0ms (0.3%)

prune52.0ms (0.9%)

localize5.0ms (0.1%)

series30.0ms (0.5%)

rewrite44.0ms (0.7%)

simplify23.0ms (0.4%)

prune63.0ms (1.1%)

localize6.0ms (0.1%)

series44.0ms (0.7%)

rewrite53.0ms (0.9%)

simplify22.0ms (0.4%)

prune124.0ms (2.1%)

localize7.0ms (0.1%)

series43.0ms (0.7%)

rewrite56.0ms (1%)

simplify21.0ms (0.3%)

prune89.0ms (1.5%)

regimes2.9s (49.3%)

bsearch4.0ms (0.1%)

simplify12.0ms (0.2%)

end360.0ms (6.1%)

Profiling

Iter	Nodes	Cost
0	40	131
1	62	129
2	90	113
3	134	113
4	182	113
5	219	113
6	281	113
7	348	113
8	418	113
9	470	113
10	491	113
11	495	113