Metrics for sqrt A (should all be same)

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 10 to 5 computations (50% saved)

sample656.0ms (12.7%)

Results

642.0ms	8248×	body	256	valid
1.0ms	8×	body	256	infinite

Bogosity

preprocess62.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

82×	`fma-def`
60×	`associate-r`
31×	`*-commutative`
18×	`associate-l`
17×	`associate-+r-`

Problems

131×	No Errors
125×	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	33	39
2	75	39
3	215	39
4	389	39
5	480	39

Stop Event

1×

saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 x))))

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)
(sqrt.f64 (+.f64 (.f64 (neg.f64 x) (neg.f64 x)) (.f64 (neg.f64 x) (neg.f64 x))))
(hypot.f64 x x)

Symmetry

(abs x)

Compiler

Compiled 30 to 9 computations (70% saved)

eval0.0ms (0%)

Compiler: Compiled 4 to 2 computations (50% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(hypot.f64 x x)
▶	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
▶	100.0%	(hypot.f64 x x)
▶	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 26 to 12 computations (53.8% saved)

localize28.0ms (0.5%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	100.0%	(+.f64 (.f64 x x) (.f64 x x))
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Compiler

Compiled 25 to 6 computations (76% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(hypot.f64 x x)
1.0ms	x	@	0	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
1.0ms	x	@	inf	(+.f64 (.f64 x x) (.f64 x x))
0.0ms	x	@	inf	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
0.0ms	x	@	0	(hypot.f64 x x)

rewrite263.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`associate-r`
411×	`associate-l`
231×	`*-un-lft-identity`
178×	`add-sqr-sqrt`
158×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	113	39
2	1252	39

Stop Event

1×	node limit

Counts

3 → 108

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(+.f64 (.f64 x x) (.f64 x x))
(hypot.f64 x x)

Outputs
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64

simplify134.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-+l+`
528×	`distribute-lft-neg-in`
501×	`distribute-lft-in`
457×	`fma-def`
325×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	668
1	61	668
2	88	668
3	130	668
4	240	668
5	562	668
6	940	668
7	1553	668
8	1909	668
9	2835	668
10	3727	668
11	5053	668
12	7689	668

Stop Event

1×	node limit

Counts

144 → 42

Calls

Call 1

Inputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64

Outputs
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 2 (pow.f64 x 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 x (sqrt.f64 2)))
(neg.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64
-3
-2
-3/2
-1
-1/2
-1/4
0
1/16
1/12
1/8
1/6
1/4
3/8
1/2
2/3
3/4
1
4/3
3/2
7/4
2
9/4
5/2
3
13/4
7/2
4
9/2
5
6
8
9
12
16
18
64

eval5.0ms (0.1%)

Compiler: Compiled 68 to 62 computations (8.8% saved)

prune10.0ms (0.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	38	6	44

Accuracy

100.0%

Counts

44 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0

Compiler

Compiled 42 to 28 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	0	0
Done	2	2
Total	6	6

Accuracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0

Compiler

Compiled 42 to 28 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune4.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	0	0
Done	2	2
Total	6	6

Accuracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0

Compiler

Compiled 42 to 28 computations (33.3% saved)

localize0.0ms (0%)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune3.0ms (0.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	0	0
Done	2	2
Total	6	6

Accuracy

100.0%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(hypot.f64 x x)
✓	55.6%	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
	5.4%	64
	5.4%	1
	5.3%	1/16
	3.8%	0

Compiler

Compiled 37 to 23 computations (37.8% saved)

regimes123.0ms (2.4%)

Counts

6 → 1

Calls

Call 1

Inputs
0
1/16
1
64
(hypot.f64 x x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Outputs
(hypot.f64 x x)

Calls

4 calls:

109.0ms	(+.f64 (.f64 x x) (.f64 x x))
5.0ms	x
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
4.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
100.0%	1	`(+.f64 (.f64 x x) (.f64 x x))`
100.0%	1	`(*.f64 x x)`

Compiler

Compiled 39 to 19 computations (51.3% saved)

regimes6.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
0
1/16
1
64

Outputs
1

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
5.4%	1	`x`

Compiler

Compiled 7 to 6 computations (14.3% saved)

regimes4.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
0
1/16

Outputs
1/16

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
5.3%	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
0

Outputs
0

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
3.8%	1	`x`

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3× 1-exp

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	14	16

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
1
1/16
0

Outputs
(hypot.f64 x x)
1
1/16
0

Compiler

Compiled 10 to 8 computations (20% saved)

soundness3.8s (73.7%)

Rules

657×	`associate-r`
657×	`associate-r`
657×	`associate-r`
411×	`associate-l`
411×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	33	39
2	75	39
3	215	39
4	389	39
5	480	39
0	10	39
1	113	39
2	1252	39
0	10	39
1	113	39
2	1252	39
0	10	39
1	113	39
2	1252	39

Stop Event

1×	node limit
1×	node limit
1×	node limit
1×	saturated

Compiler

Compiled 12 to 5 computations (58.3% saved)

end0.0ms (0%)

preprocess42.0ms (0.8%)

Remove: (abs x)
Compiler: Compiled 40 to 22 computations (45% saved)

analyze0.0ms (0%)

sample656.0ms (12.7%)

preprocess62.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize28.0ms (0.5%)

series4.0ms (0.1%)

rewrite263.0ms (5.1%)

simplify134.0ms (2.6%)

eval5.0ms (0.1%)

prune10.0ms (0.2%)

localize0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune4.0ms (0.1%)

localize0.0ms (0%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes123.0ms (2.4%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify4.0ms (0.1%)

soundness3.8s (73.7%)

end0.0ms (0%)

preprocess42.0ms (0.8%)

Profiling