Metrics for Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze1.0ms (0.1%)

Memory

2.7MiB live, 2.7MiB allocated; 0ms collecting garbage

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
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample831.0ms (43.7%)

Memory

25.0MiB live, 1 114.6MiB allocated; 510ms collecting garbage

Samples

545.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 167.0ms

ival-mult: 78.0ms (46.8% of total)

ival-div: 73.0ms (43.8% of total)

ival-true: 6.0ms (3.6% of total)

exact: 5.0ms (3% of total)

ival-assert: 3.0ms (1.8% of total)

adjust: 2.0ms (1.2% of total)

Bogosity

explain89.0ms (4.7%)

Memory

13.8MiB live, 59.0MiB allocated; 8ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	1	(1.481749363847056e+161)	-	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(*.f64 x x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`	n/o	3	0
↳	`(*.f64 x x)`	overflow	61

Confusion

	Predicted +	Predicted -
+	2	0
-	1	253

Precision

0.6666666666666666

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	1	0	253

Precision?

0.6666666666666666

Recall?

1.0

Freqs

test

number	freq
0	253
1	3

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

66.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 4.0ms (47.4% of total)

ival-div: 3.0ms (35.5% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess277.0ms (14.5%)

Memory

8.6MiB live, 189.4MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	24	10
2	67	10
3	108	10
4	230	10
5	1301	10
6	7100	10
0	4	5
0	6	5
1	14	5
2	34	5
3	76	5
4	182	5
5	1037	5
0	8422	5

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify145.0ms (7.6%)

Memory

-19.5MiB live, 166.6MiB allocated; 38ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	14	10
2	34	10
3	76	10
4	182	10
5	1037	10
0	8422	10

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)
x

localize12.0ms (0.6%)

Memory

21.2MiB live, 21.2MiB allocated; 0ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	0.3166866267002109	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Samples

8.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (50.5% of total)

ival-mult: 2.0ms (50.5% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
#s(approx (/ 1 (* x x)) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((/ 1 (* x x)) (* x x))
0.0ms	x	@	inf	((/ 1 (* x x)) (* x x))
0.0ms	x	@	-inf	((/ 1 (* x x)) (* x x))

simplify157.0ms (8.3%)

Memory

-31.9MiB live, 114.6MiB allocated; 48ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	20	18
2	43	18
3	88	18
4	259	18
5	2362	18
0	8048	18

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (/ 1 (* x x)) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))

Outputs
#s(approx (/ 1 (* x x)) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (/ 1 (* x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (* x x) (*.f64 x x))

rewrite51.0ms (2.7%)

Memory

16.0MiB live, 59.0MiB allocated; 15ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	22	6
2	82	6
0	342	6

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 43

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 x x)

Outputs
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal -1 binary64))) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x)
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x)
(/.f64 (pow.f64 x #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (pow.f64 x #s(literal -1 binary64)) x)
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 #s(literal -1 binary64) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (pow.f64 x #s(literal -2 binary64)))
(fma.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 0 binary64) (*.f64 x x)))
(fma.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (*.f64 x x)))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (neg.f64 (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(+.f64 (cosh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))) (sinh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(+.f64 (pow.f64 x #s(literal -2 binary64)) (/.f64 #s(literal 0 binary64) (*.f64 x x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (neg.f64 x) x)
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64)))
(neg.f64 (*.f64 x x))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x x)))
(fabs.f64 (*.f64 x x))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval4.0ms (0.2%)

Memory: 10.2MiB live, 10.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 330 to 97 computations (70.6% saved)

prune2.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	2	46

Accuracy

100.0%

Counts

46 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	99.5%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify4.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f64 x #s(literal -2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)

Outputs
(pow.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)

localize19.0ms (1%)

Memory

-16.3MiB live, 27.1MiB allocated; 11ms collecting garbage

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(pow.f64 x #s(literal -2 binary64))

Samples

8.0ms

256×

valid

Compiler

Compiled 7 to 5 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-pow: 3.0ms (87.4% of total)

ival-true: 0.0ms (0% of total)

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated; 0ms collecting garbage

Counts

1 → 1

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))

Outputs
#s(approx (pow x -2) #s(hole binary64 (/ 1 (pow x 2))))

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	((pow x -2))
0.0ms	x	@	-inf	((pow x -2))
0.0ms	x	@	inf	((pow x -2))

simplify197.0ms (10.4%)

Memory

-18.4MiB live, 177.6MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	24	9
3	56	9
4	201	9
5	2236	9
0	8845	9

Stop Event

1×	iter limit
1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (pow x -2) #s(hole binary64 (/ 1 (pow x 2))))

Outputs
#s(approx (pow x -2) #s(hole binary64 (/ 1 (pow x 2))))
#s(approx (pow x -2) (/.f64 #s(literal 1 binary64) (*.f64 x x)))

rewrite22.0ms (1.2%)

Memory

-9.8MiB live, 44.6MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	4	3
1	12	3
0	39	3

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

1 → 9

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))

Outputs
(*.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64))) (neg.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (fabs.f64 (pow.f64 x #s(literal -1 binary64))) (fabs.f64 (pow.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal -2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal -2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal -2 binary64))))

eval7.0ms (0.4%)

Memory: 17.5MiB live, 17.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 68 to 27 computations (60.3% saved)

prune1.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	10	2	12

Accuracy

100.0%

Counts

12 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	99.5%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes4.0ms (0.2%)

Memory

13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(pow.f64 x #s(literal -2 binary64))

Outputs
(pow.f64 x #s(literal -2 binary64))

Calls

3 calls:

1.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 x x)`
100.0%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
100.0%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes5.0ms (0.3%)

Memory

-34.4MiB live, 11.5MiB allocated; 4ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Calls

3 calls:

3.0ms	(*.f64 x x)
1.0ms	x
1.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 x x)`
99.5%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
99.5%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify50.0ms (2.6%)

Memory

21.3MiB live, 64.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
3	19	8
4	42	8
5	215	8
6	2161	8
7	5325	8

Stop Event

1×	node limit

Calls

Call 1

Inputs
(pow.f64 x #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

Outputs
(pow.f64 x #s(literal -2 binary64))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

derivations2.0ms (0.1%)

Memory

5.0MiB live, 4.9MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 8 to 6 computations (25% saved)

preprocess18.0ms (1%)

Memory: 6.4MiB live, 51.4MiB allocated; 4ms collecting garbage
Remove: (abs x)
Compiler: Compiled 48 to 40 computations (16.7% saved)

end0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze1.0ms (0.1%)

sample831.0ms (43.7%)

explain89.0ms (4.7%)

preprocess277.0ms (14.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify145.0ms (7.6%)

localize12.0ms (0.6%)

series1.0ms (0.1%)

simplify157.0ms (8.3%)

rewrite51.0ms (2.7%)

eval4.0ms (0.2%)

prune2.0ms (0.1%)

simplify4.0ms (0.2%)

localize19.0ms (1%)

series1.0ms (0%)

simplify197.0ms (10.4%)

rewrite22.0ms (1.2%)

eval7.0ms (0.4%)

prune1.0ms (0.1%)

regimes4.0ms (0.2%)

regimes5.0ms (0.3%)

simplify50.0ms (2.6%)

derivations2.0ms (0.1%)

preprocess18.0ms (1%)

end0.0ms (0%)

Profiling