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

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

analyze1.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB 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)

sample594.0ms (64.4%)

Memory

-10.4MiB live, 596.8MiB allocated; 171ms collecting garbage

Samples

236.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 89.0ms

ival-mult!: 47.0ms (53% of total)

ival-div!: 40.0ms (45.1% of total)

adjust: 2.0ms (2.3% of total)

Bogosity

explain52.0ms (5.6%)

Memory

24.3MiB live, 118.7MiB allocated; 27ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	3	(3.05775409280087e+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	5	0
↳	`(*.f64 x x)`	overflow	59

Confusion

	Predicted +	Predicted -
+	2	0
-	3	251

Precision

0.4

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	3	0	251

Precision?

0.4

Recall?

1.0

Freqs

test

number	freq
0	251
1	5

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult!: 3.0ms (55.1% of total)

ival-div!: 2.0ms (36.8% of total)

adjust: 0.0ms (0% of total)

preprocess123.0ms (13.3%)

Memory

-31.7MiB live, 56.1MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	30	15
2	72	15
3	114	15
4	236	15
5	1307	15
6	7105	15

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 10 to 8 computations (20% saved)

series2.0ms (0.2%)

Memory

3.5MiB live, 3.5MiB allocated; 0ms collecting garbage

Counts

4 → 3

Calls

Call 1

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

Calls

3 calls:

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

rewrite36.0ms (3.9%)

Memory

39.4MiB live, 39.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
0	13	25
1	40	25
0	143	25

Stop Event

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

Counts

7 → 41

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal -1 binary64)) (pow.f64 (neg.f64 x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal -1 binary64)) (pow.f64 (fabs.f64 x) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) (fabs.f64 x)) (fabs.f64 x))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (neg.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 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -2 binary64)))
#s(literal 1 binary64)
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.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 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(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))))
x
#s(approx (/ 1 (* x x)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)

eval16.0ms (1.7%)

Memory: -39.2MiB live, 6.0MiB allocated; 11ms collecting garbage
Compiler: Compiled 276 to 96 computations (65.2% saved)

prune1.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	3	39

Accuracy

100.0%

Counts

39 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal -2 binary64))
▶	99.8%	(/.f64 (/.f64 #s(literal 1 binary64) x) x)
✓	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 13 to 11 computations (15.4% saved)

series2.0ms (0.2%)

Memory

2.0MiB live, 2.0MiB allocated; 0ms collecting garbage

Counts

6 → 4

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (/ 1 x) x) (/ 1 x) 1 x (pow x -2) -2)
1.0ms	x	@	0	((/ (/ 1 x) x) (/ 1 x) 1 x (pow x -2) -2)
0.0ms	x	@	inf	((/ (/ 1 x) x) (/ 1 x) 1 x (pow x -2) -2)

rewrite24.0ms (2.6%)

Memory

24.9MiB live, 24.9MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
0	18	36
1	45	36
0	166	36

Stop Event

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

Counts

10 → 74

Calls

Call 1

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

Outputs
(.f64 (pow.f64 (.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) x)) (fabs.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1 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))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(pow.f64 x #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) x))
(/.f64 #s(literal -2 binary64) (*.f64 #s(literal 2 binary64) (neg.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 x)))
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1 binary64)))
#s(literal 1 binary64)
x
(.f64 (pow.f64 (.f64 x x) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(*.f64 (fabs.f64 (/.f64 #s(literal 1 binary64) x)) (fabs.f64 (/.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(pow.f64 x #s(literal -2 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (neg.f64 x))
(/.f64 (*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) (neg.f64 x))
(/.f64 (*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x)
(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 x))
(/.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) x))
(/.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (neg.f64 x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) x)
(/.f64 #s(literal -2 binary64) (.f64 #s(literal 2 binary64) (.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 (neg.f64 x) x)))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(neg.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x))
(neg.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)))
(neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 x)))
(neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) x)))
(exp.f64 (-.f64 #s(literal 0 binary64) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1 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))))
#s(literal -2 binary64)
#s(approx (/ (/ 1 x) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
#s(approx (/ 1 x) (/.f64 #s(literal 1 binary64) x))
#s(approx x x)
#s(approx (/ (/ 1 x) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)))

eval3.0ms (0.3%)

Memory: 7.5MiB live, 7.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 277 to 94 computations (66.1% saved)

prune2.0ms (0.2%)

Memory

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

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	39	3	42

Accuracy

100.0%

Counts

42 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	99.8%	(/.f64 (/.f64 #s(literal 1 binary64) x) x)
✓	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 26 to 19 computations (26.9% saved)

regimes25.0ms (2.7%)

Memory

-40.6MiB live, 13.4MiB allocated; 23ms collecting garbage

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

22.0ms	(/.f64 #s(literal 1 binary64) (*.f64 x x))
2.0ms	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)

regimes4.0ms (0.4%)

Memory

8.4MiB live, 8.4MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.8%	1	`(*.f64 x x)`
99.8%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
99.8%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes3.0ms (0.3%)

Memory

6.8MiB live, 6.8MiB allocated; 0ms 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:

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

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 x x)`
99.4%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
99.4%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

derivations2.0ms (0.2%)

Memory

2.2MiB live, 2.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 13 to 8 computations (38.5% saved)

preprocess32.0ms (3.5%)

Memory: -17.2MiB live, 29.8MiB allocated; 8ms collecting garbage
Remove: (abs x)
Compiler: Compiled 62 to 46 computations (25.8% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0.1%)

sample594.0ms (64.4%)

explain52.0ms (5.6%)

preprocess123.0ms (13.3%)

series2.0ms (0.2%)

rewrite36.0ms (3.9%)

eval16.0ms (1.7%)

prune1.0ms (0.1%)

series2.0ms (0.2%)

rewrite24.0ms (2.6%)

eval3.0ms (0.3%)

prune2.0ms (0.2%)

regimes25.0ms (2.7%)

regimes4.0ms (0.4%)

regimes3.0ms (0.3%)

derivations2.0ms (0.2%)

preprocess32.0ms (3.5%)

end0.0ms (0%)

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