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

analyze3.0ms (0.2%)

Memory

-40.2MiB live, 5.8MiB allocated; 3ms 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)

sample709.0ms (45.6%)

Memory

64.1MiB live, 983.1MiB allocated; 398ms collecting garbage

Samples

471.0ms

8 256×

valid

Precisions

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

ival-mult: 90.0ms (53.8% of total)

ival-div: 60.0ms (35.9% of total)

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

exact: 5.0ms (3% of total)

adjust: 3.0ms (1.8% of total)

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

Bogosity

explain96.0ms (6.2%)

Memory

-29.2MiB live, 81.4MiB allocated; 68ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
5	1	(-1.8853813765480478e+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	6	0
↳	`(*.f64 x x)`	overflow	49

Confusion

	Predicted +	Predicted -
+	5	0
-	1	250

Precision

0.8333333333333334

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	1	0	250

Precision?

0.8333333333333334

Recall?

1.0

Freqs

test

number	freq
0	250
1	6

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

25.0ms

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 (48.2% of total)

ival-div: 3.0ms (36.2% 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)

preprocess226.0ms (14.5%)

Memory

6.2MiB live, 188.1MiB allocated; 43ms 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: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 5 to 4 computations (20% saved)

series2.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB 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
(/ 1 (pow x 2))
(pow x 2)
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)

simplify145.0ms (9.3%)

Memory

42.9MiB live, 130.5MiB allocated; 18ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	9	9
2	21	9
3	53	9
4	199	9
5	2232	9
0	8823	9

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 2

Calls

Call 1

Inputs
(/ 1 (pow x 2))
(pow x 2)
x

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

rewrite52.0ms (3.4%)

Memory

-36.7MiB live, 63.5MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	22	8
2	82	8
0	342	8

Stop Event

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

Counts

4 → 45

Calls

Call 1

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

eval4.0ms (0.3%)

Memory: 13.1MiB live, 13.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 345 to 97 computations (71.9% saved)

prune2.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	47	1	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	47	2	49

Accuracy

100.0%

Counts

49 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 8 to 7 computations (12.5% saved)

series1.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

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

Outputs
(/ 1 (pow x 2))
x

Calls

3 calls:

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

simplify145.0ms (9.3%)

Memory

-23.3MiB live, 165.3MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	9	6
2	21	6
3	53	6
4	199	6
5	2232	6
0	8823	6

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 1

Calls

Call 1

Inputs
(/ 1 (pow x 2))
x

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

rewrite19.0ms (1.2%)

Memory

21.1MiB live, 21.1MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
0	4	5
1	12	5
0	39	5

Stop Event

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

Counts

3 → 11

Calls

Call 1

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

eval1.0ms (0.1%)

Memory: 2.0MiB live, 2.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 74 to 27 computations (63.5% saved)

prune1.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	12	0	12
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	12	2	14

Accuracy

100.0%

Counts

14 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(pow.f64 x #s(literal -2 binary64))
✓	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes4.0ms (0.2%)

Memory

7.8MiB live, 7.8MiB 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)

regimes3.0ms (0.2%)

Memory

6.7MiB live, 6.7MiB 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
98.9%	1	`(*.f64 x x)`
98.9%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
98.9%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify70.0ms (4.5%)

Memory

-23.5MiB live, 65.8MiB allocated; 12ms 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

3.0MiB live, 3.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 8 to 6 computations (25% saved)

preprocess69.0ms (4.4%)

Memory: -7.7MiB live, 144.6MiB allocated; 33ms collecting garbage
Remove: (abs x)
Compiler: Compiled 48 to 40 computations (16.7% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze3.0ms (0.2%)

sample709.0ms (45.6%)

explain96.0ms (6.2%)

preprocess226.0ms (14.5%)

eval0.0ms (0%)

prune0.0ms (0%)

series2.0ms (0.1%)

simplify145.0ms (9.3%)

rewrite52.0ms (3.4%)

eval4.0ms (0.3%)

prune2.0ms (0.1%)

series1.0ms (0.1%)

simplify145.0ms (9.3%)

rewrite19.0ms (1.2%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

regimes4.0ms (0.2%)

regimes3.0ms (0.2%)

simplify70.0ms (4.5%)

derivations2.0ms (0.1%)

preprocess69.0ms (4.4%)

end0.0ms (0%)

Profiling