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

2.4MiB live, 2.4MiB 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)

sample567.0ms (52.5%)

Memory

21.9MiB live, 673.7MiB allocated; 158ms collecting garbage

Samples

409.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-mult!: 67.0ms (60.8% of total)

ival-div!: 42.0ms (38.1% of total)

adjust: 1.0ms (0.9% of total)

Bogosity

preprocess247.0ms (22.8%)

Memory

-31.2MiB live, 67.1MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	37	10
2	96	10
3	169	10
4	757	10
5	7816	10

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Symmetry

(abs x)

Compiler

Compiled 8 to 8 computations (0% saved)

series2.0ms (0.2%)

Memory

4.2MiB live, 4.2MiB 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	@	0	((/ 1 (* x x)) 1 (* x x) x)
1.0ms	x	@	-inf	((/ 1 (* x x)) 1 (* x x) x)
1.0ms	x	@	inf	((/ 1 (* x x)) 1 (* x x) x)

rewrite31.0ms (2.8%)

Memory

11.3MiB live, 57.2MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	31
0	13	25
1	40	25
0	144	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)

eval3.0ms (0.3%)

Memory: 9.8MiB live, 9.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 154 to 94 computations (39% saved)

prune2.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Accuracy

100.0%

Counts

38 → 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)
✓	99.0%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 11 to 11 computations (0% saved)

series2.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB 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)

rewrite27.0ms (2.5%)

Memory

7.0MiB live, 52.9MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	44
0	18	36
1	45	36
0	167	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: 9.3MiB live, 9.3MiB allocated; 0ms collecting garbage
Compiler: Compiled 144 to 93 computations (35.4% saved)

prune7.0ms (0.7%)

Memory

-37.0MiB live, 8.9MiB allocated; 5ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	38	3	41

Accuracy

100.0%

Counts

41 → 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)
✓	99.0%	(/.f64 #s(literal 1 binary64) (*.f64 x x))

Compiler

Compiled 19 to 19 computations (0% saved)

regimes5.0ms (0.4%)

Memory

17.2MiB live, 17.2MiB allocated; 0ms 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:

2.0ms	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 7 to 7 computations (0% saved)

regimes4.0ms (0.3%)

Memory

11.9MiB live, 11.9MiB 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 #s(literal 1 binary64) (*.f64 x x))
1.0ms	(*.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 7 to 7 computations (0% saved)

regimes3.0ms (0.3%)

Memory

9.8MiB live, 9.8MiB 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
99.0%	1	`(*.f64 x x)`
99.0%	1	`(/.f64 #s(literal 1 binary64) (*.f64 x x))`
99.0%	1	`x`

Compiler

Compiled 7 to 7 computations (0% saved)

derivations158.0ms (14.6%)

Memory

-72.7MiB live, 55.5MiB allocated; 168ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 8 to 8 computations (0% saved)

preprocess21.0ms (2%)

Memory: 23.2MiB live, 68.6MiB allocated; 6ms collecting garbage
Remove: (abs x)
Compiler: Compiled 34 to 34 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze1.0ms (0.1%)

sample567.0ms (52.5%)

preprocess247.0ms (22.8%)

series2.0ms (0.2%)

rewrite31.0ms (2.8%)

eval3.0ms (0.3%)

prune2.0ms (0.1%)

series2.0ms (0.1%)

rewrite27.0ms (2.5%)

eval3.0ms (0.3%)

prune7.0ms (0.7%)

regimes5.0ms (0.4%)

regimes4.0ms (0.3%)

regimes3.0ms (0.3%)

derivations158.0ms (14.6%)

preprocess21.0ms (2%)

end0.0ms (0%)

Profiling