Metrics for Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample639.0ms (49.2%)

Memory

27.4MiB live, 598.1MiB allocated; 110ms collecting garbage

Samples

414.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 151.0ms

ival-sub: 86.0ms (56.8% of total)

ival-mult: 54.0ms (35.7% of total)

exact: 6.0ms (4% of total)

adjust: 2.0ms (1.3% of total)

ival-assert: 2.0ms (1.3% of total)

Bogosity

explain54.0ms (4.2%)

Memory

-8.4MiB live, 91.7MiB allocated; 14ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 x (-.f64 x #s(literal 1 binary64)))`
-	-	`(-.f64 x #s(literal 1 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

20.0ms

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 (52.5% of total)

ival-sub: 3.0ms (39.4% 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)

preprocess304.0ms (23.4%)

Memory

-14.2MiB live, 221.9MiB allocated; 31ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	18	18
2	26	18
3	45	18
4	88	18
5	298	18
6	2471	16
7	6405	16
0	4	5
0	6	5
1	9	5
2	12	5
3	21	5
4	51	5
5	216	5
6	1799	5
7	5137	5
0	8310	5

Stop Event

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

Calls

Call 1

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

Outputs
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 x #s(literal 1 binary64)) 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
▶	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))

Compiler

Compiled 5 to 4 computations (20% saved)

series2.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

4 → 10

Calls

Call 1

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

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

Calls

3 calls:

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

rewrite87.0ms (6.7%)

Memory

0.2MiB live, 102.2MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	98
0	28	96
1	82	96
0	528	96

Stop Event

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

Counts

14 → 26

Calls

Call 1

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

Outputs
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (-.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) x) (fma.f64 x x (-.f64 x #s(literal -1 binary64))))
(/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (-.f64 x #s(literal -1 binary64))))
x
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (neg.f64 (-.f64 x #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x (-.f64 x #s(literal -1 binary64)))))
(/.f64 (fma.f64 x x #s(literal -1 binary64)) (-.f64 x #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (*.f64 x x) (-.f64 x #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x #s(literal -1 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 x #s(literal -1 binary64)))))
(-.f64 x #s(literal 1 binary64))
(+.f64 x #s(literal -1 binary64))
#s(literal 1 binary64)
#s(approx (* x (- x 1)) (neg.f64 x))
#s(approx (* x (- x 1)) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (- x 1) #s(literal -1 binary64))
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64)))
#s(approx (* x (- x 1)) (*.f64 x x))
#s(approx (* x (- x 1)) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x) x))
#s(approx (- x 1) x)
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x))
#s(approx (- x 1) (*.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (neg.f64 x)))

eval3.0ms (0.2%)

Memory: 5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 278 to 71 computations (74.5% saved)

prune2.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Accuracy

100.0%

Counts

29 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
▶	45.9%	(*.f64 x #s(approx (- x 1) x))
▶	56.7%	#s(approx (* x (- x 1)) (neg.f64 x))

Compiler

Compiled 20 to 15 computations (25% saved)

series1.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated; 0ms collecting garbage

Counts

5 → 11

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))
(neg.f64 x)
x
(*.f64 x #s(approx (- x 1) x))
#s(approx (- x 1) x)

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

Calls

3 calls:

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

rewrite73.0ms (5.6%)

Memory

-22.6MiB live, 68.2MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	117
0	32	114
1	86	114
0	532	114

Stop Event

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

Counts

16 → 19

Calls

Call 1

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

Outputs
#s(approx (* x (- x 1)) (neg.f64 x))
(*.f64 #s(literal -1 binary64) x)
(*.f64 x #s(literal -1 binary64))
(neg.f64 x)
x
(*.f64 #s(approx (- x 1) x) x)
(*.f64 x #s(approx (- x 1) x))
#s(approx (- x 1) x)
#s(approx (* x (- x 1)) (neg.f64 x))
#s(approx (* x (- x 1)) (*.f64 (-.f64 x #s(literal 1 binary64)) x))
#s(approx (neg x) (neg.f64 x))
#s(approx x x)
#s(approx (- x 1) #s(literal -1 binary64))
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64)))
#s(approx (* x (- x 1)) (*.f64 x x))
#s(approx (* x (- x 1)) (.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x) x))
#s(approx (- x 1) x)
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x))
#s(approx (- x 1) (*.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) (neg.f64 x)))

eval2.0ms (0.1%)

Memory: 6.4MiB live, 6.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 194 to 44 computations (77.3% saved)

prune2.0ms (0.2%)

Memory

10.9MiB live, 10.9MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	21	3	24

Accuracy

100.0%

Counts

24 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
✓	45.9%	(*.f64 x #s(approx (- x 1) x))
✓	56.7%	#s(approx (* x (- x 1)) (neg.f64 x))

Compiler

Compiled 40 to 26 computations (35% saved)

regimes3.0ms (0.3%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))
(*.f64 x #s(approx (- x 1) x))
(*.f64 x (-.f64 x #s(literal 1 binary64)))

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes3.0ms (0.2%)

Memory

10.1MiB live, 10.1MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))
(*.f64 x #s(approx (- x 1) x))

Outputs
#s(approx (* x (- x 1)) (neg.f64 x))
(*.f64 x #s(approx (- x 1) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.5%	2	`(*.f64 x (-.f64 x #s(literal 1 binary64)))`
97.5%	3	`x`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes6.0ms (0.4%)

Memory

-30.3MiB live, 8.6MiB allocated; 8ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))

Outputs
#s(approx (* x (- x 1)) (neg.f64 x))

Calls

2 calls:

4.0ms	(*.f64 x (-.f64 x #s(literal 1 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
56.7%	1	`x`
56.7%	1	`(*.f64 x (-.f64 x #s(literal 1 binary64)))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.4200024913855427e-8	92.78625598254331

Compiler

Compiled 8 to 8 computations (0% saved)

simplify76.0ms (5.9%)

Memory

28.4MiB live, 71.9MiB allocated; 43ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	22	36
2	29	36
3	45	36
4	82	36
5	326	36
6	3207	36
7	7184	36

Stop Event

1×	node limit

Calls

Call 1

Inputs

(*.f64 x (-.f64 x #s(literal 1 binary64)))

(if (<=.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (* x (- x 1)) (neg.f64 x)) (*.f64 x #s(approx (- x 1) x)))

#s(approx (* x (- x 1)) (neg.f64 x))

Outputs

(*.f64 x (-.f64 x #s(literal 1 binary64)))

(if (<=.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 3022314549036573/151115727451828646838272 binary64)) #s(approx (* x (- x 1)) (neg.f64 x)) (*.f64 x #s(approx (- x 1) x)))

#s(approx (* x (- x 1)) (neg.f64 x))

derivations4.0ms (0.3%)

Memory

11.4MiB live, 11.4MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 36 to 14 computations (61.1% saved)

preprocess37.0ms (2.9%)

Memory: -24.5MiB live, 63.1MiB allocated; 26ms collecting garbage
Compiler: Compiled 92 to 42 computations (54.3% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample639.0ms (49.2%)

explain54.0ms (4.2%)

preprocess304.0ms (23.4%)

eval0.0ms (0%)

prune0.0ms (0%)

series2.0ms (0.1%)

rewrite87.0ms (6.7%)

eval3.0ms (0.2%)

prune2.0ms (0.1%)

series1.0ms (0.1%)

rewrite73.0ms (5.6%)

eval2.0ms (0.1%)

prune2.0ms (0.2%)

regimes3.0ms (0.3%)

regimes3.0ms (0.2%)

regimes6.0ms (0.4%)

bsearch0.0ms (0%)

simplify76.0ms (5.9%)

derivations4.0ms (0.3%)

preprocess37.0ms (2.9%)

end0.0ms (0%)

Profiling