Metrics for Statistics.Distribution.Binomial:directEntropy from math-functions-0.1.5.2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

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
100%	50%	0%	0%	0%	50%	0%	2

Compiler

Compiled 6 to 5 computations (16.7% saved)

sample535.0ms (63.3%)

Memory

36.8MiB live, 822.8MiB allocated

Samples

357.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 192.0ms

ival-log: 125.0ms (65.3% of total)

ival-mult: 57.0ms (29.8% of total)

ival-true: 6.0ms (3.1% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain47.0ms (5.5%)

Memory

-37.6MiB live, 60.6MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(log.f64 x)`
-	-	`(*.f64 x (log.f64 x))`
-	-	`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

22.0ms

512×

valid

Compiler

Compiled 23 to 13 computations (43.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-log: 8.0ms (65.5% of total)

ival-mult: 4.0ms (32.7% of total)

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

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

preprocess13.0ms (1.5%)

Memory

15.6MiB live, 15.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`distribute-lft-neg-in`
9×	`associate-r`
9×	`cancel-sign-sub-inv`
8×	`unsub-neg`
8×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	18	11
2	38	11
3	104	11
4	144	11
5	155	11
6	157	11
0	3	4
0	5	4
1	6	4
0	6	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(*.f64 x (log.f64 x))

Outputs
(*.f64 x (log.f64 x))
(*.f64 (log.f64 x) x)

Compiler

Compiled 5 to 3 computations (40% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0.1%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(*.f64 x (log.f64 x))

Compiler

Compiled 5 to 3 computations (40% saved)

simplify3.0ms (0.3%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(log.f64 x)
cost-diff	0	(*.f64 x (log.f64 x))

Rules

2×	`lower-*.f32`
1×	`*-commutative`
1×	`lower-*.f64`
1×	`lift-*.f64`
1×	`lift-log.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	7
0	5	7
1	6	7
0	6	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 x (log.f64 x))
x
(log.f64 x)

Outputs
(*.f64 x (log.f64 x))
(*.f64 (log.f64 x) x)
x
(log.f64 x)

localize47.0ms (5.5%)

Memory

-20.4MiB live, 17.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(log.f64 x)
accuracy	0.25	(*.f64 x (log.f64 x))

Samples

11.0ms

256×

valid

Compiler

Compiled 9 to 5 computations (44.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-log: 4.0ms (65.5% of total)

ival-mult: 2.0ms (32.8% of total)

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

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

series99.0ms (11.7%)

Memory

-1.2MiB live, 77.1MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())
#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* x (log x)) (taylor 0 x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (log x)) (taylor 0 x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (log x)) (taylor 0 x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (log x)) (taylor 0 x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (log (/ 1 x)))) (taylor inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (log (/ 1 x)))) (taylor inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (log (/ 1 x)))) (taylor inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (log (/ 1 x)))) (taylor inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (log -1) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (log -1) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (log -1) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ (log -1) (* -1 (log (/ -1 x))))) (taylor -inf x) (#s(alt (.f64 x (log.f64 x)) (patch (.f64 x (log.f64 x)) #<representation binary64>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (log x) (taylor 0 x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log.f64 x) (patch (log.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
47.0ms	x	@	0	(* x (log x))
45.0ms	x	@	-inf	(* x (log x))
6.0ms	x	@	inf	(* x (log x))
0.0ms	x	@	0	(log x)
0.0ms	x	@	inf	(log x)

simplify17.0ms (2%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Rules

160×	`lower-fma.f64`
160×	`lower-fma.f32`
112×	`lower-*.f64`
112×	`lower-*.f32`
52×	`unsub-neg`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	16	120
1	37	112
2	63	112
3	104	112
4	167	112
5	298	112
6	553	104
7	612	104
8	616	104
9	620	104
0	620	104

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* x (log x))
(* x (log x))
(* x (log x))
(* x (log x))
(* -1 (* x (log (/ 1 x))))
(* -1 (* x (log (/ 1 x))))
(* -1 (* x (log (/ 1 x))))
(* -1 (* x (log (/ 1 x))))
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(log x)
(log x)
(log x)
(log x)
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))

Outputs
(* x (log x))
(*.f64 (log.f64 x) x)
(* x (log x))
(*.f64 (log.f64 x) x)
(* x (log x))
(*.f64 (log.f64 x) x)
(* x (log x))
(*.f64 (log.f64 x) x)
(* -1 (* x (log (/ 1 x))))
(*.f64 (log.f64 x) x)
(* -1 (* x (log (/ 1 x))))
(*.f64 (log.f64 x) x)
(* -1 (* x (log (/ 1 x))))
(*.f64 (log.f64 x) x)
(* -1 (* x (log (/ 1 x))))
(*.f64 (log.f64 x) x)
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(*.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) x)
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(*.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) x)
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(*.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) x)
(* x (+ (log -1) (* -1 (log (/ -1 x)))))
(*.f64 (+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64))) x)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(* -1 (log (/ 1 x)))
(log.f64 x)
(* -1 (log (/ 1 x)))
(log.f64 x)
(* -1 (log (/ 1 x)))
(log.f64 x)
(* -1 (log (/ 1 x)))
(log.f64 x)
(+ (log -1) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+.f64 (log.f64 (neg.f64 x)) (log.f64 #s(literal -1 binary64)))

rewrite34.0ms (4%)

Memory

-25.2MiB live, 12.0MiB allocated

Rules

2×	`lower-*.f32`
1×	`lower-*.f64`
1×	`*-commutative`
1×	`lift-*.f64`
1×	`lift-log.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
0	5	6
1	6	6
0	6	6

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 x (log.f64 x))
(log.f64 x)

Outputs
(*.f64 (log.f64 x) x)
(*.f64 x (log.f64 x))
(log.f64 x)

eval2.0ms (0.3%)

Memory: 2.8MiB live, 2.8MiB allocated
Compiler: Compiled 165 to 11 computations (93.3% saved)

prune2.0ms (0.2%)

Memory

2.5MiB live, 2.5MiB allocated

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	1	28

Accuracy

99.6%

Counts

28 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.6%	(*.f64 x (log.f64 x))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify5.0ms (0.6%)

Memory

5.6MiB live, 5.6MiB allocated

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	4	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 x (log.f64 x))

Outputs
(*.f64 x (log.f64 x))
(*.f64 (log.f64 x) x)

soundness0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Stop Event

1×

done

Compiler

Compiled 5 to 3 computations (40% saved)

preprocess41.0ms (4.9%)

Memory: -12.3MiB live, 26.6MiB allocated
Compiler: Compiled 20 to 12 computations (40% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	120
1	37	112
2	63	112
3	104	112
4	167	112
5	298	112
6	553	104
7	612	104
8	616	104
9	620	104
0	620	104

Iter	Nodes	Cost
0	16	120
1	37	112
2	63	112
3	104	112
4	167	112
5	298	112
6	553	104
7	612	104
8	616	104
9	620	104
0	620	104

start0.0ms (0%)

analyze0.0ms (0%)

sample535.0ms (63.3%)

explain47.0ms (5.5%)

preprocess13.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0.1%)

simplify3.0ms (0.3%)

localize47.0ms (5.5%)

series99.0ms (11.7%)

simplify17.0ms (2%)

rewrite34.0ms (4%)

eval2.0ms (0.3%)

prune2.0ms (0.2%)

simplify5.0ms (0.6%)

soundness0.0ms (0%)

preprocess41.0ms (4.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	120
1	37	112
2	63	112
3	104	112
4	167	112
5	298	112
6	553	104
7	612	104
8	616	104
9	620	104
0	620	104