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

0.2MiB live, 0.2MiB 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)

sample691.0ms (72.4%)

Memory

-7.5MiB live, 840.4MiB allocated

Samples

462.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 213.0ms

ival-log: 127.0ms (59.7% of total)

ival-mult: 78.0ms (36.7% of total)

ival-true: 5.0ms (2.3% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain46.0ms (4.8%)

Memory

-24.6MiB live, 90.1MiB 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

23.0ms

512×

valid

Compiler

Compiled 22 to 13 computations (40.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-log: 7.0ms (66.4% of total)

ival-mult: 3.0ms (28.5% of total)

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

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

preprocess13.0ms (1.4%)

Memory

28.1MiB live, 28.1MiB allocated

Algorithm

1×	egg-herbie

Rules

32×	`distribute-lft-neg-in`
18×	`associate-r`
18×	`cancel-sign-sub-inv`
16×	`unsub-neg`
16×	`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 4 to 3 computations (25% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.9%)

Memory

-36.1MiB live, 5.8MiB 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

4×	`lower-*.f32`
2×	`*-commutative`
2×	`lower-*.f64`
2×	`lift-*.f64`
2×	`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)

localize13.0ms (1.4%)

Memory

25.9MiB live, 25.9MiB 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

9.0ms

256×

valid

Compiler

Compiled 9 to 5 computations (44.4% saved)

Precisions

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

ival-log: 3.0ms (59.1% of total)

ival-mult: 2.0ms (39.4% of total)

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

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

series66.0ms (6.9%)

Memory

18.4MiB live, 126.7MiB 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 (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 (* 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 (* -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 (* 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 -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

3 calls:

Time	Variable		Point	Expression
39.0ms	x	@	0	((* x (log x)) (log x))
20.0ms	x	@	-inf	((* x (log x)) (log x))
7.0ms	x	@	inf	((* x (log x)) (log x))

simplify25.0ms (2.7%)

Memory

-21.9MiB live, 17.8MiB allocated

Algorithm

1×	egg-herbie

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
224×	`lower-*.f64`
224×	`lower-*.f32`
104×	`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	555	104
7	616	104
8	620	104
9	624	104
0	624	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))
(log x)
(log x)
(log x)
(log x)
(* -1 (* x (log (/ 1 x))))
(* -1 (* x (log (/ 1 x))))
(* -1 (* x (log (/ 1 x))))
(* -1 (* x (log (/ 1 x))))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -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)))))
(* 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))))
(+ (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)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(log x)
(log.f64 x)
(log x)
(log.f64 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)
(* -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)
(* 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 -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)))

rewrite16.0ms (1.7%)

Memory

-4.1MiB live, 31.9MiB allocated

Rules

4×	`lower-*.f32`
2×	`lower-*.f64`
2×	`*-commutative`
2×	`lift-*.f64`
2×	`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 (0.2%)

Memory: 5.9MiB live, 5.9MiB allocated
Compiler: Compiled 164 to 16 computations (90.2% saved)

prune2.0ms (0.2%)

Memory

6.1MiB live, 6.1MiB 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 8 to 6 computations (25% saved)

simplify26.0ms (2.7%)

Memory

24.7MiB live, 62.2MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

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)

soundness3.0ms (0.3%)

Memory

-36.6MiB live, 0.8MiB allocated

Stop Event

1×

done

Compiler

Compiled 4 to 3 computations (25% saved)

preprocess41.0ms (4.3%)

Memory: -2.1MiB live, 51.7MiB allocated
Compiler: Compiled 16 to 12 computations (25% 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	555	104
7	616	104
8	620	104
9	624	104
0	624	104

Iter	Nodes	Cost
0	16	120
1	37	112
2	63	112
3	104	112
4	167	112
5	298	112
6	555	104
7	616	104
8	620	104
9	624	104
0	624	104

start0.0ms (0%)

analyze0.0ms (0%)

sample691.0ms (72.4%)

explain46.0ms (4.8%)

preprocess13.0ms (1.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.9%)

localize13.0ms (1.4%)

series66.0ms (6.9%)

simplify25.0ms (2.7%)

rewrite16.0ms (1.7%)

eval2.0ms (0.2%)

prune2.0ms (0.2%)

simplify26.0ms (2.7%)

soundness3.0ms (0.3%)

preprocess41.0ms (4.3%)

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	555	104
7	616	104
8	620	104
9	624	104
0	624	104