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

Time bar (total: 1.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory
1.3MiB live, 1.3MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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)

sample1.0s (76.7%)

Memory
-0.6MiB live, 766.6MiB allocated
Samples
524.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 349.0ms
ival-log: 283.0ms (81% of total)
ival-mult: 56.0ms (16% of total)
ival-true: 7.0ms (2% of total)
ival-assert: 4.0ms (1.1% of total)
Bogosity

explain55.0ms (4%)

Memory
-15.0MiB live, 64.5MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
00-0-(log.f64 x)
00-0-(*.f64 x (log.f64 x))
00-0-x
Confusion
Predicted +Predicted -
+00
-0256
Precision
0/0
Recall
0/0
Confusion?
Predicted +Predicted MaybePredicted -
+000
-00256
Precision?
0/0
Recall?
0/0
Freqs
test
numberfreq
0256
Total Confusion?
Predicted +Predicted MaybePredicted -
+000
-001
Precision?
0/0
Recall?
0/0
Samples
20.0ms512×0valid
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 (63.5% of total)
ival-mult: 4.0ms (36.3% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess41.0ms (3%)

Memory
-10.7MiB live, 26.6MiB 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)

IterNodesCost
0513
11811
23811
310411
414411
515511
615711
034
054
164
064
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
1.3MiB live, 1.3MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.6%
(*.f64 x (log.f64 x))
Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.2%)

Memory
7.0MiB live, 7.1MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(log.f64 x)
cost-diff0
(*.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)

IterNodesCost
037
057
167
067
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)

localize17.0ms (1.3%)

Memory
-0.5MiB live, 34.3MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0
(log.f64 x)
accuracy0.27734375
(*.f64 x (log.f64 x))
Samples
12.0ms256×0valid
Compiler

Compiled 9 to 5 computations (44.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 8.0ms
ival-mult: 4.0ms (50.8% of total)
ival-log: 3.0ms (38.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series109.0ms (8%)

Memory
-9.1MiB live, 74.9MiB 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:

TimeVariablePointExpression
57.0ms
x
@0
((* x (log x)) (log x))
44.0ms
x
@-inf
((* x (log x)) (log x))
7.0ms
x
@inf
((* x (log x)) (log x))

simplify20.0ms (1.5%)

Memory
-2.8MiB live, 30.7MiB 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)

IterNodesCost
016120
137112
263112
3104112
4167112
5298112
6555104
7616104
8620104
9624104
0624104
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 (1.2%)

Memory
-3.4MiB live, 33.2MiB allocated
Rules
4×lower-*.f32
2×lower-*.f64
2×*-commutative
2×lift-*.f64
2×lift-log.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
036
056
166
066
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)

eval3.0ms (0.2%)

Memory
8.7MiB live, 8.7MiB allocated
Compiler

Compiled 164 to 16 computations (90.2% saved)

prune2.0ms (0.1%)

Memory
5.9MiB live, 5.9MiB allocated
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New27027
Fresh000
Picked011
Done000
Total27128
Accuracy
99.6%
Counts
28 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.6%
(*.f64 x (log.f64 x))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify31.0ms (2.3%)

Memory
-17.6MiB live, 66.4MiB allocated
Algorithm
1×egg-herbie
Rules
2×*-commutative-binary64-*.f64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
034
144
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
0.6MiB live, 0.6MiB allocated
Stop Event
1×done
Compiler

Compiled 4 to 3 computations (25% saved)

preprocess18.0ms (1.3%)

Memory
-0.7MiB live, 36.8MiB allocated
Compiler

Compiled 16 to 12 computations (25% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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