Numeric.Integration.TanhSinh:simpson from integration-0.2.1

Time bar (total: 1.1s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 7 to 6 computations (14.3% saved)

sample637.0ms (56%)

Memory
23.7MiB live, 820.0MiB allocated
Samples
376.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 114.0ms
ival-mult: 65.0ms (57% of total)
ival-add: 40.0ms (35.1% of total)
ival-true: 6.0ms (5.3% of total)
ival-assert: 3.0ms (2.6% of total)
Bogosity

explain99.0ms (8.7%)

Memory
12.0MiB live, 118.4MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
10-0-(*.f64 x (+.f64 y y))
00-0-(+.f64 y y)
00-0-y
00-0-x
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
*.f64(*.f64 x (+.f64 y y))n*o10
Confusion
Predicted +Predicted -
+10
-0255
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+100
-00255
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0255
11
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
18.0ms512×0valid
Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-add: 3.0ms (45.1% of total)
ival-mult: 3.0ms (45.1% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess28.0ms (2.5%)

Memory
-28.9MiB live, 64.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01233
14025
29925
316425
419225
521225
623225
045
065
1135
2295
3485
4665
51005
61645
71895
82095
92195
02195
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
Outputs
(*.f64 x (+.f64 y y))
(*.f64 (*.f64 #s(literal 2 binary64) y) x)
Symmetry

(negabs y)

(negabs x)

(sort x y)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory
0.2MiB live, 0.2MiB allocated
Compiler

Compiled 0 to 2 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 (+.f64 y y))
Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.6%)

Memory
15.9MiB live, 15.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 y y)
cost-diff0
(*.f64 x (+.f64 y y))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0410
0610
11310
22910
34810
46610
510010
616410
718910
820910
921910
021910
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
x
(+.f64 y y)
y
Outputs
(*.f64 x (+.f64 y y))
(*.f64 (*.f64 #s(literal 2 binary64) y) x)
x
(+.f64 y y)
(*.f64 #s(literal 2 binary64) y)
y

localize25.0ms (2.2%)

Memory
-35.7MiB live, 30.8MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 y y)
accuracy0.2391640349123043
(*.f64 x (+.f64 y y))
Samples
10.0ms256×0valid
Compiler

Compiled 12 to 6 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 3.0ms
ival-mult: 2.0ms (63.3% of total)
ival-add: 1.0ms (31.6% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.4%)

Memory
11.5MiB live, 11.5MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
(+.f64 y y)
Outputs
(* 2 (* x y))
(* 2 y)
Calls

6 calls:

TimeVariablePointExpression
1.0ms
y
@0
((* x (+ y y)) (+ y y))
1.0ms
y
@inf
((* x (+ y y)) (+ y y))
1.0ms
y
@-inf
((* x (+ y y)) (+ y y))
1.0ms
x
@0
((* x (+ y y)) (+ y y))
1.0ms
x
@inf
((* x (+ y y)) (+ y y))

simplify8.0ms (0.7%)

Memory
-23.7MiB live, 23.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1158
2308
3438
4618
5958
61598
71848
82048
92148
02148
Stop Event
1×iter limit
1×saturated
Counts
2 → 2
Calls
Call 1
Inputs
(* 2 (* x y))
(* 2 y)
Outputs
(* 2 (* x y))
(*.f64 (*.f64 y x) #s(literal 2 binary64))
(* 2 y)
(*.f64 #s(literal 2 binary64) y)

rewrite58.0ms (5.1%)

Memory
42.9MiB live, 86.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
068
1228
01378
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
2 → 24
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
(+.f64 y y)
Outputs
(*.f64 (*.f64 x #s(literal 2 binary64)) y)
(*.f64 #s(literal 2 binary64) (*.f64 y x))
(*.f64 (*.f64 #s(literal 2 binary64) y) x)
(*.f64 y (+.f64 x x))
(*.f64 x (*.f64 #s(literal 2 binary64) y))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) x) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (*.f64 x #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 x (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 y x) (*.f64 y x)) (*.f64 (*.f64 y x) (*.f64 y x))) (-.f64 (*.f64 y x) (*.f64 y x)))
(/.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 3 binary64)) (pow.f64 (*.f64 y x) #s(literal 3 binary64))) (fma.f64 (*.f64 y x) (*.f64 y x) (-.f64 (*.f64 (*.f64 y x) (*.f64 y x)) (*.f64 (*.f64 y x) (*.f64 y x)))))
(fma.f64 y x (*.f64 y x))
(fma.f64 x y (*.f64 y x))
(-.f64 (*.f64 y x) (*.f64 (neg.f64 y) x))
(-.f64 (*.f64 y x) (*.f64 (neg.f64 x) y))
(+.f64 (*.f64 y x) (*.f64 y x))
(*.f64 #s(literal 2 binary64) y)
(*.f64 y #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y #s(literal 0 binary64)))
(-.f64 (/.f64 (*.f64 y y) #s(literal 0 binary64)) (/.f64 (*.f64 y y) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y #s(literal 0 binary64))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y #s(literal 0 binary64))))
(+.f64 y y)

eval42.0ms (3.7%)

Memory
-31.9MiB live, 12.9MiB allocated
Compiler

Compiled 249 to 67 computations (73.1% saved)

prune1.0ms (0.1%)

Memory
4.7MiB live, 4.7MiB allocated
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New25126
Fresh000
Picked101
Done000
Total26127
Accuracy
100.0%
Counts
27 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 y (+.f64 x x))
Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.6%)

Memory
25.2MiB live, 25.2MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 x x)
cost-diff0
(*.f64 y (+.f64 x x))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0410
0610
11310
22910
34810
46610
510010
616410
718910
820910
921910
021910
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(*.f64 y (+.f64 x x))
y
(+.f64 x x)
x
Outputs
(*.f64 y (+.f64 x x))
(*.f64 (*.f64 #s(literal 2 binary64) x) y)
y
(+.f64 x x)
(*.f64 #s(literal 2 binary64) x)
x

localize47.0ms (4.1%)

Memory
-17.0MiB live, 37.6MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 x x)
accuracy0.0
(*.f64 y (+.f64 x x))
Samples
44.0ms256×0valid
Compiler

Compiled 12 to 6 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (62.4% of total)
ival-add: 1.0ms (20.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.2%)

Memory
5.3MiB live, 5.3MiB allocated
Counts
2 → 2
Calls
Call 1
Inputs
(*.f64 y (+.f64 x x))
(+.f64 x x)
Outputs
(* 2 (* x y))
(* 2 x)
Calls

6 calls:

TimeVariablePointExpression
1.0ms
x
@inf
((* y (+ x x)) (+ x x))
1.0ms
x
@-inf
((* y (+ x x)) (+ x x))
0.0ms
x
@0
((* y (+ x x)) (+ x x))
0.0ms
y
@-inf
((* y (+ x x)) (+ x x))
0.0ms
y
@inf
((* y (+ x x)) (+ x x))

simplify7.0ms (0.6%)

Memory
12.6MiB live, 12.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1148
2308
3448
4628
5968
61668
71918
82118
92218
02218
Stop Event
1×iter limit
1×saturated
Counts
2 → 2
Calls
Call 1
Inputs
(* 2 (* x y))
(* 2 x)
Outputs
(* 2 (* x y))
(*.f64 (*.f64 x y) #s(literal 2 binary64))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)

rewrite36.0ms (3.1%)

Memory
-9.1MiB live, 36.2MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
068
1228
01378
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
2 → 24
Calls
Call 1
Inputs
(*.f64 y (+.f64 x x))
(+.f64 x x)
Outputs
(*.f64 (*.f64 y #s(literal 2 binary64)) x)
(*.f64 #s(literal 2 binary64) (*.f64 x y))
(*.f64 (*.f64 #s(literal 2 binary64) x) y)
(*.f64 x (+.f64 y y))
(*.f64 y (*.f64 #s(literal 2 binary64) x))
(/.f64 (*.f64 #s(literal 0 binary64) y) #s(literal 0 binary64))
(/.f64 (*.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) y) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 y #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (*.f64 y (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y))) (-.f64 (*.f64 x y) (*.f64 x y)))
(/.f64 (+.f64 (pow.f64 (*.f64 x y) #s(literal 3 binary64)) (pow.f64 (*.f64 x y) #s(literal 3 binary64))) (fma.f64 (*.f64 x y) (*.f64 x y) (-.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (*.f64 x y) (*.f64 x y)))))
(fma.f64 x y (*.f64 x y))
(fma.f64 y x (*.f64 x y))
(-.f64 (*.f64 x y) (*.f64 (neg.f64 x) y))
(-.f64 (*.f64 x y) (*.f64 (neg.f64 y) x))
(+.f64 (*.f64 x y) (*.f64 x y))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(-.f64 (/.f64 (*.f64 x x) #s(literal 0 binary64)) (/.f64 (*.f64 x x) #s(literal 0 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)

eval2.0ms (0.2%)

Memory
5.8MiB live, 5.8MiB allocated
Compiler

Compiled 249 to 67 computations (73.1% saved)

prune1.0ms (0.1%)

Memory
4.4MiB live, 4.5MiB allocated
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New26026
Fresh000
Picked011
Done000
Total26127
Accuracy
100.0%
Counts
27 → 1
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 y (+.f64 x x))
Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.9%)

Memory
-24.9MiB live, 19.4MiB allocated
Counts
2 → 1
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
(*.f64 y (+.f64 x x))
Outputs
(*.f64 y (+.f64 x x))
Calls

4 calls:

6.0ms
(*.f64 x (+.f64 y y))
1.0ms
x
1.0ms
(+.f64 y y)
1.0ms
y
Results
AccuracySegmentsBranch
100.0%1(+.f64 y y)
100.0%1(*.f64 x (+.f64 y y))
100.0%1x
100.0%1y
Compiler

Compiled 10 to 11 computations (-10% saved)

regimes4.0ms (0.4%)

Memory
13.6MiB live, 13.5MiB allocated
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
Calls
Call 1
Inputs
(*.f64 x (+.f64 y y))
Outputs
(*.f64 x (+.f64 y y))
Calls

4 calls:

1.0ms
y
1.0ms
x
1.0ms
(+.f64 y y)
1.0ms
(*.f64 x (+.f64 y y))
Results
AccuracySegmentsBranch
99.6%1(+.f64 y y)
99.6%1(*.f64 x (+.f64 y y))
99.6%1x
99.6%1y
Compiler

Compiled 10 to 11 computations (-10% saved)

simplify11.0ms (1%)

Memory
-16.4MiB live, 28.6MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0610
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 y (+.f64 x x))
(*.f64 x (+.f64 y y))
Outputs
(*.f64 y (+.f64 x x))
(*.f64 x (+.f64 y y))

soundness19.0ms (1.7%)

Memory
39.8MiB live, 39.8MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048
068
1228
01378
Stop Event
1×done
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Compiler

Compiled 20 to 12 computations (40% saved)

preprocess80.0ms (7%)

Memory
-46.6MiB live, 55.9MiB allocated
Remove

(sort x y)

(negabs x)

(negabs y)

Compiler

Compiled 90 to 68 computations (24.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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