Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

Time bar (total: 2.0s)

start0.0ms (0%)

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

analyze1.0ms (0.1%)

Memory
0.8MiB live, 0.8MiB allocated; 0ms collecting garbage
Algorithm
search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%100%0%0%0%0%0
0%0%100%0%0%0%0%1
50%50%50%0%0%0%0%2
75%75%25%0%0%0%0%3
87.5%87.5%12.5%0%0%0%0%4
93.8%93.7%6.2%0%0%0%0%5
96.9%96.8%3.1%0%0%0%0%6
98.4%98.4%1.6%0%0%0%0%7
99.2%99.2%0.8%0%0%0%0%8
99.6%99.6%0.4%0%0%0%0%9
99.8%99.8%0.2%0%0%0%0%10
99.9%99.9%0.1%0%0%0%0%11
100%99.9%0%0%0%0%0%12
Compiler

Compiled 7 to 6 computations (14.3% saved)

sample562.0ms (28.6%)

Memory
6.1MiB live, 487.4MiB allocated; 133ms collecting garbage
Samples
304.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 129.0ms
ival-sub!: 76.0ms (58.9% of total)
ival-div!: 52.0ms (40.3% of total)
adjust: 2.0ms (1.5% of total)
Bogosity

preprocess48.0ms (2.5%)

Memory
-17.0MiB live, 76.5MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0820
14318
Stop Event
iter-limit
iter-limit
unsound
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Compiler

Compiled 10 to 8 computations (20% saved)

series194.0ms (9.9%)

Memory
7.9MiB live, 112.8MiB allocated; 63ms collecting garbage
Counts
4 → 14
Calls
Call 1
Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
#s(approx (/ x (- 1 x)) x)
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))))
#s(approx (- 1 x) #s(literal 1 binary64))
#s(approx (- 1 x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) x)))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (- 1 x) (*.f64 #s(literal -1 binary64) x))
#s(approx (- 1 x) (*.f64 x (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) x)) #s(literal 1 binary64)))
#s(approx (- 1 x) (*.f64 #s(literal -1 binary64) (*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
Calls

3 calls:

TimeVariablePoint
1.0ms
x
-inf
0.0ms
x
inf
0.0ms
x
0

rewrite220.0ms (11.2%)

Memory
-22.2MiB live, 210.4MiB allocated; 38ms collecting garbage
Counts
4 → 20
Calls
Call 1
Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
(*.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) x)))
(*.f64 x (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 x x) x))) (fma.f64 (+.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x))) (+.f64 x #s(literal 1 binary64)))
(*.f64 (/.f64 x (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (neg.f64 (+.f64 x #s(literal 1 binary64))))
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (fma.f64 (*.f64 x x) x #s(literal 1 binary64))) (fma.f64 x (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (fma.f64 (+.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) x) (fma.f64 (+.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 #s(literal 1 binary64)))
(*.f64 (pow.f64 (neg.f64 #s(literal 1 binary64)) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))) (pow.f64 (neg.f64 #s(literal 1 binary64)) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))))
(*.f64 (pow.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))) (pow.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) #s(literal 2 binary64))))

eval6.0ms (0.3%)

Memory
14.1MiB live, 14.2MiB allocated; 0ms collecting garbage
Compiler

Compiled 413 to 122 computations (70.5% saved)

prune3.0ms (0.1%)

Memory
6.8MiB live, 6.8MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New29332
Fresh000
Picked011
Done000
Total29433
Accuracy
100.0%
Counts
33 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
48.9%
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
49.8%
#s(approx (/ x (- 1 x)) x)
51.7%
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Compiler

Compiled 30 to 23 computations (23.3% saved)

series142.0ms (7.2%)

Memory
33.7MiB live, 112.0MiB allocated; 41ms collecting garbage
Counts
8 → 14
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (- 1 x)) x)
x
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
#s(approx (/ x (- 1 x)) x)
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))))
#s(approx (+ 1 x) #s(literal 1 binary64))
#s(approx (+ 1 x) (+.f64 #s(literal 1 binary64) x))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (* x (+ 1 x)) (pow.f64 x #s(literal 2 binary64)))
#s(approx (* x (+ 1 x)) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (+ 1 x) (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) x)) #s(literal 1 binary64)))
Calls

3 calls:

TimeVariablePoint
2.0ms
x
-inf
1.0ms
x
inf
1.0ms
x
0

rewrite245.0ms (12.5%)

Memory
1.1MiB live, 242.5MiB allocated; 108ms collecting garbage
Counts
8 → 24
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (- 1 x)) x)
x
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(approx (/ x (- 1 x)) x)
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) x)
(*.f64 (/.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(*.f64 (fma.f64 x x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x x x))
(*.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 (*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 (+.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64))) #s(literal 1 binary64)) (fma.f64 (+.f64 #s(literal 1 binary64) x) x #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 1 binary64) x)))
#s(literal 1 binary64)
(*.f64 #s(literal 1 binary64) #s(literal 1 binary64))
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (pow.f64 (neg.f64 #s(literal 1 binary64)) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))) (pow.f64 (neg.f64 #s(literal 1 binary64)) (/.f64 #s(literal 3 binary64) #s(literal 2 binary64))))

eval14.0ms (0.7%)

Memory
-33.8MiB live, 12.0MiB allocated; 13ms collecting garbage
Compiler

Compiled 522 to 129 computations (75.3% saved)

prune2.0ms (0.1%)

Memory
5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New32133
Fresh000
Picked123
Done011
Total33437
Accuracy
100.0%
Counts
37 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
48.9%
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
49.8%
#s(approx (/ x (- 1 x)) x)
51.7%
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Compiler

Compiled 29 to 21 computations (27.6% saved)

series149.0ms (7.6%)

Memory
-5.7MiB live, 40.3MiB allocated; 47ms collecting garbage
Counts
3 → 11
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(fma.f64 x x x)
x
Outputs
#s(approx (/ x (- 1 x)) x)
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)) #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (pow.f64 x #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (+ (* x x) x) (pow.f64 x #s(literal 2 binary64)))
#s(approx (+ (* x x) x) (*.f64 (pow.f64 x #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (/ x (- 1 x)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 2 binary64))))) x)) #s(literal 1 binary64)))
Calls

3 calls:

TimeVariablePoint
0.0ms
x
-inf
0.0ms
x
inf
0.0ms
x
0

rewrite258.0ms (13.1%)

Memory
7.3MiB live, 106.8MiB allocated; 98ms collecting garbage
Counts
3 → 11
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(fma.f64 x x x)
x
Outputs
#s(approx (/ x (+ 1 x)) (fma.f64 x x x))
(*.f64 (-.f64 #s(literal 1 binary64) x) x)
(*.f64 (-.f64 #s(literal 1 binary64) x) (fabs.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 x))
(*.f64 (fma.f64 x x x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x x x))
x
(*.f64 x #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) x)
(*.f64 (neg.f64 #s(literal 1 binary64)) (neg.f64 x))
(*.f64 (neg.f64 x) (neg.f64 #s(literal 1 binary64)))

eval4.0ms (0.2%)

Memory
6.0MiB live, 6.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 302 to 73 computations (75.8% saved)

prune3.0ms (0.1%)

Memory
3.9MiB live, 3.9MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New19019
Fresh000
Picked011
Done033
Total19423
Accuracy
100.0%
Counts
23 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
100.0%
(/.f64 x (-.f64 #s(literal 1 binary64) x))
48.9%
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
49.8%
#s(approx (/ x (- 1 x)) x)
51.7%
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Compiler

Compiled 29 to 21 computations (27.6% saved)

regimes27.0ms (1.4%)

Memory
-16.2MiB live, 34.7MiB allocated; 9ms collecting garbage
Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts
1 → 1
2 → 2
4 → 2
5 → 1
Calls
Call 1
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
Call 2
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) x)
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) x)
Call 3
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) x)
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
Call 4
Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) x)
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
#s(approx (/ x (- 1 x)) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Calls

7 calls:

7.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
4.0ms
x
3.0ms
x
3.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
3.0ms
(/.f64 x (-.f64 #s(literal 1 binary64) x))
Results
AccuracySegmentsBranch
51.7%1x
51.7%1(/.f64 x (-.f64 #s(literal 1 binary64) x))
97.8%2(/.f64 x (-.f64 #s(literal 1 binary64) x))
98.2%2(/.f64 x (-.f64 #s(literal 1 binary64) x))
98.2%3x
100.0%1(/.f64 x (-.f64 #s(literal 1 binary64) x))
100.0%1x
Compiler

Compiled 63 to 34 computations (46% saved)

bsearch1.0ms (0%)

Memory
0.7MiB live, 0.7MiB allocated; 0ms collecting garbage
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-0.9920572025397058
-2.8444321723135564e-10
Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated; 0ms collecting garbage
Algorithm
left-value
Steps
TimeLeftRight
0.0ms
-0.9920572025397058
-2.8444321723135564e-10
Compiler

Compiled 8 to 8 computations (0% saved)

derivations2.0ms (0.1%)

Memory
2.1MiB live, 2.1MiB allocated; 0ms collecting garbage
Stop Event
done
Compiler

Compiled 59 to 16 computations (72.9% saved)

preprocess85.0ms (4.3%)

Memory
-2.5MiB live, 43.7MiB allocated; 5ms collecting garbage
Compiler

Compiled 64 to 20 computations (68.8% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...