Toniolo and Linder, Equation (13)

Time bar (total: 2.8s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze478.0ms (16.8%)

Memory
2.8MiB live, 200.0MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.7%0.3%0%0%0%0
0%0%99.7%0.3%0%0%0%1
0%0%99.7%0.3%0%0%0%2
0%0%99.7%0.3%0%0%0%3
0%0%99.7%0.3%0%0%0%4
0%0%99.7%0.3%0%0%0%5
0%0%99.7%0.3%0%0%0%6
0%0%99.7%0.3%0%0%0%7
0%0%99.7%0.3%0%0%0%8
0%0%99.7%0.3%0%0%0%9
0%0%97.8%0.3%0%1.9%0%10
0%0%97.4%0.3%0%2.3%0%11
0%0%94.8%0.3%0%4.9%0%12
Compiler

Compiled 30 to 23 computations (23.3% saved)

sample95.0ms (3.4%)

Memory
6.4MiB live, 36.7MiB allocated
Samples
42.0ms392×0invalid
28.0ms260×0valid
Precisions
Click to see histograms. Total time spent on operations: 50.0ms
ival-mult: 24.0ms (48.2% of total)
ival-div: 8.0ms (16.1% of total)
ival-sub: 8.0ms (16.1% of total)
ival-pow2: 6.0ms (12.1% of total)
ival-sqrt: 3.0ms (6% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
Bogosity

explain2.0s (71.5%)

Memory
3.7MiB live, 1 616.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
680-1(-1.948719277823438e-289 -7.32772843950899e-93 5.362665755649549e+60 -2.554324943403626e-299 1.045137256871977e-283 -1.9762396963960337e-236)(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))
470-4(-1.5319420548704328e-131 7.410144722190543e-187 -2.8688186153234924e-194 -1.0764356978471845e+149 4.2507922981062686e+162 -7.996634734869904e-143)(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))))
370-0-(/.f64 (*.f64 l l) Om)
330-3(3.3375600544917796e+243 3.396455803835093e-278 1.1008271645314162e-302 -2.2056915688026942e+104 1.1825554967892736e+261 3.021434210284346e+112)(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))
2410(3.853051839927027e-292 5.823325446188965e-283 8.170244049859947e-225 -2.949467972394588e+258 -3.5686901720378927e-241 1.319147866974133e-205)12(2.115605969784302e-189 -6.036986664589213e-192 -4.2348921593458065e+234 -1.0458086537490134e+208 -4.677681662786702e-215 -5.807826287371679e-21)(-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))
190-0-(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))
10-0-(*.f64 (*.f64 #s(literal 2 binary64) n) U)
00-0-Om
00-0-t
00-0-(/.f64 l Om)
00-0-U
00-0-U*
00-0-(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))
00-0-(*.f64 #s(literal 2 binary64) n)
00-0-n
00-0-(pow.f64 (/.f64 l Om) #s(literal 2 binary64))
00-0-(*.f64 l l)
00-0-(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))
00-0-#s(literal 2 binary64)
00-0-(-.f64 U U*)
00-0-l
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))oflow-rescue450
↳(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))overflow57
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))overflow71
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))overflow54
↳(*.f64 #s(literal 2 binary64) n)overflow1
↳(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))))overflow80
↳(-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))overflow80
↳(/.f64 (*.f64 l l) Om)overflow57
↳(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))overflow35
↳(*.f64 (*.f64 #s(literal 2 binary64) n) U)overflow18
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))overflow62
↳(/.f64 l Om)overflow22
↳(*.f64 l l)overflow66
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))overflow57
-.f64(-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))nan-rescue220
↳(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))overflow57
↳(/.f64 (*.f64 l l) Om)overflow57
↳(*.f64 l l)overflow66
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))overflow57
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))overflow71
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))overflow54
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))overflow62
↳(/.f64 l Om)overflow22
sqrt.f64(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))uflow-rescue220
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))underflow72
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))underflow82
↳(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))))underflow24
↳(/.f64 (*.f64 l l) Om)underflow66
↳(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))underflow2
↳(*.f64 (*.f64 #s(literal 2 binary64) n) U)underflow44
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))underflow84
↳(/.f64 l Om)underflow34
↳(*.f64 l l)underflow69
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))underflow66
/.f64(/.f64 (*.f64 l l) Om)o/n180
↳(*.f64 l l)overflow66
*.f64(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))))u*o170
↳(*.f64 (*.f64 #s(literal 2 binary64) n) U)underflow44
↳(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))overflow57
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))overflow71
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))overflow54
↳(/.f64 (*.f64 l l) Om)overflow57
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))overflow62
↳(-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))overflow80
↳(/.f64 l Om)overflow22
↳(*.f64 l l)overflow66
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))overflow57
*.f64(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))n*o140
*.f64(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))))n*o130
*.f64(*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))))n*u130
*.f64(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))n*u40
*.f64(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))n*o20
*.f64(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))n*u10
*.f64(*.f64 (*.f64 #s(literal 2 binary64) n) U)n*o10
Confusion
Predicted +Predicted -
+13212
-8104
Precision
0.9428571428571428
Recall
0.9166666666666666
Confusion?
Predicted +Predicted MaybePredicted -
+132012
-80104
Precision?
0.9428571428571428
Recall?
0.9166666666666666
2:
4:
8:
16:
32:
64:
128:
256:
512:
1024:
2048:
Freqs
test
numberfreq
0116
1111
226
33
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Total Time
11.96630859375
Average Time
0.04674339294433594
Samples
374.0ms3 072×0valid
Compiler

Compiled 5 544 to 1 032 computations (81.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 233.0ms
ival-mult: 111.0ms (47.6% of total)
ival-div: 37.0ms (15.9% of total)
ival-sub: 35.0ms (15% of total)
ival-pow2: 27.0ms (11.6% of total)
ival-sqrt: 17.0ms (7.3% of total)
ival-true: 2.0ms (0.9% of total)
exact: 2.0ms (0.9% of total)
adjust: 1.0ms (0.4% of total)
ival-assert: 1.0ms (0.4% of total)

preprocess178.0ms (6.3%)

Memory
-0.1MiB live, 49.0MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0221780
1714766
22813762
37848762
02128
03528
16628
219128
389926
4359924
5724524
0801923
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))
Outputs
(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))
(sqrt.f64 (*.f64 (fma.f64 (/.f64 (*.f64 l l) Om) (-.f64 #s(literal -2 binary64) (*.f64 n (/.f64 (-.f64 U U*) Om))) t) (*.f64 U (*.f64 n #s(literal 2 binary64)))))
Symmetry

(abs l)

Compiler

Compiled 28 to 21 computations (25% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 6 computations (-∞% saved)

prune1.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
47.8%
(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))
Compiler

Compiled 56 to 42 computations (25% saved)

simplify41.0ms (1.5%)

Memory
3.0MiB live, 18.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02128
13928
27028
39628
413128
516328
618228
729428
855428
971828
1073028
1177528
1280428
1384028
1487428
1590228
1692328
1793828
1894428
1994528
Stop Event
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))
Outputs
(sqrt.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) n) U) (-.f64 (-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))) (*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*)))))
(sqrt.f64 (*.f64 (-.f64 (*.f64 (-.f64 U* U) (*.f64 (pow.f64 (/.f64 l Om) #s(literal 2 binary64)) n)) (-.f64 (*.f64 (/.f64 (*.f64 l l) Om) #s(literal 2 binary64)) t)) (*.f64 U (*.f64 n #s(literal 2 binary64)))))

soundness1.0ms (0%)

Memory
-10.5MiB live, 0.2MiB allocated
Stop Event
1×fuel
Compiler

Compiled 28 to 21 computations (25% saved)

preprocess15.0ms (0.5%)

Memory
1.8MiB live, 1.8MiB allocated
Remove

(abs l)

Compiler

Compiled 224 to 168 computations (25% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

Loading profile data...