Toniolo and Linder, Equation (13)

Time bar (total: 10.8s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

analyze504.0ms (4.6%)

Memory
5.1MiB live, 201.1MiB 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)

sample93.0ms (0.9%)

Memory
1.2MiB live, 33.0MiB allocated
Samples
38.0ms334×0invalid
31.0ms260×0valid
Precisions
Click to see histograms. Total time spent on operations: 50.0ms
ival-mult: 24.0ms (48.3% of total)
ival-div: 8.0ms (16.1% of total)
ival-sub: 7.0ms (14.1% of total)
ival-pow2: 6.0ms (12.1% of total)
ival-sqrt: 4.0ms (8% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
Bogosity

explain10.0s (92.3%)

Memory
49.5MiB live, 5 942.6MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
740-3(-6.574051164330109e-211 -2.360453860146265e-160 -2.7645346313601296e-306 6.459670628358447e+77 -9.076952731785626e+107 -1.0828920027297683e+268)(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*)))))
410-3(-2.3569844364146073e-88 -2.5739816505386744e-223 2.924713978626919e+196 -4.828532291140182e+93 -2.911628688325394e+140 1.1542537853011299e+100)(*.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*))))
330-5(7.214433938344616e-148 4.5792788844110874e+110 3.8466255231472706e-191 -4.0987332164551665e+86 -7.164057084532718e+167 -24364232262207700.0)(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))
260-0-(-.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*)))
220-1(-4.2494260824950894e-277 -5.029161899390556e+162 2.966616780418258e-64 2.258476818671939e-157 -1.1115742907609015e-60 -6.256817836275493e+187)(/.f64 (*.f64 l l) Om)
211(1.1761615819915883e+30 -6.684463512623637e-211 -28.3047999632901 16075.199203601707 7.999774706601107e+180 -1.6214293142351229e+25)2(-1.8817423737892747e+56 6.186834845770218e-97 5.048428809228481e-155 -6.315220602199489e+54 -2.9702384988674923e+214 1.1995145909765214e+228)(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))
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 (*.f64 #s(literal 2 binary64) n) U)
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-rescue490
↳(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))overflow51
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))overflow69
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))overflow61
↳(*.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*))))overflow82
↳(-.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*)))overflow77
↳(/.f64 (*.f64 l l) Om)overflow51
↳(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*)))))overflow33
↳(*.f64 (*.f64 #s(literal 2 binary64) n) U)overflow10
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))overflow61
↳(/.f64 l Om)overflow22
↳(*.f64 l l)overflow53
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))overflow51
-.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-rescue260
↳(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))overflow51
↳(/.f64 (*.f64 l l) Om)overflow51
↳(*.f64 l l)overflow53
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))overflow51
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))overflow69
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))overflow61
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))overflow61
↳(/.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*))underflow75
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))underflow96
↳(*.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*))))underflow23
↳(/.f64 (*.f64 l l) Om)underflow69
↳(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*)))))underflow1
↳(*.f64 (*.f64 #s(literal 2 binary64) n) U)underflow37
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))underflow83
↳(/.f64 l Om)underflow50
↳(*.f64 l l)underflow55
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))underflow69
*.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*u160
*.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 l l) Om)o/n130
↳(*.f64 l l)overflow53
*.f64(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))n*o120
*.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*o90
↳(*.f64 (*.f64 #s(literal 2 binary64) n) U)underflow37
↳(-.f64 t (*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om)))overflow51
↳(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))overflow69
↳(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))overflow61
↳(/.f64 (*.f64 l l) Om)overflow51
↳(pow.f64 (/.f64 l Om) #s(literal 2 binary64))overflow61
↳(-.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*)))overflow77
↳(/.f64 l Om)overflow22
↳(*.f64 l l)overflow53
↳(*.f64 #s(literal 2 binary64) (/.f64 (*.f64 l l) Om))overflow51
*.f64(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))n*o60
*.f64(*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64)))n*u30
*.f64(*.f64 (*.f64 n (pow.f64 (/.f64 l Om) #s(literal 2 binary64))) (-.f64 U U*))n*u30
/.f64(/.f64 (*.f64 l l) Om)u/n10
↳(*.f64 l l)underflow55
Confusion
Predicted +Predicted -
+1345
-2115
Precision
0.9852941176470589
Recall
0.9640287769784173
Confusion?
Predicted +Predicted MaybePredicted -
+13405
-20115
Precision?
0.9852941176470589
Recall?
0.9640287769784173
Freqs
test
numberfreq
0120
1101
233
32
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Total Time
35.98583984375
Average Time
0.14056968688964844
Samples
3.0s23 040×0valid
Compiler

Compiled 20 880 to 3 960 computations (81% saved)

Precisions
Click to see histograms. Total time spent on operations: 1.9s
ival-mult: 856.0ms (45.1% of total)
ival-div: 317.0ms (16.7% of total)
ival-sub: 304.0ms (16% of total)
ival-pow2: 224.0ms (11.8% of total)
ival-sqrt: 152.0ms (8% of total)
ival-true: 23.0ms (1.2% of total)
exact: 15.0ms (0.8% of total)
ival-assert: 9.0ms (0.5% of total)

preprocess191.0ms (1.8%)

Memory
0.4MiB live, 48.9MiB 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
49.6%
(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)

simplify43.0ms (0.4%)

Memory
3.1MiB 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)))))

soundness0.0ms (0%)

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

Compiled 28 to 21 computations (25% saved)

preprocess3.0ms (0%)

Memory
-6.1MiB 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

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