Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A

Time bar (total: 17.9s)

analyze130.0ms (0.7%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
25%25%74.9%0.1%0%0%0%3
37.5%37.5%62.4%0.1%0%0%0%4
56.3%56.2%43.7%0.1%0%0%0%5
62.5%62.4%37.5%0.1%0%0%0%6
71.9%71.8%28.1%0.1%0%0%0%7
76.6%76.5%23.4%0.1%0%0%0%8
83.6%83.5%16.4%0.1%0%0%0%9
87.1%87%12.9%0.1%0%0%0%10
91.2%91.1%8.8%0.1%0%0%0%11
93.3%93.2%6.7%0.1%0%0%0%12
Compiler

Compiled 20 to 10 computations (50% saved)

sample17.2s (96.5%)

Results
1.8s8256×0valid-rival
887.0ms8209×0valid-sollya
235.0ms47×0exit-sollya
Bogosity

preprocess312.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
697×times-frac
461×distribute-lft-neg-in
354×distribute-rgt-neg-in
293×unsub-neg
288×distribute-lft-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
037559
1182519
2826491
34588483
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))
(/.f64 (*.f64 (neg.f64 x) y) (*.f64 (*.f64 (+.f64 (neg.f64 x) y) (+.f64 (neg.f64 x) y)) (+.f64 (+.f64 (neg.f64 x) y) #s(literal 1 binary64))))
(/.f64 (*.f64 x (neg.f64 y)) (*.f64 (*.f64 (+.f64 x (neg.f64 y)) (+.f64 x (neg.f64 y))) (+.f64 (+.f64 x (neg.f64 y)) #s(literal 1 binary64))))
(neg.f64 (/.f64 (*.f64 (neg.f64 x) y) (*.f64 (*.f64 (+.f64 (neg.f64 x) y) (+.f64 (neg.f64 x) y)) (+.f64 (+.f64 (neg.f64 x) y) #s(literal 1 binary64)))))
(neg.f64 (/.f64 (*.f64 x (neg.f64 y)) (*.f64 (*.f64 (+.f64 x (neg.f64 y)) (+.f64 x (neg.f64 y))) (+.f64 (+.f64 x (neg.f64 y)) #s(literal 1 binary64)))))
(/.f64 (*.f64 y x) (*.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 (+.f64 y x) #s(literal 1 binary64))))
Outputs
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))
(*.f64 x (/.f64 y (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x (+.f64 y #s(literal 1 binary64))))))
(*.f64 x (/.f64 y (+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (pow.f64 (+.f64 x y) #s(literal 3 binary64)))))
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) #s(literal 3 binary64))))
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))
(*.f64 x (/.f64 y (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x (+.f64 y #s(literal 1 binary64))))))
(*.f64 x (/.f64 y (+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (pow.f64 (+.f64 x y) #s(literal 3 binary64)))))
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) #s(literal 3 binary64))))
(/.f64 (*.f64 (neg.f64 x) y) (*.f64 (*.f64 (+.f64 (neg.f64 x) y) (+.f64 (neg.f64 x) y)) (+.f64 (+.f64 (neg.f64 x) y) #s(literal 1 binary64))))
(/.f64 (*.f64 x (neg.f64 y)) (*.f64 (+.f64 y (neg.f64 x)) (*.f64 (+.f64 y (neg.f64 x)) (+.f64 #s(literal 1 binary64) (+.f64 y (neg.f64 x))))))
(*.f64 (neg.f64 x) (/.f64 (/.f64 y (*.f64 (-.f64 y x) (-.f64 y x))) (+.f64 #s(literal 1 binary64) (-.f64 y x))))
(*.f64 x (/.f64 (/.f64 y (-.f64 x (+.f64 y #s(literal 1 binary64)))) (*.f64 (-.f64 y x) (-.f64 y x))))
(/.f64 (*.f64 x y) (fma.f64 (-.f64 y x) (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal 3 binary64))))
(/.f64 (*.f64 x (neg.f64 y)) (*.f64 (*.f64 (+.f64 x (neg.f64 y)) (+.f64 x (neg.f64 y))) (+.f64 (+.f64 x (neg.f64 y)) #s(literal 1 binary64))))
(*.f64 x (/.f64 (neg.f64 y) (*.f64 (*.f64 (-.f64 x y) (-.f64 x y)) (+.f64 #s(literal 1 binary64) (-.f64 x y)))))
(*.f64 x (/.f64 (/.f64 (neg.f64 y) (-.f64 x (-.f64 y #s(literal 1 binary64)))) (*.f64 (-.f64 x y) (-.f64 x y))))
(*.f64 y (/.f64 x (+.f64 (pow.f64 (-.f64 y x) #s(literal 3 binary64)) (*.f64 (-.f64 y x) (-.f64 x y)))))
(*.f64 y (/.f64 x (fma.f64 (-.f64 y x) (-.f64 x y) (pow.f64 (-.f64 y x) #s(literal 3 binary64)))))
(neg.f64 (/.f64 (*.f64 (neg.f64 x) y) (*.f64 (*.f64 (+.f64 (neg.f64 x) y) (+.f64 (neg.f64 x) y)) (+.f64 (+.f64 (neg.f64 x) y) #s(literal 1 binary64)))))
(/.f64 (*.f64 x (neg.f64 y)) (neg.f64 (*.f64 (+.f64 y (neg.f64 x)) (*.f64 (+.f64 y (neg.f64 x)) (+.f64 #s(literal 1 binary64) (+.f64 y (neg.f64 x)))))))
(/.f64 (*.f64 x y) (+.f64 (*.f64 (-.f64 y x) (-.f64 y x)) (pow.f64 (-.f64 y x) #s(literal 3 binary64))))
(*.f64 y (/.f64 x (fma.f64 (-.f64 y x) (-.f64 y x) (pow.f64 (-.f64 y x) #s(literal 3 binary64)))))
(neg.f64 (/.f64 (*.f64 x (neg.f64 y)) (*.f64 (*.f64 (+.f64 x (neg.f64 y)) (+.f64 x (neg.f64 y))) (+.f64 (+.f64 x (neg.f64 y)) #s(literal 1 binary64)))))
(/.f64 (*.f64 x (neg.f64 y)) (neg.f64 (*.f64 (*.f64 (-.f64 x y) (-.f64 x y)) (+.f64 #s(literal 1 binary64) (-.f64 x y)))))
(/.f64 (/.f64 (*.f64 x y) (*.f64 (-.f64 x y) (-.f64 x y))) (-.f64 x (-.f64 y #s(literal 1 binary64))))
(*.f64 x (/.f64 y (fma.f64 (-.f64 x y) (-.f64 x y) (pow.f64 (-.f64 x y) #s(literal 3 binary64)))))
(/.f64 (*.f64 y x) (*.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 (+.f64 y x) #s(literal 1 binary64))))
(*.f64 x (/.f64 y (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 x (+.f64 y #s(literal 1 binary64))))))
(*.f64 x (/.f64 y (+.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (pow.f64 (+.f64 x y) #s(literal 3 binary64)))))
(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) #s(literal 3 binary64))))
Symmetry

(sort x y)

Compiler

Compiled 19 to 9 computations (52.6% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune3.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
65.9%
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))
Compiler

Compiled 38 to 18 computations (52.6% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
3×1-exp
2×*-commutative
2×+-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01473
12473
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))
Outputs
(/.f64 (*.f64 x y) (*.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) #s(literal 1 binary64))))

soundness1.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 19 to 9 computations (52.6% saved)

preprocess184.0ms (1%)

Remove

(sort x y)

Compiler

Compiled 194 to 94 computations (51.5% saved)

end0.0ms (0%)

Profiling

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