Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, A

Time bar (total: 1.9s)

analyze94.0ms (5%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.8%0.2%0%0%0%0
0%0%99.8%0.2%0%0%0%1
0%0%99.8%0.2%0%0%0%2
0%0%99.8%0.2%0%0%0%3
50%49.9%49.9%0.2%0%0%0%4
50%49.9%49.9%0.2%0%0%0%5
50%49.9%49.9%0.2%0%0%0%6
50%49.9%49.9%0.2%0%0%0%7
66.7%49.9%25%0.2%0%25%0%8
66.7%49.9%25%0.2%0%25%0%9
66.7%49.9%25%0.2%0%25%0%10
66.7%49.9%25%0.2%0%25%0%11
80%49.9%12.5%0.2%0%37.4%0%12
Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.5s (79%)

Results
663.0ms4575×body256infinite
547.0ms3681×body256valid
277.0ms1993×body256invalid
Bogosity

preprocess304.0ms (16%)

Algorithm
1×egg-herbie
Rules
478×distribute-lft-in
410×fma-def
405×distribute-rgt-in
378×associate--r+
348×*-commutative
Problems
256×No Errors
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0811056
12071024
25061016
314981008
444171008
Stop Event
1×node limit
Calls
Call 1
Inputs
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 (neg.f64 x) 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) (neg.f64 y)) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 (neg.f64 z) 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) 2)))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 (neg.f64 x) 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2))))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) (neg.f64 y)) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2))))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 (neg.f64 z) 2))) (exp.f64 (/.f64 (*.f64 t t) 2))))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) 2))))
(*.f64 (*.f64 (-.f64 (*.f64 y 1/2) x) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 z 1/2) y) (sqrt.f64 (*.f64 x 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 t 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 x x) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) z) (sqrt.f64 (*.f64 y 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) t) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 y y) 2)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 t 2))) (exp.f64 (/.f64 (*.f64 z z) 2)))
Outputs
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (exp.f64 (*.f64 t t)))))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (neg.f64 (fma.f64 x -1/2 y)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (exp.f64 (*.f64 t t)))))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (neg.f64 (fma.f64 x -1/2 y)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
(*.f64 (*.f64 (-.f64 (*.f64 (neg.f64 x) 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (sqrt.f64 (*.f64 z 2)) (fma.f64 (neg.f64 x) 1/2 (neg.f64 y))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (-.f64 (*.f64 x -1/2) y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (neg.f64 (fma.f64 x 1/2 y))))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 x -1/2) y)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) (neg.f64 y)) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 x 1/2) (neg.f64 y))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (fma.f64 x 1/2 y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (sqrt.f64 (*.f64 z 2)) (fma.f64 x 1/2 y)))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (sqrt.f64 (*.f64 z 2)) (fma.f64 x 1/2 y)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 (neg.f64 z) 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (neg.f64 (*.f64 z 2))) (sqrt.f64 (exp.f64 (*.f64 t t)))))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (sqrt.f64 (*.f64 z -2))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z -2))))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (neg.f64 (fma.f64 x -1/2 y)) (sqrt.f64 (*.f64 z -2))))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) 2)))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (exp.f64 (*.f64 t t)))))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (neg.f64 (fma.f64 x -1/2 y)) (pow.f64 (sqrt.f64 (exp.f64 t)) t)))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 (neg.f64 x) 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2))))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 x 1/2) (neg.f64 y))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (fma.f64 x 1/2 y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (sqrt.f64 (*.f64 z 2)) (fma.f64 x 1/2 y)))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (sqrt.f64 (*.f64 z 2)) (fma.f64 x 1/2 y)))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) (neg.f64 y)) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2))))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (sqrt.f64 (*.f64 z 2)) (fma.f64 (neg.f64 x) 1/2 (neg.f64 y))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (-.f64 (*.f64 x -1/2) y) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (neg.f64 (fma.f64 x 1/2 y))))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 x -1/2) y)))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 (neg.f64 z) 2))) (exp.f64 (/.f64 (*.f64 t t) 2))))
(*.f64 (neg.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (neg.f64 (*.f64 z 2))))) (sqrt.f64 (exp.f64 (*.f64 t t))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (-.f64 (*.f64 x 1/2) y) (neg.f64 (sqrt.f64 (*.f64 z -2)))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (sqrt.f64 (*.f64 z -2)) (+.f64 y (*.f64 x -1/2))))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (sqrt.f64 (*.f64 z -2)) (fma.f64 x -1/2 y)))
(neg.f64 (*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 (neg.f64 t) (neg.f64 t)) 2))))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 z 2))) (neg.f64 (sqrt.f64 (exp.f64 (*.f64 t t)))))
(*.f64 (-.f64 (*.f64 x 1/2) y) (neg.f64 (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (pow.f64 (exp.f64 t) t)))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (+.f64 y (*.f64 x -1/2)) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (fma.f64 x -1/2 y)))
(*.f64 (*.f64 (-.f64 (*.f64 y 1/2) x) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 1/2 y) x)))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (-.f64 (*.f64 1/2 y) x) (sqrt.f64 (pow.f64 (exp.f64 t) t))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 1/2 y) x)))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (-.f64 (*.f64 1/2 y) x)))
(*.f64 (*.f64 (-.f64 (*.f64 z 1/2) y) (sqrt.f64 (*.f64 x 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (-.f64 (*.f64 1/2 z) y) (sqrt.f64 (*.f64 x 2))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (-.f64 (*.f64 1/2 z) y) (sqrt.f64 (*.f64 x 2))))
(*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (*.f64 (-.f64 (*.f64 1/2 z) y) (sqrt.f64 (*.f64 x 2))))
(*.f64 (*.f64 (-.f64 (*.f64 t 1/2) y) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 x x) 2)))
(*.f64 (-.f64 (*.f64 1/2 t) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (exp.f64 (*.f64 x x)))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (-.f64 (*.f64 1/2 t) y) (sqrt.f64 (exp.f64 (*.f64 x x)))))
(*.f64 (-.f64 (*.f64 1/2 t) y) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (pow.f64 (exp.f64 x) x))))
(*.f64 (sqrt.f64 (*.f64 z 2)) (*.f64 (-.f64 (*.f64 1/2 t) y) (pow.f64 (sqrt.f64 (exp.f64 x)) x)))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) z) (sqrt.f64 (*.f64 y 2))) (exp.f64 (/.f64 (*.f64 t t) 2)))
(*.f64 (sqrt.f64 (exp.f64 (*.f64 t t))) (*.f64 (-.f64 (*.f64 x 1/2) z) (sqrt.f64 (*.f64 y 2))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (-.f64 (*.f64 x 1/2) z) (sqrt.f64 (*.f64 y 2))))
(*.f64 (sqrt.f64 (pow.f64 (exp.f64 t) t)) (*.f64 (fma.f64 x 1/2 (neg.f64 z)) (sqrt.f64 (*.f64 y 2))))
(*.f64 (fma.f64 x 1/2 (neg.f64 z)) (*.f64 (pow.f64 (sqrt.f64 (exp.f64 t)) t) (sqrt.f64 (*.f64 y 2))))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) t) (sqrt.f64 (*.f64 z 2))) (exp.f64 (/.f64 (*.f64 y y) 2)))
(*.f64 (-.f64 (*.f64 x 1/2) t) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (exp.f64 (*.f64 y y)))))
(*.f64 (-.f64 (*.f64 x 1/2) t) (*.f64 (sqrt.f64 (*.f64 z 2)) (sqrt.f64 (pow.f64 (exp.f64 y) y))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 x 1/2) t)) (sqrt.f64 (pow.f64 (exp.f64 y) y)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 z 2)) (-.f64 (*.f64 x 1/2) t)) (sqrt.f64 (exp.f64 (*.f64 y y))))
(*.f64 (*.f64 (-.f64 (*.f64 x 1/2) y) (sqrt.f64 (*.f64 t 2))) (exp.f64 (/.f64 (*.f64 z z) 2)))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 2 t)) (sqrt.f64 (exp.f64 (*.f64 z z)))))
(*.f64 (-.f64 (*.f64 x 1/2) y) (*.f64 (sqrt.f64 (*.f64 2 t)) (sqrt.f64 (pow.f64 (exp.f64 z) z))))
(*.f64 (neg.f64 (fma.f64 x -1/2 y)) (*.f64 (sqrt.f64 (*.f64 2 t)) (pow.f64 (sqrt.f64 (exp.f64 z)) z)))
Symmetry

(abs t)

Compiler

Compiled 67 to 41 computations (38.8% saved)

end0.0ms (0%)

Profiling

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