Toniolo and Linder, Equation (7)

Time bar (total: 3.3s)

analyze323.0ms (9.9%)

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
0%0%99.9%0.1%0%0%0%3
0%0%99.9%0.1%0%0%0%4
0%0%99.9%0.1%0%0%0%5
0%0%99.9%0.1%0%0%0%6
0%0%99.9%0.1%0%0%0%7
0%0%74.9%0.1%0%25%0%8
4.2%3.1%71.8%0.1%0%25%0%9
6.3%4.7%70.2%0.1%0%25%0%10
11.3%7%55.4%0.1%0%37.4%0%11
16.9%10.5%51.9%0.1%0%37.4%0%12
Compiler

Compiled 31 to 21 computations (32.3% saved)

sample2.7s (83.3%)

Results
1.2s6195×body256valid
437.0ms1119×body1024valid
408.0ms3172×body256invalid
270.0ms804×body1024invalid
226.0ms879×body512valid
115.0ms488×body512invalid
30.0ms63×body2048valid
Bogosity

preprocess224.0ms (6.8%)

Algorithm
1×egg-herbie
Rules
665×distribute-lft-in
554×distribute-rgt-in
522×*-commutative
367×associate-/l*
297×fma-neg
Problems
106×(sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l)))
93×No Errors
57×(-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0781172
12551160
26981156
323541156
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 (neg.f64 x) 1) (-.f64 (neg.f64 x) 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 (neg.f64 l) (neg.f64 l)) (*.f64 2 (*.f64 t t)))) (*.f64 (neg.f64 l) (neg.f64 l)))))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 (neg.f64 t) (neg.f64 t))))) (*.f64 l l))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 (neg.f64 x) 1) (-.f64 (neg.f64 x) 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l)))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 (neg.f64 l) (neg.f64 l)) (*.f64 2 (*.f64 t t)))) (*.f64 (neg.f64 l) (neg.f64 l))))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 (neg.f64 t) (neg.f64 t))))) (*.f64 l l)))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 l 1) (-.f64 l 1)) (+.f64 (*.f64 x x) (*.f64 2 (*.f64 t t)))) (*.f64 x x))))
(/.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 t 1) (-.f64 t 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 x x)))) (*.f64 l l))))
(/.f64 (*.f64 (sqrt.f64 2) l) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 t t) (*.f64 2 (*.f64 l l)))) (*.f64 t t))))
Outputs
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l))) t))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l)))) t)
(*.f64 t (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (neg.f64 (*.f64 l l))))))
(*.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l))) t))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l)))) t)
(*.f64 t (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (neg.f64 (*.f64 l l))))))
(*.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 (neg.f64 x) 1) (-.f64 (neg.f64 x) 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 1 (neg.f64 x)) (+.f64 (neg.f64 x) -1)) (fma.f64 l l (*.f64 2 (*.f64 t t))) (neg.f64 (*.f64 l l)))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l)) (/.f64 (-.f64 1 x) (fma.f64 -1 x -1))) (*.f64 l l))))
(*.f64 t (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l)) (/.f64 (-.f64 1 x) (-.f64 -1 x)) (neg.f64 (*.f64 l l))))))
(*.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (fma.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l)) (/.f64 (-.f64 1 x) (-.f64 -1 x)) (*.f64 l (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 (neg.f64 l) (neg.f64 l)) (*.f64 2 (*.f64 t t)))) (*.f64 (neg.f64 l) (neg.f64 l)))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l))) t))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l)))) t)
(*.f64 t (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (neg.f64 (*.f64 l l))))))
(*.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 (neg.f64 t) (neg.f64 t))))) (*.f64 l l))))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (neg.f64 t) (/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l))) (sqrt.f64 2)))
(*.f64 (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (neg.f64 (*.f64 l l))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 (neg.f64 x) 1) (-.f64 (neg.f64 x) 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 t t)))) (*.f64 l l)))))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (fma.f64 (/.f64 (+.f64 1 (neg.f64 x)) (+.f64 (neg.f64 x) -1)) (fma.f64 l l (*.f64 2 (*.f64 t t))) (neg.f64 (*.f64 l l)))))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l)) (/.f64 (-.f64 1 x) (fma.f64 -1 x -1))) (*.f64 l l))))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l)) (/.f64 (-.f64 1 x) (-.f64 -1 x)) (neg.f64 (*.f64 l l))))) (neg.f64 t))
(*.f64 t (/.f64 (neg.f64 (sqrt.f64 2)) (sqrt.f64 (fma.f64 (fma.f64 2 (*.f64 t t) (*.f64 l l)) (/.f64 (-.f64 1 x) (-.f64 -1 x)) (*.f64 l (neg.f64 l))))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 (neg.f64 l) (neg.f64 l)) (*.f64 2 (*.f64 t t)))) (*.f64 (neg.f64 l) (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l))))
(/.f64 (neg.f64 t) (/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l))) (sqrt.f64 2)))
(*.f64 (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (neg.f64 (*.f64 l l))))) (sqrt.f64 2))
(*.f64 (sqrt.f64 2) (/.f64 (neg.f64 t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 2) (neg.f64 t)) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 (neg.f64 t) (neg.f64 t))))) (*.f64 l l)))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 l l (*.f64 2 (*.f64 t t)))) (*.f64 l l))) t))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l))) (*.f64 l l)))) t)
(*.f64 t (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (neg.f64 (*.f64 l l))))))
(*.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 t t) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 l 1) (-.f64 l 1)) (+.f64 (*.f64 x x) (*.f64 2 (*.f64 t t)))) (*.f64 x x))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 1 l) (+.f64 l -1)) (fma.f64 x x (*.f64 2 (*.f64 t t))) (neg.f64 (*.f64 x x)))) t))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 1 l) (+.f64 l -1)) (fma.f64 2 (*.f64 t t) (*.f64 x x)) (*.f64 x (neg.f64 x)))) t))
(*.f64 t (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 1 l) (+.f64 l -1)) (fma.f64 2 (*.f64 t t) (*.f64 x x)) (neg.f64 (*.f64 x x))))))
(*.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (fma.f64 (/.f64 (+.f64 1 l) (+.f64 l -1)) (fma.f64 2 (*.f64 t t) (*.f64 x x)) (*.f64 x (neg.f64 x))))))
(/.f64 (*.f64 (sqrt.f64 2) x) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 t 1) (-.f64 t 1)) (+.f64 (*.f64 l l) (*.f64 2 (*.f64 x x)))) (*.f64 l l))))
(/.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (fma.f64 (/.f64 (+.f64 t 1) (+.f64 t -1)) (fma.f64 l l (*.f64 2 (*.f64 x x))) (neg.f64 (*.f64 l l)))) x))
(*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 t 1) (+.f64 t -1)) (fma.f64 2 (*.f64 x x) (*.f64 l l)) (neg.f64 (*.f64 l l))))) x)
(*.f64 x (/.f64 (sqrt.f64 2) (sqrt.f64 (fma.f64 (/.f64 (+.f64 t 1) (+.f64 t -1)) (fma.f64 2 (*.f64 x x) (*.f64 l l)) (neg.f64 (*.f64 l l))))))
(*.f64 (sqrt.f64 2) (/.f64 x (sqrt.f64 (fma.f64 (/.f64 (+.f64 t 1) (+.f64 t -1)) (fma.f64 2 (*.f64 x x) (*.f64 l l)) (*.f64 l (neg.f64 l))))))
(/.f64 (*.f64 (sqrt.f64 2) l) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (*.f64 t t) (*.f64 2 (*.f64 l l)))) (*.f64 t t))))
(/.f64 (*.f64 (sqrt.f64 2) l) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 t t (*.f64 2 (*.f64 l l))) (neg.f64 (*.f64 t t)))))
(/.f64 (*.f64 (sqrt.f64 2) l) (sqrt.f64 (-.f64 (*.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (*.f64 l l) (*.f64 t t))) (*.f64 t t))))
(/.f64 (*.f64 (sqrt.f64 2) l) (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (fma.f64 2 (*.f64 l l) (*.f64 t t))) (+.f64 x -1)) (*.f64 t t))))
(*.f64 (sqrt.f64 2) (/.f64 l (sqrt.f64 (-.f64 (/.f64 (*.f64 (+.f64 x 1) (fma.f64 2 (*.f64 l l) (*.f64 t t))) (+.f64 x -1)) (*.f64 t t)))))
Symmetry

(abs l)

(negabs t)

Compiler

Compiled 135 to 72 computations (46.7% saved)

end0.0ms (0%)

Profiling

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