Falkner and Boettcher, Equation (20:1,3)

Time bar (total: 3.2s)

analyze54.0ms (1.7%)

Memory
-14.3MiB live, 21.3MiB allocated
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%50%0.1%0%50%0%4
0%0%50%0.1%0%50%0%5
37.5%18.7%31.2%0.1%0%50%0%6
43.8%21.9%28.1%0.1%0%50%0%7
65.6%32.8%17.2%0.1%0%50%0%8
70.3%35.1%14.8%0.1%0%50%0%9
82%41%9%0.1%0%50%0%10
84.8%42.3%7.6%0.1%0%50%0%11
90.8%45.4%4.6%0.1%0%50%0%12
Compiler

Compiled 61 to 41 computations (32.8% saved)

sample3.0s (94.8%)

Memory
1.3MiB live, 943.4MiB allocated
Samples
747.0ms8 256×0valid-baseline
728.0ms8 256×0valid-rival
595.0ms8 256×0valid-sollya
Bogosity

preprocess82.0ms (2.6%)

Memory
4.0MiB live, 21.8MiB allocated
Algorithm
1×egg-herbie
Rules
991×times-frac
692×fma-define
575×associate-/r*
413×div-sub
388×distribute-lft-in
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056750
1193742
2648672
34512620
Stop Event
1×node limit
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) (neg.f64 t)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) (neg.f64 t)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 t t))) (*.f64 (*.f64 (*.f64 (PI.f64) v) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 t t)))))) (-.f64 #s(literal 1 binary64) (*.f64 t t))))
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (*.f64 (*.f64 (PI.f64) t) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 3 binary64) v) v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 5 binary64) v))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (PI.f64) t) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (*.f64 (PI.f64) (*.f64 t (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))))
(/.f64 (/.f64 (/.f64 (fma.f64 #s(literal 5 binary64) (*.f64 v v) #s(literal -1 binary64)) (*.f64 (PI.f64) t)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (fma.f64 v v #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (*.f64 (*.f64 (PI.f64) t) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 3 binary64) v) v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 5 binary64) v))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (PI.f64) t) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (*.f64 (PI.f64) (*.f64 t (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))))
(/.f64 (/.f64 (/.f64 (fma.f64 #s(literal 5 binary64) (*.f64 v v) #s(literal -1 binary64)) (*.f64 (PI.f64) t)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (fma.f64 v v #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (*.f64 (*.f64 (PI.f64) t) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 3 binary64) v) v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 5 binary64) v))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (PI.f64) t) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (*.f64 (PI.f64) (*.f64 t (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))))
(/.f64 (/.f64 (/.f64 (fma.f64 #s(literal 5 binary64) (*.f64 v v) #s(literal -1 binary64)) (*.f64 (PI.f64) t)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (fma.f64 v v #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) (neg.f64 t)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 3 binary64) v) v)))) (*.f64 (PI.f64) (neg.f64 t)))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 #s(literal 5 binary64) v))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (PI.f64) t) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (*.f64 t (*.f64 (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 (fma.f64 v (*.f64 v #s(literal -5 binary64)) #s(literal 1 binary64)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (*.f64 t (fma.f64 v v #s(literal -1 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 (neg.f64 v) (neg.f64 v)))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))))) (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 v) (neg.f64 v))))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 v v)) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 3 binary64) v) v)))) (*.f64 (PI.f64) (neg.f64 t)))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 v (*.f64 #s(literal 5 binary64) v))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (PI.f64) t) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (*.f64 t (*.f64 (*.f64 (PI.f64) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (+.f64 (*.f64 v v) #s(literal -1 binary64)))))
(/.f64 (fma.f64 v (*.f64 v #s(literal -5 binary64)) #s(literal 1 binary64)) (*.f64 (PI.f64) (*.f64 (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64))) (*.f64 t (fma.f64 v v #s(literal -1 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) (neg.f64 t)) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 v v))) (*.f64 (*.f64 (PI.f64) t) (*.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 #s(literal 3 binary64) v) v)))) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 v (*.f64 #s(literal 5 binary64) v))) (*.f64 (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 v v) #s(literal -3 binary64)) #s(literal 2 binary64)))) (*.f64 (*.f64 (PI.f64) t) (-.f64 #s(literal 1 binary64) (*.f64 v v)))))
(/.f64 (/.f64 (fma.f64 (*.f64 v v) #s(literal -5 binary64) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 v v) #s(literal -6 binary64))))) (*.f64 (PI.f64) (*.f64 t (fma.f64 v (neg.f64 v) #s(literal 1 binary64)))))
(/.f64 (/.f64 (/.f64 (fma.f64 #s(literal 5 binary64) (*.f64 v v) #s(literal -1 binary64)) (*.f64 (PI.f64) t)) (sqrt.f64 (fma.f64 (*.f64 v v) #s(literal -6 binary64) #s(literal 2 binary64)))) (fma.f64 v v #s(literal -1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 t t))) (*.f64 (*.f64 (*.f64 (PI.f64) v) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 t t)))))) (-.f64 #s(literal 1 binary64) (*.f64 t t))))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -5 binary64) (*.f64 t t))) (*.f64 (*.f64 (PI.f64) (*.f64 v (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal -3 binary64) (*.f64 t t))))))) (-.f64 #s(literal 1 binary64) (*.f64 t t))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 t t))) (*.f64 (PI.f64) (*.f64 (*.f64 v (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 (*.f64 t t) #s(literal -3 binary64)) #s(literal 2 binary64))))) (-.f64 #s(literal 1 binary64) (*.f64 t t)))))
(/.f64 (/.f64 (fma.f64 (*.f64 t t) #s(literal -5 binary64) #s(literal 1 binary64)) (sqrt.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 t t) #s(literal -6 binary64))))) (*.f64 v (*.f64 (PI.f64) (fma.f64 t (neg.f64 t) #s(literal 1 binary64)))))
(/.f64 (/.f64 (fma.f64 t (*.f64 t #s(literal -5 binary64)) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (*.f64 t t) #s(literal -6 binary64) #s(literal 2 binary64)))) (*.f64 v (*.f64 (PI.f64) (fma.f64 t (neg.f64 t) #s(literal 1 binary64)))))
Symmetry

(abs v)

(negabs t)

Compiler

Compiled 30 to 19 computations (36.7% saved)

eval0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated
Compiler

Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory
1.0MiB live, 1.0MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
99.4%
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
Compiler

Compiled 60 to 38 computations (36.7% saved)

simplify3.0ms (0.1%)

Memory
0.8MiB live, 0.8MiB allocated
Algorithm
1×egg-herbie
Rules
12×*-commutative
9×sub-neg
9×+-commutative
6×neg-sub0
6×neg-mul-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025106
151106
276106
388106
494106
Stop Event
1×saturated
Calls
Call 1
Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 3 binary64) (*.f64 v v)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 #s(literal 5 binary64) (*.f64 v v))) (*.f64 (*.f64 (*.f64 (PI.f64) t) (sqrt.f64 (*.f64 #s(literal 2 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 v v) #s(literal 3 binary64)))))) (-.f64 #s(literal 1 binary64) (*.f64 v v))))

soundness0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Stop Event
1×fuel
Compiler

Compiled 30 to 19 computations (36.7% saved)

preprocess22.0ms (0.7%)

Memory
-4.4MiB live, 27.0MiB allocated
Remove

(negabs t)

(abs v)

Compiler

Compiled 360 to 228 computations (36.7% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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