Bouland and Aaronson, Equation (26)

Time bar (total: 10.6s)

analyze1.0ms (0%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 20 to 13 computations (35% saved)

sample10.3s (97.2%)

Results
2.1s8256×0valid-rival
910.0ms8208×0valid-sollya
240.0ms48×0exit-sollya
Bogosity

preprocess178.0ms (1.7%)

Algorithm
1×egg-herbie
Rules
821×unsub-neg
800×fma-neg
601×sub-neg
410×fma-define
374×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038449
199421
2233413
3700413
42734413
57202413
Stop Event
1×node limit
Calls
Call 1
Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 a a))) #s(literal 1 binary64))
Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 b b) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 b (*.f64 b #s(literal 4 binary64)) #s(literal -1 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 (neg.f64 a) (neg.f64 a)) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 (*.f64 b b) #s(literal 4 binary64) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (fma.f64 b (*.f64 b #s(literal 4 binary64)) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(-.f64 (fma.f64 b (*.f64 b #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)))
(neg.f64 (-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 (neg.f64 b) (neg.f64 b))) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 (neg.f64 b) (neg.f64 b)))) #s(literal 1 binary64)))
(neg.f64 (+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 b b) #s(literal 4 binary64)) #s(literal 1 binary64))))
(+.f64 (neg.f64 (fma.f64 (*.f64 b b) #s(literal 4 binary64) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)))) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) (fma.f64 b (*.f64 b #s(literal 4 binary64)) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64))))
(-.f64 (fma.f64 b (*.f64 b #s(literal -4 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 b b) (*.f64 a a)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 a a))) #s(literal 1 binary64))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 a a) #s(literal 4 binary64)) #s(literal 1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 (*.f64 a a) #s(literal 4 binary64) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 a a (*.f64 b b)) #s(literal 2 binary64)) (fma.f64 a (*.f64 a #s(literal 4 binary64)) #s(literal -1 binary64)))
Symmetry

(abs a)

(abs b)

Compiler

Compiled 19 to 12 computations (36.8% saved)

eval0.0ms (0%)

Compiler

Compiled 2 to 2 computations (0% saved)

prune2.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
99.9%
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
Compiler

Compiled 38 to 24 computations (36.8% saved)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Rules
4×+-commutative
3×1-exp
2×unsub-neg
2×sub-neg
2×*-commutative
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01767
12867
23267
33567
43867
54167
Stop Event
1×saturated
Calls
Call 1
Inputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
Outputs
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 #s(literal 4 binary64) (*.f64 b b))) #s(literal 1 binary64))
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 (*.f64 b b) #s(literal 4 binary64))) #s(literal 1 binary64))
(+.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) #s(literal 2 binary64)) (*.f64 (*.f64 b b) #s(literal 4 binary64))) #s(literal -1 binary64))

soundness0.0ms (0%)

Stop Event
1×fuel
Compiler

Compiled 19 to 12 computations (36.8% saved)

preprocess109.0ms (1%)

Remove

(abs b)

(abs a)

Compiler

Compiled 228 to 144 computations (36.8% saved)

end0.0ms (0%)

Profiling

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