Details

Time bar (total: 1.6s)

analyze197.0ms (12.4%)

Algorithm
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
12.5%12.5%87.4%0.1%0%0%0%7
18.8%18.7%81.1%0.1%0%0%0%8
28.1%28.1%71.8%0.1%0%0%0%9
42.2%42.1%57.7%0.1%0%0%0%10
48.2%46.8%50.3%0.1%2.7%0%0%11
56.2%53.8%41.9%0.1%4.1%0%0%12
Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.1s (68.2%)

Results
996.0ms8256×body256valid
70.0ms746×body256infinite
Bogosity

preprocess106.0ms (6.7%)

Algorithm
egg-herbie
Rules
960×fma-def
408×associate-+l-
376×associate--r+
344×associate-*r*
294×associate-+r+
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
022100
139100
265100
3106100
418584
531884
667884
7172684
8260184
9333984
10342384
11342984
12342984
13343384
033
133
Stop Event
unsound
saturated
Calls
Call 1
Inputs
0
1
2
Outputs
0
1
0
2
Call 2
Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))
Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(-.f64 (*.f64 y (/.f64 x 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (*.f64 1/2 y) (*.f64 z -1/8))
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (/.f64 (*.f64 y x) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(-.f64 (*.f64 y (/.f64 x 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (*.f64 z -1/8))
(fma.f64 x (*.f64 1/2 y) (*.f64 z -1/8))
(fma.f64 x (*.f64 y 1/2) (*.f64 z -1/8))
(-.f64 (/.f64 (*.f64 z y) 2) (/.f64 x 8))
(-.f64 (/.f64 z (/.f64 2 y)) (/.f64 x 8))
(-.f64 (*.f64 (/.f64 z 2) y) (/.f64 x 8))
(fma.f64 (/.f64 z 2) y (/.f64 (neg.f64 x) 8))
(-.f64 (*.f64 z (/.f64 y 2)) (/.f64 x 8))
(fma.f64 y (/.f64 z 2) (*.f64 -1/8 x))
(fma.f64 y (/.f64 z 2) (*.f64 x -1/8))
(fma.f64 x -1/8 (/.f64 z (/.f64 2 y)))
(-.f64 (/.f64 (*.f64 x z) 2) (/.f64 y 8))
(-.f64 (*.f64 (/.f64 x 2) z) (/.f64 y 8))
(-.f64 (*.f64 z (/.f64 x 2)) (/.f64 y 8))
(fma.f64 z (/.f64 x 2) (*.f64 -1/8 y))
(fma.f64 -1/8 y (*.f64 z (/.f64 x 2)))
(fma.f64 x (/.f64 z 2) (*.f64 y -1/8))
(fma.f64 x (*.f64 1/2 z) (*.f64 y -1/8))
(fma.f64 x (*.f64 z 1/2) (*.f64 y -1/8))
Symmetry

(sort x y)

Compiler

Compiled 15 to 12 computations (20% saved)

simplify46.0ms (2.9%)

Algorithm
egg-herbie
Rules
384×fma-def
182×associate-*r*
134×associate--r+
130×*-commutative
106×associate-*r/
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01125
11725
22825
34325
47221
512421
624521
752321
886821
9116121
10126821
11129221
12129521
Stop Event
saturated
Counts
1 → 9
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
(-.f64 (/.f64 x (/.f64 2 y)) (/.f64 z 8))
(-.f64 (*.f64 (/.f64 x 2) y) (/.f64 z 8))
(-.f64 (*.f64 y (/.f64 x 2)) (/.f64 z 8))
(-.f64 (*.f64 x (/.f64 y 2)) (/.f64 z 8))
(fma.f64 x (/.f64 y 2) (*.f64 -1/8 z))
(fma.f64 x (/.f64 y 2) (/.f64 z -8))
(fma.f64 x (*.f64 1/2 y) (/.f64 z -8))
(fma.f64 x (*.f64 y 1/2) (/.f64 z -8))

eval2.0ms (0.1%)

Compiler

Compiled 80 to 53 computations (33.8% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New819
Fresh011
Picked000
Done000
Total8210
Error
0b
Counts
10 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
0b
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Compiler

Compiled 12 to 9 computations (25% saved)

localize10.0ms (0.6%)

Local error

Found 1 expressions with local error:

NewErrorProgram
0.0b
(/.f64 (*.f64 x y) 2)
Compiler

Compiled 28 to 15 computations (46.4% saved)

series5.0ms (0.3%)

Counts
1 → 24
Calls

6 calls:

TimeVariablePointExpression
2.0ms
y
@0
(/.f64 (*.f64 x y) 2)
1.0ms
x
@0
(/.f64 (*.f64 x y) 2)
1.0ms
x
@inf
(/.f64 (*.f64 x y) 2)
0.0ms
y
@inf
(/.f64 (*.f64 x y) 2)
0.0ms
y
@-inf
(/.f64 (*.f64 x y) 2)

rewrite54.0ms (3.4%)

Algorithm
batch-egg-rewrite
Rules
1460×add-sqr-sqrt
1434×*-un-lft-identity
1344×add-cube-cbrt
1328×add-cbrt-cube
1314×add-exp-log
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
114913
2181013
Stop Event
node limit
Counts
1 → 28
Calls
Call 1
Inputs
(/.f64 (*.f64 x y) 2)
Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (*.f64 y 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 y 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (/.f64 2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x y) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 y 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (*.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (*.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) (sqrt.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2) (cbrt.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (neg.f64 y)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x 2) y)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 y 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (*.f64 x y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 x y) -2))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 x y) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 y 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 y 1/2))))))))

simplify51.0ms (3.2%)

Algorithm
egg-herbie
Rules
1356×associate-+r+
1138×associate-+l+
1070×associate-*r/
930×associate-/l*
750×distribute-lft-in
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
073692
1160692
2713686
32156686
Stop Event
node limit
Counts
52 → 31
Calls
Call 1
Inputs
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(-.f64 (+.f64 1 (*.f64 x (*.f64 y 1/2))) 1)
(*.f64 x (*.f64 y 1/2))
(*.f64 x (/.f64 1 (/.f64 2 y)))
(*.f64 y (*.f64 x 1/2))
(*.f64 (*.f64 x y) 1/2)
(*.f64 (*.f64 x (*.f64 y 1/2)) 1)
(*.f64 1 (*.f64 x (*.f64 y 1/2)))
(*.f64 (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (*.f64 x y)) 1/2))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) (sqrt.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))
(*.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2) (cbrt.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 1/2 (*.f64 x y))
(*.f64 (*.f64 x (neg.f64 y)) -1/2)
(*.f64 (/.f64 x 2) y)
(pow.f64 (*.f64 x (*.f64 y 1/2)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 3)
(pow.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3) 1/3)
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(neg.f64 (/.f64 (*.f64 x y) -2))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 x y) 2) 1/4))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2))))
(exp.f64 (log.f64 (*.f64 x (*.f64 y 1/2))))
(exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 y 1/2))) 1))
(log1p.f64 (expm1.f64 (*.f64 x (*.f64 y 1/2))))
Outputs
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 y x))
(-.f64 (+.f64 1 (*.f64 x (*.f64 y 1/2))) 1)
(*.f64 1/2 (*.f64 y x))
(*.f64 x (*.f64 y 1/2))
(*.f64 1/2 (*.f64 y x))
(*.f64 x (/.f64 1 (/.f64 2 y)))
(*.f64 1/2 (*.f64 y x))
(*.f64 y (*.f64 x 1/2))
(*.f64 1/2 (*.f64 y x))
(*.f64 (*.f64 x y) 1/2)
(*.f64 1/2 (*.f64 y x))
(*.f64 (*.f64 x (*.f64 y 1/2)) 1)
(*.f64 1/2 (*.f64 y x))
(*.f64 1 (*.f64 x (*.f64 y 1/2)))
(*.f64 1/2 (*.f64 y x))
(*.f64 (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (*.f64 x y)) 1/2))
(*.f64 1/2 (*.f64 y x))
(*.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) (sqrt.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 1/2 (*.f64 y x))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 1/2))
(*.f64 1/2 (*.f64 y x))
(*.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2))
(*.f64 1/2 (*.f64 y x))
(*.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 2) (cbrt.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 1/2 (*.f64 y x))
(*.f64 1/2 (*.f64 x y))
(*.f64 1/2 (*.f64 y x))
(*.f64 (*.f64 x (neg.f64 y)) -1/2)
(*.f64 1/2 (*.f64 y x))
(*.f64 (/.f64 x 2) y)
(*.f64 1/2 (*.f64 y x))
(pow.f64 (*.f64 x (*.f64 y 1/2)) 1)
(*.f64 1/2 (*.f64 y x))
(pow.f64 (sqrt.f64 (*.f64 x (*.f64 y 1/2))) 2)
(*.f64 1/2 (*.f64 y x))
(pow.f64 (cbrt.f64 (*.f64 x (*.f64 y 1/2))) 3)
(*.f64 1/2 (*.f64 y x))
(pow.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3) 1/3)
(*.f64 1/2 (*.f64 y x))
(pow.f64 (/.f64 2 (*.f64 x y)) -1)
(*.f64 1/2 (*.f64 y x))
(neg.f64 (/.f64 (*.f64 x y) -2))
(*.f64 1/2 (*.f64 y x))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 x y) 2) 1/4))
(sqrt.f64 (*.f64 (pow.f64 (*.f64 y x) 2) 1/4))
(fabs.f64 (*.f64 1/2 (*.f64 y x)))
(log.f64 (sqrt.f64 (pow.f64 (exp.f64 y) x)))
(cbrt.f64 (pow.f64 (*.f64 x (*.f64 y 1/2)) 3))
(*.f64 1/2 (*.f64 y x))
(expm1.f64 (log1p.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 1/2 (*.f64 y x))
(exp.f64 (log.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 1/2 (*.f64 y x))
(exp.f64 (*.f64 (log.f64 (*.f64 x (*.f64 y 1/2))) 1))
(*.f64 1/2 (*.f64 y x))
(log1p.f64 (expm1.f64 (*.f64 x (*.f64 y 1/2))))
(*.f64 1/2 (*.f64 y x))

eval7.0ms (0.4%)

Compiler

Compiled 371 to 256 computations (31% saved)

prune5.0ms (0.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New31031
Fresh000
Picked011
Done000
Total31132
Error
0b
Counts
32 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
0b
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Compiler

Compiled 24 to 18 computations (25% saved)

simplify4.0ms (0.3%)

Algorithm
egg-herbie
Rules
sub-neg
+-commutative
*-commutative
neg-mul-1
neg-sub0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01125
11525
22225
32625
42925
53025
Stop Event
done
saturated
Calls
Call 1
Inputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Outputs
(-.f64 (/.f64 (*.f64 x y) 2) (/.f64 z 8))
Compiler

Compiled 12 to 9 computations (25% saved)

soundness0.0ms (0%)

end16.0ms (1%)

Remove

(sort x y)

Compiler

Compiled 36 to 27 computations (25% saved)

Profiling

Loading profile data...