Details

Time bar (total: 13.7s)

analyze108.0ms (0.8%)

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%50%0.1%0%50%0%2
0%0%50%0.1%0%50%0%3
0%0%50%0.1%0%50%0%4
25%12.5%37.5%0.1%0%50%0%5
26.7%12.5%34.3%0.1%0%53.1%0%6
37%15.6%26.5%0.1%1.6%54.6%1.6%7
40.8%15.6%22.6%0.1%2.3%57%2.3%8
49.4%17.2%17.6%0.1%3.5%58.1%3.5%9
53.3%17.2%15%0.1%4.1%59.5%4.1%10
59.5%18%12.2%0.1%4.8%60.2%4.8%11
62.5%18%10.8%0.1%5.1%60.9%5.1%12
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.1s (22.4%)

Results
1.5s8256×body256valid
953.0ms1373×body1024invalid
203.0ms667×body512invalid
194.0ms1558×body256invalid
88.0ms515×body256infinite
60.0ms258×body256unsamplable
Bogosity

preprocess95.0ms (0.7%)

Algorithm
egg-herbie
Rules
1178×rational_best_oopsla_all_46_json_45_simplify-49
1140×rational_best_oopsla_all_46_json_45_simplify-23
942×rational_best_oopsla_all_46_json_45_simplify-10
908×rational_best_oopsla_all_46_json_45_simplify-7
904×rational_best_oopsla_all_46_json_45_simplify-30
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02498
14898
215198
356698
4273298
5645598
022
Stop Event
saturated
node limit
Calls
Call 1
Inputs
0
1
Outputs
0
1
Call 2
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) k) (/.f64 (-.f64 1 n) 2)))
(*.f64 (/.f64 1 (sqrt.f64 n)) (pow.f64 (*.f64 k (*.f64 2 (PI.f64))) (/.f64 (-.f64 1 n) 2)))
Compiler

Compiled 20 to 17 computations (15% saved)

simplify95.0ms (0.7%)

Algorithm
egg-herbie
Rules
1534×rational_best_oopsla_all_46_json_45_simplify-89
1242×rational_best_oopsla_all_46_json_45_simplify-74
1000×rational_best_oopsla_all_46_json_45_simplify-24
884×rational_best_oopsla_all_46_json_45_simplify-23
648×rational_best_oopsla_all_46_json_45_simplify-49
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01749
13249
29249
333749
4162249
5602449
Stop Event
node limit
Counts
1 → 3
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (/.f64 (-.f64 1 k) 2)))

eval1.0ms (0%)

Compiler

Compiled 50 to 37 computations (26% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New213
Fresh011
Picked000
Done000
Total224
Error
0.5b
Counts
4 → 1
Alt Table
Click to see full alt table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 18 to 15 computations (16.7% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)
0.3b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
Compiler

Compiled 56 to 38 computations (32.1% saved)

series57.0ms (0.4%)

Counts
4 → 48
Calls

18 calls:

TimeVariablePointExpression
24.0ms
n
@0
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
19.0ms
n
@-inf
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
7.0ms
n
@inf
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
2.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
1.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))

rewrite104.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
954×rational_best_oopsla_all_46_json_45_simplify-35
674×rational_best_oopsla_all_46_json_45_simplify-89
662×rational_best_oopsla_all_46_json_45_simplify-23
602×rational_best_oopsla_all_46_json-2
602×rational_best_oopsla_all_46_json-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
017108
198108
2288108
31284108
45914108
Stop Event
node limit
Counts
4 → 120
Calls
Call 1
Inputs
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2))
(*.f64 (*.f64 2 (PI.f64)) n)
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(/.f64 1 (sqrt.f64 k))
Outputs
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simplify177.0ms (1.3%)

Algorithm
egg-herbie
Rules
1418×rational_best_oopsla_all_46_json_45_simplify-72
1184×rational_best_oopsla_all_46_json_45_simplify-7
966×rational_best_oopsla_all_46_json_45_simplify-89
800×rational_best_oopsla_all_46_json_45_simplify-24
738×rational_best_oopsla_all_46_json_45_simplify-74
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02967414
110507368
247457336
Stop Event
node limit
Counts
168 → 178
Calls
Call 1
Inputs
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
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(+.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(+.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(+.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
(+.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(+.f64 0 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 0 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0)
(-.f64 0 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(-.f64 0 (*.f64 1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(-.f64 0 (*.f64 -1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(-.f64 0 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 0 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(neg.f64 (*.f64 -1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) -1)
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (/.f64 1 (sqrt.f64 k))))
(*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))
Outputs
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))
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(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(-.f64 0 (*.f64 -1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(-.f64 0 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 0 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (neg.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(neg.f64 (*.f64 1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(neg.f64 (*.f64 -1 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(neg.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(neg.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(neg.f64 (*.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(+.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(+.f64 0 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(-.f64 (/.f64 1 (sqrt.f64 k)) 0)
(/.f64 1 (sqrt.f64 k))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 1 (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) 1)
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) -1)
(/.f64 1 (sqrt.f64 k))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 1 (sqrt.f64 k))
(*.f64 -1 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(*.f64 (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))
(*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 1 (sqrt.f64 k))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))
(/.f64 1 (sqrt.f64 k))

eval75.0ms (0.5%)

Compiler

Compiled 5656 to 3243 computations (42.7% saved)

prune34.0ms (0.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1708178
Fresh000
Picked011
Done000
Total1709179
Error
0.3b
Counts
179 → 9
Alt Table
Click to see full alt table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
22.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
21.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))))
21.9b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))))
21.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
22.2b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
3.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
3.7b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
Compiler

Compiled 606 to 439 computations (27.6% saved)

localize48.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
0.3b
(*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2)))
0.3b
(pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))
Compiler

Compiled 112 to 78 computations (30.4% saved)

series3.0ms (0%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
0.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
0.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
0.0ms
k
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
0.0ms
k
@0
(pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))
0.0ms
n
@0
(pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))

rewrite84.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
1154×rational_best_oopsla_all_46_json_45_simplify-23
1138×rational_best_oopsla_all_46_json_45_simplify-13
1120×rational_best_oopsla_all_46_json_45_simplify-37
1016×rational_best_oopsla_all_46_json-2
1016×rational_best_oopsla_all_46_json-1
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
023193
1144193
2466163
32421145
Stop Event
node limit
Counts
3 → 133
Calls
Call 1
Inputs
(pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2))
(*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
Outputs
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simplify155.0ms (1.1%)

Algorithm
egg-herbie
Rules
1338×rational_best_oopsla_all_46_json_45_simplify-49
1124×rational_best_oopsla_all_46_json_45_simplify-37
1000×rational_best_oopsla_all_46_json_45_simplify-89
920×rational_best_oopsla_all_46_json_45_simplify-7
880×rational_best_oopsla_all_46_json_45_simplify-24
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
035111315
1126011229
2468611229
Stop Event
node limit
Counts
181 → 234
Calls
Call 1
Inputs
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
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(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(-.f64 0 (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))
(-.f64 0 (*.f64 1 (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))
(-.f64 0 (*.f64 -1 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))
(-.f64 0 (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(-.f64 (*.f64 0 (neg.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (neg.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) 0)
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))) (*.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) 0))
(-.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))) (*.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) 0))
(-.f64 (*.f64 0 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))))
Outputs
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
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(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))))
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (pow.f64 (*.f64 n (*.f64 (*.f64 2 (PI.f64)) (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 (PI.f64) (PI.f64)) (*.f64 2 (*.f64 n (PI.f64)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 n (PI.f64))
0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
0.5b
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
Compiler

Compiled 41 to 21 computations (48.8% saved)

series6.0ms (0%)

Counts
3 → 0
Calls

12 calls:

TimeVariablePointExpression
1.0ms
n
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
1.0ms
n
@0
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))

rewrite118.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
944×rational_best_oopsla_all_46_json_45_simplify-89
788×rational_best_oopsla_all_46_json_45_simplify-23
754×rational_best_oopsla_all_46_json_45_simplify-37
746×rational_best_oopsla_all_46_json_45_simplify-87
746×rational_best_oopsla_all_46_json_45_simplify-13
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01671
19871
232871
3159771
4736071
Stop Event
node limit
Counts
3 → 134
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 n (PI.f64))
Outputs
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simplify145.0ms (1.1%)

Algorithm
egg-herbie
Rules
1730×rational_best_oopsla_all_46_json_45_simplify-10
896×rational_best_oopsla_all_46_json_45_simplify-72
870×rational_best_oopsla_all_46_json_45_simplify-23
720×rational_best_oopsla_all_46_json_45_simplify-30
664×rational_best_oopsla_all_46_json_45_simplify-77
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02605426
18595426
230095388
377485388
Stop Event
node limit
Counts
134 → 158
Calls
Call 1
Inputs
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(neg.f64 (*.f64 (/.f64 n n) (*.f64 n (neg.f64 (PI.f64)))))
(neg.f64 (*.f64 -1 (*.f64 n (PI.f64))))
(neg.f64 (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) n))
Outputs
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 0)
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 0 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 0)
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(-.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(-.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2)))))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 n (PI.f64))))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (neg.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (sqrt.f64 2)))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) 1)
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
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(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2))) (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))) -1)
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2)))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
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(neg.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 (*.f64 n (PI.f64))))))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (neg.f64 (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (sqrt.f64 2)))
(neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (neg.f64 (sqrt.f64 2))))
(*.f64 1 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0)
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(+.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) n)) 0))
(*.f64 n (PI.f64))
(+.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) 0))
(*.f64 n (PI.f64))
(+.f64 (*.f64 n (PI.f64)) (*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) 0))
(*.f64 n (PI.f64))
(+.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) 0))
(*.f64 n (PI.f64))
(+.f64 0 (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(+.f64 (*.f64 0 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) n))) (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(+.f64 (*.f64 0 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (*.f64 n (PI.f64)))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) 0)
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) 0))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (PI.f64)) 0))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 n (/.f64 (PI.f64) n)) 0))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) 0))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) 0))
(*.f64 n (PI.f64))
(-.f64 (*.f64 n (PI.f64)) (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) 0))
(*.f64 n (PI.f64))
(-.f64 0 (*.f64 n (neg.f64 (PI.f64))))
(*.f64 n (PI.f64))
(-.f64 0 (*.f64 1 (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 n (PI.f64))
(-.f64 0 (*.f64 (/.f64 n n) (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 n (PI.f64))
(-.f64 0 (*.f64 -1 (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) n))
(*.f64 n (PI.f64))
(-.f64 (*.f64 0 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))) (*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (neg.f64 (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (PI.f64)) 1)
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) (/.f64 n n))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (PI.f64) (PI.f64)))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (/.f64 n n) (/.f64 n n)))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (PI.f64) (/.f64 n n)) (*.f64 (PI.f64) (/.f64 n n))))
(*.f64 n (PI.f64))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64)))))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64)))))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 n (/.f64 (PI.f64) n)) (*.f64 n (/.f64 (PI.f64) n))))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n))) (*.f64 (/.f64 n n) (*.f64 (PI.f64) (/.f64 n n)))))
(/.f64 (*.f64 n (PI.f64)) (/.f64 (*.f64 (PI.f64) (*.f64 (/.f64 n n) (/.f64 n n))) (*.f64 (PI.f64) (*.f64 (/.f64 n n) (/.f64 n n)))))
(neg.f64 (*.f64 n (neg.f64 (PI.f64))))
(*.f64 n (PI.f64))
(neg.f64 (*.f64 1 (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 n (PI.f64))
(neg.f64 (*.f64 (/.f64 n n) (*.f64 n (neg.f64 (PI.f64)))))
(*.f64 n (PI.f64))
(neg.f64 (*.f64 -1 (*.f64 n (PI.f64))))
(*.f64 n (PI.f64))
(neg.f64 (*.f64 (neg.f64 (*.f64 (PI.f64) (/.f64 n n))) n))
(*.f64 n (PI.f64))

localize102.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
0.4b
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
1.0b
(log.f64 (*.f64 2 (PI.f64)))
3.3b
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
Compiler

Compiled 85 to 60 computations (29.4% saved)

series169.0ms (1.2%)

Counts
4 → 48
Calls

15 calls:

TimeVariablePointExpression
86.0ms
n
@-inf
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
60.0ms
n
@inf
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
16.0ms
n
@0
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
2.0ms
k
@0
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
1.0ms
k
@-inf
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))

rewrite80.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
968×rational_best_oopsla_all_46_json_45_simplify-13
968×rational_best_oopsla_all_46_json_45_simplify-37
944×rational_best_oopsla_all_46_json_45_simplify-89
828×rational_best_oopsla_all_46_json-2
828×rational_best_oopsla_all_46_json-1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021142
1130142
2393142
31781142
Stop Event
node limit
Counts
4 → 114
Calls
Call 1
Inputs
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(log.f64 (*.f64 2 (PI.f64)))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
Outputs
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simplify417.0ms (3.1%)

Algorithm
egg-herbie
Rules
1016×rational_best_oopsla_all_46_json_45_simplify-72
908×rational_best_oopsla_all_46_json_45_simplify-89
760×rational_best_oopsla_all_46_json_45_simplify-24
722×rational_best_oopsla_all_46_json_45_simplify-74
564×rational_best_oopsla_all_46_json_45_simplify-82
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02778294
110328238
241018230
Stop Event
node limit
Counts
162 → 165
Calls
Call 1
Inputs
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(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k)))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k)))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))))))
Outputs
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 -1) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 n))))))))
(exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (*.f64 k (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 -1/2 (*.f64 k (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))) (*.f64 -1/2 (*.f64 k (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2))))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2))))))
(+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3)))) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))) (*.f64 -1/2 (*.f64 k (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))))
(+.f64 (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))))) (*.f64 -1/48 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 3) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3)))))
(+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (+.f64 (*.f64 -1/2 (*.f64 k (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (+.f64 (*.f64 -1/48 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 3) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3)))) (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))))))
(+.f64 (*.f64 1/8 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 2) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 2)))) (+.f64 (*.f64 k (*.f64 -1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))))))) (+.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 -1/48 (*.f64 (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))) (*.f64 (pow.f64 k 3) (pow.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) 3)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (+.f64 1 (*.f64 -1 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n))
(+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n))))
(+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n))))
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(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (/.f64 1 k)))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))))))
(/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (/.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (sqrt.f64 (/.f64 1 k))) (/.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))) (*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (+.f64 1/2 (*.f64 k -1/2)))))

localize56.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 n (*.f64 2 (PI.f64)))
0.5b
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
0.5b
(*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
4.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
Compiler

Compiled 145 to 86 computations (40.7% saved)

series12.0ms (0.1%)

Counts
3 → 24
Calls

12 calls:

TimeVariablePointExpression
2.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
2.0ms
k
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
2.0ms
n
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
2.0ms
n
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
1.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))

rewrite70.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
1836×rational_best_oopsla_all_46_json-2
1836×rational_best_oopsla_all_46_json-1
1836×rational_best_oopsla_all_46_json-4
1836×rational_best_oopsla_all_46_json-3
924×rational_best_oopsla_all_46_json_45_simplify-7
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
025147
1175129
2693129
33969129
Stop Event
node limit
Counts
3 → 42
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
(*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))
(*.f64 n (*.f64 2 (PI.f64)))
Outputs
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(*.f64 2 (PI.f64))))))))))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 -2 (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 0 (*.f64 -2 (PI.f64))) (*.f64 (*.f64 -2 (PI.f64)) n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 n n))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 2 (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (PI.f64) (PI.f64)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))

simplify102.0ms (0.7%)

Algorithm
egg-herbie
Rules
1024×rational_best_oopsla_all_46_json_45_simplify-10
996×rational_best_oopsla_all_46_json_45_simplify-30
954×rational_best_oopsla_all_46_json_45_simplify-77
836×rational_best_oopsla_all_46_json_45_simplify-13
714×rational_best_oopsla_all_46_json_45_simplify-35
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01322922
14612906
220302906
350432906
Stop Event
node limit
Counts
66 → 61
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) 0)
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))))
(+.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(-.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) 0)
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(-.f64 (*.f64 0 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) 1)
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))))))
(+.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0)
(+.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
(+.f64 0 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(+.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(-.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 0)
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(-.f64 (*.f64 0 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (neg.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 2)))
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) 1)
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
(+.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)
(+.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))
(+.f64 0 (*.f64 n (*.f64 2 (PI.f64))))
(+.f64 (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (*.f64 2 (PI.f64))))
(-.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)
(-.f64 0 (*.f64 -2 (*.f64 n (PI.f64))))
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (*.f64 2 (PI.f64))))
(-.f64 (*.f64 0 (*.f64 -2 (PI.f64))) (*.f64 (*.f64 -2 (PI.f64)) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) 1)
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 n n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 2 (PI.f64))))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (PI.f64) (PI.f64)))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64)))))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))
(neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))
Outputs
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 (sqrt.f64 2) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 (sqrt.f64 2) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))
(*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))
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(+.f64 (*.f64 0 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))) (*.f64 n (*.f64 2 (PI.f64))))
(*.f64 2 (*.f64 (PI.f64) n))
(-.f64 (*.f64 n (*.f64 2 (PI.f64))) 0)
(*.f64 2 (*.f64 (PI.f64) n))
(-.f64 0 (*.f64 -2 (*.f64 n (PI.f64))))
(neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))
(*.f64 (*.f64 (PI.f64) -2) (neg.f64 n))
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (*.f64 2 (PI.f64))))
(*.f64 2 (*.f64 (PI.f64) n))
(-.f64 (*.f64 0 (*.f64 -2 (PI.f64))) (*.f64 (*.f64 -2 (PI.f64)) n))
(neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))
(*.f64 (*.f64 (PI.f64) -2) (neg.f64 n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) 1)
(*.f64 2 (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 n n))
(*.f64 2 (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 2 (PI.f64))))
(*.f64 2 (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (PI.f64) (PI.f64)))
(*.f64 2 (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (PI.f64)) (*.f64 n (PI.f64))))
(*.f64 2 (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 n (*.f64 2 (PI.f64)))))
(*.f64 2 (*.f64 (PI.f64) n))
(/.f64 (*.f64 n (*.f64 2 (PI.f64))) (/.f64 (*.f64 2 (*.f64 (PI.f64) (/.f64 n n))) (*.f64 2 (*.f64 (PI.f64) (/.f64 n n)))))
(*.f64 2 (*.f64 (PI.f64) n))
(neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))
(neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))
(*.f64 (*.f64 (PI.f64) -2) (neg.f64 n))

localize175.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))))
1.5b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))
2.1b
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))
12.0b
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))
Compiler

Compiled 504 to 310 computations (38.5% saved)

series54.0ms (0.4%)

Counts
4 → 27
Calls

24 calls:

TimeVariablePointExpression
11.0ms
k
@0
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))
7.0ms
k
@0
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))
4.0ms
n
@inf
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))
4.0ms
n
@-inf
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))
4.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))))

rewrite117.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
894×rational_best_oopsla_all_46_json_45_simplify-89
826×rational_best_oopsla_all_46_json_45_simplify-35
802×rational_best_oopsla_all_46_json_45_simplify-74
744×rational_best_oopsla_all_46_json_45_simplify-37
672×rational_best_oopsla_all_46_json-2
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
041532
1295532
21175514
35905514
Stop Event
node limit
Counts
4 → 66
Calls
Call 1
Inputs
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))))
Outputs
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simplify204.0ms (1.5%)

Algorithm
egg-herbie
Rules
1292×rational_best_oopsla_all_46_json_45_simplify-37
846×rational_best_oopsla_all_46_json_45_simplify-72
694×rational_best_oopsla_all_46_json_45_simplify-49
682×rational_best_oopsla_all_46_json_45_simplify-89
578×rational_best_oopsla_all_46_json_45_simplify-7
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
019512439
170211935
2327111935
Stop Event
node limit
Counts
93 → 110
Calls
Call 1
Inputs
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(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (*.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 0 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))))
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(+.f64 (+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) 0)
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))))
(-.f64 (*.f64 0 (neg.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))) (*.f64 (neg.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) 1)
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
Outputs
(*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))
(*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2)))))
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(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))))))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))))) (/.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2)))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))))))))

eval827.0ms (6%)

Compiler

Compiled 37850 to 23109 computations (38.9% saved)

prune193.0ms (1.4%)

Pruning

16 alts after pruning (12 fresh and 4 done)

PrunedKeptTotal
New80411815
Fresh213
Picked101
Done145
Total80816824
Error
0.2b
Counts
824 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
22.2b
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 1)
21.7b
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 0 (*.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -2 (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
21.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2)))))))))
21.9b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))))
22.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
21.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
22.2b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
3.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
21.9b
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
3.7b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
25.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
22.2b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
Compiler

Compiled 1020 to 735 computations (27.9% saved)

localize129.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.3b
(pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))
0.5b
(*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4)))
Compiler

Compiled 88 to 59 computations (33% saved)

series3.0ms (0%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
0.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.0ms
k
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.0ms
k
@0
(pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))
0.0ms
n
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))

rewrite153.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
1082×rational_best_oopsla_all_46_json_45_simplify-89
950×rational_best_oopsla_all_46_json_45_simplify-23
902×rational_best_oopsla_all_46_json_45_simplify-13
886×rational_best_oopsla_all_46_json_45_simplify-87
880×rational_best_oopsla_all_46_json_45_simplify-37
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
021163
1129163
2415163
31935163
Stop Event
node limit
Counts
3 → 124
Calls
Call 1
Inputs
(*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4)))
(pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
Outputs
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simplify240.0ms (1.8%)

Algorithm
egg-herbie
Rules
1520×rational_best_oopsla_all_46_json_45_simplify-37
1336×rational_best_oopsla_all_46_json_45_simplify-13
952×rational_best_oopsla_all_46_json_45_simplify-89
912×rational_best_oopsla_all_46_json_45_simplify-7
824×rational_best_oopsla_all_46_json_45_simplify-24
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033711798
1119111750
2457711738
Stop Event
node limit
Counts
172 → 213
Calls
Call 1
Inputs
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 2 (*.f64 n (PI.f64)))
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(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
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(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))))
Outputs
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(*.f64 2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 2 n))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 1/2 (-.f64 1 k))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 -1/2 (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (*.f64 -1/48 (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (*.f64 2 n))))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 2 n))) (+.f64 1 (neg.f64 k)))))
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(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)))) (neg.f64 (neg.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2))))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 k)) 0) (-.f64 (/.f64 1 (sqrt.f64 k)) 0)))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 n (PI.f64))
0.4b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
0.5b
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))
Compiler

Compiled 41 to 23 computations (43.9% saved)

series3.0ms (0%)

Counts
2 → 0
Calls

9 calls:

TimeVariablePointExpression
0.0ms
k
@-inf
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))
0.0ms
k
@0
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))
0.0ms
k
@inf
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))
0.0ms
k
@-inf
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
0.0ms
n
@-inf
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))

rewrite108.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
936×rational_best_oopsla_all_46_json_45_simplify-89
788×rational_best_oopsla_all_46_json_45_simplify-23
754×rational_best_oopsla_all_46_json_45_simplify-37
752×rational_best_oopsla_all_46_json_45_simplify-87
746×rational_best_oopsla_all_46_json_45_simplify-13
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01660
19860
232860
3160660
4736760
Stop Event
node limit
Counts
2 → 94
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
Outputs
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simplify132.0ms (1%)

Algorithm
egg-herbie
Rules
1236×rational_best_oopsla_all_46_json_45_simplify-10
1216×rational_best_oopsla_all_46_json_45_simplify-30
814×rational_best_oopsla_all_46_json_45_simplify-37
658×rational_best_oopsla_all_46_json_45_simplify-72
634×rational_best_oopsla_all_46_json_45_simplify-23
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01884476
16144476
221694468
355864468
Stop Event
node limit
Counts
94 → 107
Calls
Call 1
Inputs
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(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2))) -1)
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(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
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(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) 0))
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0))
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64))))) 0))
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) 0))
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) 0))
(-.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 0))
(-.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(-.f64 0 (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 0 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 0 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 0 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(-.f64 0 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 2)))
(-.f64 (*.f64 0 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 1)
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
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(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64)))))))
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(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(neg.f64 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 2)))
Outputs
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) 0)
(*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) 0))
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(-.f64 0 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(-.f64 (*.f64 0 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (neg.f64 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 1 (sqrt.f64 k))))))
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 2)))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) 1)
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (sqrt.f64 2) (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 1 (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 -1 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(neg.f64 (*.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
0.3b
(*.f64 n (*.f64 2 (PI.f64)))
3.3b
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
Compiler

Compiled 82 to 58 computations (29.3% saved)

series5.0ms (0%)

Counts
2 → 36
Calls

12 calls:

TimeVariablePointExpression
1.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
1.0ms
n
@-inf
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
1.0ms
n
@0
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
1.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
0.0ms
n
@inf
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))

rewrite103.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
1036×rational_best_oopsla_all_46_json_45_simplify-89
1008×rational_best_oopsla_all_46_json_45_simplify-13
880×rational_best_oopsla_all_46_json_45_simplify-23
866×rational_best_oopsla_all_46_json_45_simplify-87
864×rational_best_oopsla_all_46_json-2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02098
112498
240498
3188698
Stop Event
node limit
Counts
2 → 67
Calls
Call 1
Inputs
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
Outputs
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simplify108.0ms (0.8%)

Algorithm
egg-herbie
Rules
1480×rational_best_oopsla_all_46_json_45_simplify-37
1286×rational_best_oopsla_all_46_json_45_simplify-13
828×rational_best_oopsla_all_46_json_45_simplify-49
728×rational_best_oopsla_all_46_json_45_simplify-72
626×rational_best_oopsla_all_46_json_45_simplify-89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02166787
17566743
229686731
Stop Event
node limit
Counts
103 → 123
Calls
Call 1
Inputs
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(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))))
Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)) (+.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8)) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/48)))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2)))
(exp.f64 (*.f64 1/2 (*.f64 (+.f64 1 (*.f64 -1 k)) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 1 (*.f64 k -1)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (*.f64 1/2 (+.f64 1 (neg.f64 k)))))
(exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (neg.f64 k) 1/2) 1/2)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (-.f64 1/2 (*.f64 1/2 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
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(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) 0))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) 0))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 1 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 -1 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 (neg.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 0 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(*.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))))) (neg.f64 (neg.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))))))
(*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k)))
(*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (*.f64 (PI.f64) (+.f64 n n)))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (-.f64 (/.f64 1 (sqrt.f64 k)) 0) (-.f64 (/.f64 1 (sqrt.f64 k)) 0)))
(/.f64 (*.f64 (exp.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (-.f64 1/2 (*.f64 1/2 k)))) (/.f64 1 (sqrt.f64 k))) (/.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (neg.f64 (/.f64 1 (sqrt.f64 k)))))

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
0.3b
(*.f64 (PI.f64) n)
0.4b
(*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))
0.7b
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
Compiler

Compiled 111 to 66 computations (40.5% saved)

series28.0ms (0.2%)

Counts
4 → 36
Calls

21 calls:

TimeVariablePointExpression
15.0ms
k
@0
(*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))
1.0ms
n
@-inf
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
1.0ms
k
@-inf
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
1.0ms
n
@0
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
1.0ms
n
@inf
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))

rewrite75.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
1748×rational_best_oopsla_all_46_json_45_simplify-23
1482×rational_best_oopsla_all_46_json-2
1482×rational_best_oopsla_all_46_json-1
1482×rational_best_oopsla_all_46_json-4
1482×rational_best_oopsla_all_46_json-3
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
023164
1154160
2579160
33169160
Stop Event
node limit
Counts
4 → 64
Calls
Call 1
Inputs
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))
(*.f64 (PI.f64) n)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
Outputs
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simplify145.0ms (1.1%)

Algorithm
egg-herbie
Rules
1392×rational_best_oopsla_all_46_json_45_simplify-10
998×rational_best_oopsla_all_46_json_45_simplify-23
876×rational_best_oopsla_all_46_json_45_simplify-72
658×rational_best_oopsla_all_46_json_45_simplify-89
566×rational_best_oopsla_all_46_json_45_simplify-30
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01854860
16754844
230784840
379584840
Stop Event
node limit
Counts
100 → 99
Calls
Call 1
Inputs
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(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))) (+.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)) 1)) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))
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(-.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 0)
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(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 1)
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 k k))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)))))
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(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))))
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(-.f64 (*.f64 (PI.f64) n) 0)
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(/.f64 (*.f64 (PI.f64) n) 1)
(/.f64 (*.f64 (PI.f64) n) (/.f64 (PI.f64) (PI.f64)))
(/.f64 (*.f64 (PI.f64) n) (/.f64 n n))
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0)
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
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(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0)
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
Outputs
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(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)))))
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (log.f64 n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
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(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (*.f64 2 (PI.f64)))))))
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(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 k (sqrt.f64 2))))
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(*.f64 -1/2 (*.f64 (+.f64 (log.f64 (*.f64 2 (PI.f64))) (neg.f64 (log.f64 (/.f64 1 n)))) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
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(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
(*.f64 -1/2 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 (PI.f64) -2))))))
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(+.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(+.f64 (*.f64 0 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(-.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 0)
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(-.f64 (*.f64 0 (neg.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (neg.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k))) (sqrt.f64 2)))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) 1)
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 k k))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (neg.f64 k)))))
(/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (neg.f64 k))) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (neg.f64 k)))))
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (neg.f64 (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (neg.f64 (sqrt.f64 2))))))
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 k)) (*.f64 (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (neg.f64 k))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (/.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 (*.f64 -1/2 k) (/.f64 (sqrt.f64 2) (sqrt.f64 2))))))
(/.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2)))) (/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (neg.f64 k))) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (/.f64 (sqrt.f64 2) (sqrt.f64 2)) (neg.f64 k)))))
(/.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/2 k)) (*.f64 (sqrt.f64 2) (*.f64 -1/2 k))))
(*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (*.f64 k (sqrt.f64 2))))
(*.f64 -1/2 (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 k (sqrt.f64 2))))
(+.f64 (*.f64 (PI.f64) n) 0)
(*.f64 (PI.f64) n)
(+.f64 (*.f64 (PI.f64) n) (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64)))))
(*.f64 (PI.f64) n)
(+.f64 0 (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(+.f64 (*.f64 0 (*.f64 n (/.f64 (PI.f64) (PI.f64)))) (*.f64 (PI.f64) n))
(*.f64 (PI.f64) n)
(-.f64 (*.f64 (PI.f64) n) 0)
(*.f64 (PI.f64) n)
(-.f64 (*.f64 0 (neg.f64 (PI.f64))) (*.f64 (neg.f64 (PI.f64)) n))
(*.f64 (PI.f64) n)
(-.f64 (*.f64 0 (neg.f64 n)) (*.f64 (neg.f64 n) (PI.f64)))
(*.f64 (PI.f64) n)
(/.f64 (*.f64 (PI.f64) n) 1)
(*.f64 (PI.f64) n)
(/.f64 (*.f64 (PI.f64) n) (/.f64 (PI.f64) (PI.f64)))
(*.f64 (PI.f64) n)
(/.f64 (*.f64 (PI.f64) n) (/.f64 n n))
(*.f64 (PI.f64) n)
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 (PI.f64) n) (*.f64 (PI.f64) n)))
(*.f64 (PI.f64) n)
(/.f64 (*.f64 (PI.f64) n) (/.f64 (*.f64 n (/.f64 (PI.f64) (PI.f64))) (*.f64 n (/.f64 (PI.f64) (PI.f64)))))
(*.f64 (PI.f64) n)
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 0)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))

localize118.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
0.3b
(*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64)))))
0.3b
(pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))
Compiler

Compiled 322 to 223 computations (30.7% saved)

series105.0ms (0.8%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
47.0ms
n
@-inf
(pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))
15.0ms
n
@0
(pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))
7.0ms
n
@inf
(pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))
1.0ms
k
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
1.0ms
k
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))

rewrite85.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
1770×rational_best_oopsla_all_46_json-2
1770×rational_best_oopsla_all_46_json-1
1770×rational_best_oopsla_all_46_json-4
1770×rational_best_oopsla_all_46_json-3
1148×rational_best_oopsla_all_46_json_45_simplify-72
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
028387
1192387
2704375
34007375
Stop Event
node limit
Counts
3 → 40
Calls
Call 1
Inputs
(pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2))
(*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
Outputs
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simplify193.0ms (1.4%)

Algorithm
egg-herbie
Rules
1270×rational_best_oopsla_all_46_json_45_simplify-23
762×rational_best_oopsla_all_46_json_45_simplify-72
682×rational_best_oopsla_all_46_json_45_simplify-49
670×rational_best_oopsla_all_46_json_45_simplify-89
582×rational_best_oopsla_all_46_json_45_simplify-7
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01848606
16758564
229608478
Stop Event
node limit
Counts
88 → 109
Calls
Call 1
Inputs
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(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
Outputs
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (+.f64 (log.f64 (neg.f64 (*.f64 -2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 1 n)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (neg.f64 (*.f64 (PI.f64) 2)))))))
(exp.f64 (*.f64 (+.f64 (neg.f64 (log.f64 (/.f64 -1 n))) (log.f64 (*.f64 -2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k))))
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 3))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))) (*.f64 -1/48 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 3))))))))
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 3)))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) (+.f64 1 (*.f64 -1 k)))))
(exp.f64 (*.f64 1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (+.f64 1 (*.f64 k -1)))))
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(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2))))
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (pow.f64 (neg.f64 (*.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))) (/.f64 (-.f64 1 k) 2)) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))

eval1.0s (7.5%)

Compiler

Compiled 33579 to 21711 computations (35.3% saved)

prune253.0ms (1.9%)

Pruning

15 alts after pruning (8 fresh and 7 done)

PrunedKeptTotal
New8214825
Fresh347
Picked101
Done178
Total82615841
Error
0.2b
Counts
841 → 15
Alt Table
Click to see full alt table
StatusErrorProgram
21.7b
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
0.6b
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
21.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2)))))))))
21.9b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))))
22.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
21.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
22.2b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
3.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
21.9b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
3.7b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
25.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
22.2b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
22.2b
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
Compiler

Compiled 850 to 611 computations (28.1% saved)

localize180.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
0.3b
(pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2))
0.5b
(*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))
Compiler

Compiled 267 to 183 computations (31.5% saved)

series3.0ms (0%)

Counts
3 → 48
Calls

15 calls:

TimeVariablePointExpression
0.0ms
k
@0
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
0.0ms
k
@-inf
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
0.0ms
k
@inf
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
0.0ms
k
@0
(pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2))
0.0ms
n
@inf
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))

rewrite94.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
1674×rational_best_oopsla_all_46_json-2
1674×rational_best_oopsla_all_46_json-1
1674×rational_best_oopsla_all_46_json-4
1674×rational_best_oopsla_all_46_json-3
970×rational_best_oopsla_all_46_json_45_simplify-7
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
027375
1185375
2680375
33785375
Stop Event
node limit
Counts
3 → 47
Calls
Call 1
Inputs
(*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))
(pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2))
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
Outputs
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simplify128.0ms (0.9%)

Algorithm
egg-herbie
Rules
1432×rational_best_oopsla_all_46_json_45_simplify-23
778×rational_best_oopsla_all_46_json_45_simplify-72
704×rational_best_oopsla_all_46_json_45_simplify-49
650×rational_best_oopsla_all_46_json_45_simplify-89
552×rational_best_oopsla_all_46_json_45_simplify-24
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01929253
16799213
229039159
Stop Event
node limit
Counts
95 → 110
Calls
Call 1
Inputs
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 -2 (*.f64 n (PI.f64)))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
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(*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (*.f64 (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))))
(*.f64 -1 (neg.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))
(*.f64 (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))
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(/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) 1)
(/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))
(+.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0)
(+.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))))
(+.f64 0 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))) (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 0)
(-.f64 (*.f64 0 (neg.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (neg.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))) (/.f64 1 (sqrt.f64 k))))
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))))
Outputs
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(*.f64 -2 (*.f64 n (PI.f64)))
(*.f64 (PI.f64) (*.f64 n -2))
(exp.f64 (*.f64 1/2 (*.f64 (-.f64 1 k) (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))))))
(exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) (*.f64 1/2 (-.f64 1 k))))
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(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (neg.f64 (/.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2))))))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (neg.f64 (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) -4)))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) 2))) (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f64 1 (sqrt.f64 k))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))
0.3b
(*.f64 n (PI.f64))
0.5b
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
Compiler

Compiled 43 to 21 computations (51.2% saved)

series8.0ms (0.1%)

Counts
2 → 0
Calls

12 calls:

TimeVariablePointExpression
5.0ms
n
@0
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
0.0ms
n
@-inf
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
0.0ms
k
@-inf
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
0.0ms
k
@0
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
0.0ms
n
@inf
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))

rewrite111.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
944×rational_best_oopsla_all_46_json_45_simplify-89
788×rational_best_oopsla_all_46_json_45_simplify-23
758×rational_best_oopsla_all_46_json_45_simplify-87
754×rational_best_oopsla_all_46_json_45_simplify-37
746×rational_best_oopsla_all_46_json_45_simplify-13
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01668
19868
232868
3160168
4739668
Stop Event
node limit
Counts
2 → 94
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))
Outputs
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simplify131.0ms (1%)

Algorithm
egg-herbie
Rules
1220×rational_best_oopsla_all_46_json_45_simplify-10
1198×rational_best_oopsla_all_46_json_45_simplify-30
644×rational_best_oopsla_all_46_json_45_simplify-72
634×rational_best_oopsla_all_46_json_45_simplify-35
596×rational_best_oopsla_all_46_json_45_simplify-23
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01884944
16184944
221904936
357964932
Stop Event
node limit
Counts
94 → 112
Calls
Call 1
Inputs
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(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 1)
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(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))))
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(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) -1)
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(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
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Outputs
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
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(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 0)
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(+.f64 (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 0)
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) 0))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(-.f64 0 (*.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0)
(-.f64 0 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) 1)
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))) -1)
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))
(neg.f64 (*.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(neg.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (neg.f64 (sqrt.f64 (*.f64 n (PI.f64)))))))
(-.f64 (*.f64 (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 0)
(neg.f64 (*.f64 (neg.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))) (/.f64 1 (sqrt.f64 k))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))

localize50.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)
0.3b
(*.f64 (PI.f64) n)
0.7b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
Compiler

Compiled 116 to 74 computations (36.2% saved)

series7.0ms (0.1%)

Counts
1 → 0
Calls

6 calls:

TimeVariablePointExpression
1.0ms
n
@-inf
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
1.0ms
n
@0
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
1.0ms
n
@inf
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
1.0ms
k
@-inf
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
1.0ms
k
@inf
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))

rewrite64.0ms (0.5%)

Algorithm
batch-egg-rewrite
Rules
1584×rational_best_oopsla_all_46_json-2
1584×rational_best_oopsla_all_46_json-1
1584×rational_best_oopsla_all_46_json-4
1584×rational_best_oopsla_all_46_json-3
910×rational_best_oopsla_all_46_json_45_simplify-72
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02481
116381
262981
3358381
Stop Event
node limit
Counts
1 → 25
Calls
Call 1
Inputs
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
Outputs
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simplify102.0ms (0.7%)

Algorithm
egg-herbie
Rules
1544×rational_best_oopsla_all_46_json_45_simplify-89
1224×rational_best_oopsla_all_46_json_45_simplify-74
1118×rational_best_oopsla_all_46_json_45_simplify-24
836×rational_best_oopsla_all_46_json_45_simplify-13
810×rational_best_oopsla_all_46_json_45_simplify-10
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0822197
13012197
214232197
358262197
Stop Event
node limit
Counts
25 → 29
Calls
Call 1
Inputs
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(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n))))))
Outputs
(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) 0)
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(+.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 0 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n))))))
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(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))))
(/.f64 (*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) (/.f64 (*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2)))) (*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))) (*.f64 (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k)))))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (*.f64 n 2)))))) (sqrt.f64 (*.f64 (PI.f64) n))))))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 k (*.f64 -1/2 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))))))))
(*.f64 (+.f64 1 (*.f64 (log.f64 (*.f64 (PI.f64) (*.f64 n 2))) (*.f64 k -1/2))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 2))))

localize124.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))
0.5b
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)
2.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))))
3.2b
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
Compiler

Compiled 297 to 215 computations (27.6% saved)

series25.0ms (0.2%)

Counts
4 → 36
Calls

18 calls:

TimeVariablePointExpression
4.0ms
n
@inf
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
4.0ms
n
@-inf
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
3.0ms
n
@inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))))
2.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))))
2.0ms
n
@0
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))

rewrite101.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
2042×rational_best_oopsla_all_46_json-2
2042×rational_best_oopsla_all_46_json-1
2042×rational_best_oopsla_all_46_json-4
2042×rational_best_oopsla_all_46_json-3
742×rational_best_oopsla_all_46_json_45_simplify-89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
034390
1242354
2967346
34625346
Stop Event
node limit
Counts
4 → 72
Calls
Call 1
Inputs
(+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))))
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2)
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))
Outputs
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simplify140.0ms (1%)

Algorithm
egg-herbie
Rules
1466×rational_best_oopsla_all_46_json_45_simplify-37
1254×rational_best_oopsla_all_46_json_45_simplify-72
1020×rational_best_oopsla_all_46_json_45_simplify-49
828×rational_best_oopsla_all_46_json_45_simplify-7
778×rational_best_oopsla_all_46_json_45_simplify-89
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
022111208
184810510
2352510366
Stop Event
node limit
Counts
108 → 117
Calls
Call 1
Inputs
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(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
Outputs
(*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))
(*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8) (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8))
(*.f64 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) 1/8) (sqrt.f64 2)))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 -2 (*.f64 n (PI.f64))))) 2))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) (*.f64 -1/2 (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 (PI.f64) -2)))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 (PI.f64) -2)))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 (PI.f64) -2)))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 n) (log.f64 (neg.f64 (*.f64 (PI.f64) -2)))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (neg.f64 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (neg.f64 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (neg.f64 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 1 n))) (log.f64 (neg.f64 (*.f64 -2 (PI.f64))))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (*.f64 -1 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) -2))) (neg.f64 (log.f64 (/.f64 1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (neg.f64 (log.f64 (/.f64 -1 n)))) 2)
(pow.f64 (+.f64 (log.f64 (neg.f64 (*.f64 2 (PI.f64)))) (*.f64 -1 (log.f64 (/.f64 -1 n)))) 2)
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(/.f64 (*.f64 (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2))))))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) (/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))))
(+.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 0)
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(+.f64 0 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(-.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 0)
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 1)
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 1 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (*.f64 (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 1 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 -1 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(*.f64 (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) 1)
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)
(pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 0)
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(+.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) 0))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(+.f64 0 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(+.f64 (*.f64 0 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(-.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 0)
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(-.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) 0))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 2))) (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(-.f64 (*.f64 0 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))) (*.f64 (neg.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) 1)
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2)) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))
(/.f64 (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2)) (/.f64 (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2))) (*.f64 (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 (PI.f64) (*.f64 n -2)))) 2))
(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))

localize272.0ms (2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
1.6b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))
2.1b
(*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))
5.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))))
12.0b
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
Compiler

Compiled 503 to 236 computations (53.1% saved)

series30.0ms (0.2%)

Counts
4 → 36
Calls

24 calls:

TimeVariablePointExpression
4.0ms
n
@inf
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
4.0ms
n
@-inf
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))))
4.0ms
n
@-inf
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
3.0ms
n
@0
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
2.0ms
n
@0
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))))

rewrite179.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
930×rational_best_oopsla_all_46_json_45_simplify-89
822×rational_best_oopsla_all_46_json_45_simplify-74
782×rational_best_oopsla_all_46_json_45_simplify-35
726×rational_best_oopsla_all_46_json_45_simplify-37
684×rational_best_oopsla_all_46_json-2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
040574
1290538
21181538
35929538
Stop Event
node limit
Counts
4 → 62
Calls
Call 1
Inputs
(+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2)))))
(*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))))
Outputs
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simplify267.0ms (2%)

Algorithm
egg-herbie
Rules
1878×rational_best_oopsla_all_46_json_45_simplify-23
1538×rational_best_oopsla_all_46_json_45_simplify-37
742×rational_best_oopsla_all_46_json_45_simplify-89
716×rational_best_oopsla_all_46_json_45_simplify-7
608×rational_best_oopsla_all_46_json_45_simplify-10
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
019313596
173813128
2349212078
Stop Event
node limit
Counts
98 → 99
Calls
Call 1
Inputs
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(/.f64 (*.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (/.f64 1 (sqrt.f64 k))) (/.f64 (*.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)))) (*.f64 (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (+.f64 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) -1/2) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (/.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k))))))
(+.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 0)
(+.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
(+.f64 0 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))))
(+.f64 (*.f64 0 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))))
(-.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 0)
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))
(-.f64 (*.f64 0 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))) (*.f64 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) 1)
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (sqrt.f64 2) (sqrt.f64 2)))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2)))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n))))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))
(/.f64 (*.f64 (*.f64 (sqrt.f64 2) (pow.f64 k 2)) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (sqrt.f64 (*.f64 (PI.f64) n)))) (/.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2)))))))
(+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) 0)
(+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 0 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
(+.f64 0 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))))
(+.f64 (*.f64 0 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))))
(-.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) 0)
(-.f64 (*.f64 0 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (neg.f64 (sqrt.f64 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))))
(-.f64 (*.f64 0 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))) (*.f64 (neg.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) 1)
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3)))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
Outputs
(*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 -1/2 (*.f64 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (*.f64 1/8 (sqrt.f64 (*.f64 n (PI.f64))))))
(+.f64 (*.f64 -1/2 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) (*.f64 (sqrt.f64 2) k))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))
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(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))))))
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))
(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3)))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (pow.f64 k 3)))))
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))
(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3)))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3)))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))))
(*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 -1/48 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3)))))
(*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3)))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n)))) (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (sqrt.f64 (*.f64 (PI.f64) n))))))
(/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3)))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))))
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))))) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (pow.f64 k 3))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 (/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 (*.f64 n (PI.f64)))) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))))

eval969.0ms (7.1%)

Compiler

Compiled 35291 to 21418 computations (39.3% saved)

prune226.0ms (1.7%)

Pruning

16 alts after pruning (6 fresh and 10 done)

PrunedKeptTotal
New6393642
Fresh033
Picked101
Done11011
Total64116657
Error
0.2b
Counts
657 → 16
Alt Table
Click to see full alt table
StatusErrorProgram
0.6b
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
21.7b
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
0.6b
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
21.7b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2)))))))))
22.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
21.1b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
22.2b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
3.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
21.9b
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
3.7b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
25.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
21.9b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))
22.2b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
22.2b
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
Compiler

Compiled 525 to 393 computations (25.1% saved)

regimes256.0ms (1.9%)

Accuracy

Total -25.3b remaining (-4847.9%)

Threshold costs -25.3b (-4847.9%)

Counts
27 → 1
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 2) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (PI.f64)))))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))))
(/.f64 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 1 (sqrt.f64 k)))) 1)
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (exp.f64 (*.f64 (-.f64 1 k) (*.f64 1/2 (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 1/2 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))))))
(*.f64 (sqrt.f64 (/.f64 1 k)) (exp.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 (PI.f64)))) (*.f64 1/2 (-.f64 1 k)))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (*.f64 (PI.f64) (*.f64 (PI.f64) 4))) (/.f64 (-.f64 1 k) 2)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (*.f64 (/.f64 n (*.f64 2 (PI.f64))) (PI.f64))) (neg.f64 (*.f64 (PI.f64) -2))) (/.f64 (-.f64 1 k) 2)))
(*.f64 (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (*.f64 2 (PI.f64)) n)))))))
(*.f64 (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 (log.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 -1/2 k)))) (*.f64 (sqrt.f64 (*.f64 (PI.f64) n)) (/.f64 1 (sqrt.f64 k))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (*.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) (/.f64 (-.f64 1 k) 2))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 n (*.f64 2 (PI.f64)))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))
(*.f64 (pow.f64 (neg.f64 (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 -4 (*.f64 (PI.f64) (/.f64 n (*.f64 (PI.f64) 2)))))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k)))
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (neg.f64 (*.f64 -2 (*.f64 (PI.f64) (*.f64 (*.f64 2 (*.f64 (/.f64 (*.f64 2 (PI.f64)) (*.f64 (PI.f64) (*.f64 (/.f64 n (*.f64 2 (PI.f64))) 2))) (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64)))))) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
(/.f64 (*.f64 (pow.f64 (*.f64 (neg.f64 (/.f64 n (*.f64 (PI.f64) 2))) (*.f64 (PI.f64) (*.f64 (PI.f64) (*.f64 (/.f64 (*.f64 (PI.f64) 2) (*.f64 (PI.f64) (*.f64 2 (/.f64 n (*.f64 (PI.f64) 2))))) (*.f64 (/.f64 n (*.f64 (PI.f64) 2)) -4))))) (/.f64 (-.f64 1 k) 2)) (/.f64 1 (sqrt.f64 k))) 1)
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (-.f64 0 (*.f64 (*.f64 (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))) (/.f64 (*.f64 2 (PI.f64)) (*.f64 (*.f64 2 (PI.f64)) (/.f64 n (*.f64 2 (PI.f64)))))) (*.f64 -2 (*.f64 (PI.f64) (/.f64 n (*.f64 2 (PI.f64))))))) (/.f64 (-.f64 1 k) 2)))
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) (*.f64 (sqrt.f64 2) k))) (*.f64 (sqrt.f64 2) (+.f64 1 (*.f64 1/8 (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 (PI.f64) -2)))) 2))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) (*.f64 (sqrt.f64 2) k)))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (neg.f64 (*.f64 n (*.f64 -2 (PI.f64))))) 2))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/2 (*.f64 k (*.f64 (sqrt.f64 2) (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (*.f64 1/8 (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) -1/2)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 -1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3)))) (+.f64 (sqrt.f64 2) (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (*.f64 1/8 (pow.f64 k 2)))))))))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 -1/48 (pow.f64 k 3))) (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))))) (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
(*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 -1/2 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64)))) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 -1/48 (*.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3))) (sqrt.f64 (*.f64 n (PI.f64)))))))))
(+.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (+.f64 (*.f64 1/8 (*.f64 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 2) (*.f64 (sqrt.f64 2) (pow.f64 k 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 -1/48 (*.f64 (pow.f64 (log.f64 (*.f64 (PI.f64) (+.f64 n n))) 3) (*.f64 (sqrt.f64 2) (pow.f64 k 3))))) (*.f64 (*.f64 (sqrt.f64 2) (*.f64 k (log.f64 (*.f64 (PI.f64) (+.f64 n n))))) (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) -1/2))))) (*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 2) (sqrt.f64 (*.f64 n (PI.f64))))))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Calls

4 calls:

95.0ms
(*.f64 (*.f64 2 (PI.f64)) n)
16.0ms
k
14.0ms
n
8.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Results
ErrorSegmentsBranch
0.5b1k
0.5b1n
0.5b1(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.5b1(*.f64 (*.f64 2 (PI.f64)) n)
Compiler

Compiled 1018 to 646 computations (36.5% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01749
Stop Event
fuel
saturated
Calls
Call 1
Inputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Outputs
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 18 to 15 computations (16.7% saved)

soundness0.0ms (0%)

end70.0ms (0.5%)

Compiler

Compiled 18 to 15 computations (16.7% saved)

Profiling

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