Details

Time bar (total: 9.2s)

analyze511.0ms (5.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%50%50%2
0%50%50%3
0%50%50%4
12.5%37.5%50%5
15.6%31.2%53.2%6
17.2%26.5%56.3%7
18%22.6%59.4%8
18.3%19.9%61.8%9
18.5%17.8%63.7%10
18.6%16.3%65.1%11
18.7%15.2%66.1%12
18.7%14.4%66.9%13
18.7%13.8%67.4%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample151.0ms (1.6%)

Algorithm
intervals
Results
30.0ms256×body128valid
29.0ms48×body1024nan
14.0ms83×body128overflowed
4.0ms11×body512nan
3.0ms12×body256nan
2.0ms24×body128nan
1.0msbody128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify48.0ms (0.5%)

Algorithm
egg-herbie
Rules
672×associate-/l*_binary64
625×associate-/r*_binary64
461×div-sub_binary64
445×distribute-frac-neg_binary64
288×distribute-rgt-neg-out_binary64
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26522
312922
428022
563420
6133220
7312120
8491420
9455020

prune10.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.2b
(*.f64 (*.f64 2 (PI.f64)) n)
0.2b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series545.0ms (5.9%)

Counts
3 → 48
Calls

3 calls:

288.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
254.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
26×add-exp-log_binary64
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
Counts
3 → 108
Calls

3 calls:

6.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
5.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

simplify129.0ms (1.4%)

Algorithm
egg-herbie
Rules
405×distribute-rgt-in_binary64
399×distribute-lft-in_binary64
243×fma-neg_binary64
211×associate-/l*_binary64
162×associate-*l*_binary64
Counts
156 → 168
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02134057
14283712
213903636
345063636
449603636

prune278.0ms (3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New15711168
Fresh101
Picked101
Done000
Total15911170
Error
0b
Counts
170 → 11
Alt Table
StatusErrorProgram
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.3b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
0.4b
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))))
1.1b
(*.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.3b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k)))
0.4b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.6b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.7b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
0.6b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
19.8b
(cbrt.f64 (pow.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)) 3))
Compiler

Compiled 4425 to 2908 computations (34.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
0.1b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
0.2b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
0.2b
(*.f64 n (*.f64 2 (PI.f64)))

series222.0ms (2.4%)

Counts
4 → 24
Calls

4 calls:

166.0ms
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
39.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
14.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
3.0ms
(*.f64 n (*.f64 2 (PI.f64)))

rewrite32.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
40×add-exp-log_binary64
21×pow1_binary64
19×prod-exp_binary64
16×add-cbrt-cube_binary64
14×add-sqr-sqrt_binary64
Counts
4 → 98
Calls

4 calls:

12.0ms
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
7.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
4.0ms
(*.f64 n (*.f64 2 (PI.f64)))
3.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))

simplify127.0ms (1.4%)

Algorithm
egg-herbie
Rules
436×distribute-rgt-in_binary64
434×distribute-lft-in_binary64
257×associate-/l/_binary64
199×associate-*l*_binary64
198×associate-*r*_binary64
Counts
122 → 151
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01753143
13882789
215522749
346982749
450002749
549782749

prune309.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1774181
Fresh5510
Picked101
Done000
Total1839192
Error
0b
Counts
192 → 9
Alt Table
StatusErrorProgram
19.7b
(cbrt.f64 (pow.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2))) 3))
0.7b
(/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (sqrt.f64 k) (pow.f64 n (fma.f64 k -1/2 1/2))))
0.3b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (sqrt.f64 k))
0.6b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.3b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.4b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.3b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (sqrt.f64 n) (*.f64 (sqrt.f64 n) (*.f64 2 (PI.f64)))))) (sqrt.f64 k))
Compiler

Compiled 5238 to 3310 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
0.2b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.2b
(*.f64 n (*.f64 2 (PI.f64)))
0.4b
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

series163.0ms (1.8%)

Counts
2 → 0
Calls

2 calls:

84.0ms
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
79.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

rewrite57.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
308×times-frac_binary64
138×*-un-lft-identity_binary64
138×add-sqr-sqrt_binary64
138×add-cube-cbrt_binary64
130×sqrt-prod_binary64
Counts
2 → 247
Calls

2 calls:

14.0ms
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
6.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

simplify357.0ms (3.9%)

Algorithm
egg-herbie
Rules
692×associate-/r*_binary64
523×*-commutative_binary64
458×associate-*r*_binary64
445×fma-def_binary64
297×associate-/r/_binary64
Counts
247 → 298
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033512420
166512127
2229111899
3373011899
4486011899
5513511899

prune531.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3743377
Fresh448
Picked101
Done000
Total3797386
Error
0b
Counts
386 → 7
Alt Table
StatusErrorProgram
0.4b
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (PI.f64)))))
0.4b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.3b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (sqrt.f64 n) (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n))))))
0.3b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (sqrt.f64 k))
0.6b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
9.7b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
Compiler

Compiled 12946 to 8249 computations (36.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
0.2b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (sqrt.f64 k))
0.2b
(*.f64 n (PI.f64))
0.3b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))

series693.0ms (7.5%)

Counts
4 → 16
Calls

4 calls:

559.0ms
(*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
89.0ms
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (sqrt.f64 k))
42.0ms
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
2.0ms
(*.f64 n (PI.f64))

rewrite37.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
22×add-cbrt-cube_binary64
20×add-exp-log_binary64
19×pow1_binary64
17×add-sqr-sqrt_binary64
13×*-un-lft-identity_binary64
Counts
4 → 97
Calls

4 calls:

12.0ms
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (sqrt.f64 k))
9.0ms
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))))))
5.0ms
(*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64)))))
3.0ms
(*.f64 n (PI.f64))

simplify123.0ms (1.3%)

Algorithm
egg-herbie
Rules
385×associate-/r*_binary64
304×distribute-rgt-in_binary64
296×distribute-lft-in_binary64
253×associate-*l*_binary64
240×fma-def_binary64
Counts
113 → 147
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01933360
14652596
217562568
347952568
449972568
549662568

prune213.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1691170
Fresh156
Picked011
Done000
Total1707177
Error
0b
Counts
177 → 7
Alt Table
StatusErrorProgram
0.4b
(/.f64 (*.f64 (sqrt.f64 n) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (PI.f64)))))
0.4b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.3b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 (sqrt.f64 n) (*.f64 (*.f64 2 (PI.f64)) (sqrt.f64 n))))))
0.3b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))) (sqrt.f64 k))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
9.7b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (/.f64 k (*.f64 n (*.f64 2 (PI.f64))))))
0.3b
(/.f64 (sqrt.f64 (*.f64 n (PI.f64))) (/.f64 (sqrt.f64 k) (*.f64 (sqrt.f64 2) (exp.f64 (*.f64 -1/2 (*.f64 k (log.f64 (*.f64 2 (*.f64 n (PI.f64))))))))))
Compiler

Compiled 5211 to 2858 computations (45.2% saved)

regimes1.6s (17.1%)

Accuracy

Total 0.4b remaining (88.4%)

Threshold costs 0.4b (88.4%)

Counts
287 → 1
Compiler

Compiled 28125 to 21514 computations (23.5% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01635
12035
22035

end1.0ms (0%)

Compiler

Compiled 23 to 18 computations (21.7% saved)

sample3.0s (32.8%)

Algorithm
intervals
Results
844.0ms1404×body1024nan
770.0ms8000×body128valid
421.0ms2407×body128overflowed
245.0ms618×body512nan
75.0ms326×body256nan
70.0ms958×body128nan
26.0ms227×body128invalid
Compiler

Compiled 202 to 154 computations (23.8% saved)

Profiling

Loading profile data...