Details

Time bar (total: 8.4s)

analyze542.0ms (6.5%)

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)

sample167.0ms (2%)

Algorithm
intervals
Results
36.0ms59×body1024nan
25.0ms256×body128valid
15.0ms81×body128overflowed
11.0ms27×body512nan
4.0ms37×body128nan
4.0ms15×body256nan
1.0msbody128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify48.0ms (0.6%)

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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
1.0b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.9b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 97 to 77 computations (20.6% saved)

localize10.0ms (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)
0.8b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series557.0ms (6.7%)

Counts
3 → 48
Calls

3 calls:

287.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
267.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite22.0ms (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:

8.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

simplify125.0ms (1.5%)

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

prune234.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1608168
Fresh101
Picked101
Done000
Total1628170
Error
0b
Counts
170 → 8
Alt Table
StatusErrorProgram
1.0b
(/.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)))))
25.2b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2))) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) k)) (*.f64 1/48 (*.f64 (pow.f64 k 3) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3))))))) (sqrt.f64 k))
25.2b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
0.7b
(*.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)))
0.8b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
1.5b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
1.0b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 4493 to 2938 computations (34.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 n (*.f64 2 (PI.f64)))
0.3b
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
0.5b
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
0.6b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))

series314.0ms (3.7%)

Counts
4 → 36
Calls

4 calls:

242.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
55.0ms
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
13.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
3.0ms
(*.f64 n (*.f64 2 (PI.f64)))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×times-frac_binary64
23×sqrt-prod_binary64
22×*-un-lft-identity_binary64
22×add-sqr-sqrt_binary64
22×add-cube-cbrt_binary64
Counts
4 → 102
Calls

4 calls:

5.0ms
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 k))
4.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
4.0ms
(*.f64 n (*.f64 2 (PI.f64)))
3.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))

simplify92.0ms (1.1%)

Algorithm
egg-herbie
Rules
452×distribute-rgt-in_binary64
447×distribute-lft-in_binary64
212×fma-neg_binary64
203×times-frac_binary64
192×associate-/l*_binary64
Counts
138 → 125
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01822559
13642368
211452356
347622352
449492352

prune186.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1461147
Fresh257
Picked101
Done000
Total1496155
Error
0b
Counts
155 → 6
Alt Table
StatusErrorProgram
1.0b
(/.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)))))
25.2b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
9.6b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))
0.8b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
1.0b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 4191 to 2719 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 2 (PI.f64)) n)
0.4b
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
0.5b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2))
0.6b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))

series270.0ms (3.2%)

Counts
2 → 24
Calls

2 calls:

234.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2))
35.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×times-frac_binary64
22×sqrt-prod_binary64
19×*-un-lft-identity_binary64
19×add-sqr-sqrt_binary64
19×add-cube-cbrt_binary64
Counts
2 → 68
Calls

2 calls:

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

simplify85.0ms (1%)

Algorithm
egg-herbie
Rules
411×associate-*l*_binary64
399×associate-*r*_binary64
362×distribute-rgt-in_binary64
357×distribute-lft-in_binary64
344×exp-prod_binary64
Counts
92 → 90
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01562099
12991957
28521945
345441941
451801941

prune157.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1310131
Fresh055
Picked011
Done000
Total1316137
Error
0b
Counts
137 → 6
Alt Table
StatusErrorProgram
1.0b
(/.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)))))
25.2b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
9.6b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))
0.8b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
1.0b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 3764 to 2458 computations (34.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 k))
0.2b
(*.f64 n (*.f64 2 (PI.f64)))
0.2b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
0.8b
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))

series583.0ms (7%)

Counts
3 → 36
Calls

3 calls:

344.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
234.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
5.0ms
(sqrt.f64 (/.f64 1 k))

rewrite22.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt_binary64
32×sqrt-prod_binary64
24×times-frac_binary64
23×*-un-lft-identity_binary64
21×add-exp-log_binary64
Counts
3 → 99
Calls

3 calls:

8.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
4.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
2.0ms
(sqrt.f64 (/.f64 1 k))

simplify121.0ms (1.4%)

Algorithm
egg-herbie
Rules
874×fma-def_binary64
323×*-commutative_binary64
267×exp-prod_binary64
240×distribute-rgt-in_binary64
235×fma-neg_binary64
Counts
135 → 131
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01593139
13332801
29352773
326192765
445372765
550242765

prune191.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1530153
Fresh044
Picked011
Done011
Total1536159
Error
0b
Counts
159 → 6
Alt Table
StatusErrorProgram
1.0b
(/.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)))))
25.2b
(/.f64 (-.f64 (+.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (sqrt.f64 2)) (*.f64 1/8 (*.f64 (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 2) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))) (*.f64 1/48 (*.f64 (*.f64 (pow.f64 k 3) (*.f64 (pow.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) 3) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64))))))) (sqrt.f64 k))
9.6b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (/.f64 (*.f64 n (*.f64 2 (PI.f64))) k)))
0.8b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))))
1.0b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
Compiler

Compiled 3765 to 2764 computations (26.6% saved)

regimes1.4s (16.5%)

Accuracy

Total 0.4b remaining (94.3%)

Threshold costs 0.4b (94.3%)

Counts
246 → 1
Compiler

Compiled 27986 to 21302 computations (23.9% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01431
11831
21831

end1.0ms (0%)

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample3.2s (38.1%)

Algorithm
intervals
Results
849.0ms1335×body1024nan
807.0ms8000×body128valid
444.0ms2366×body128overflowed
295.0ms692×body512nan
84.0ms338×body256nan
80.0ms1041×body128nan
29.0ms225×body128invalid
Compiler

Compiled 231 to 171 computations (26% saved)

Profiling

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