Details

Time bar (total: 17.3s)

analyze580.0ms (3.3%)

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)

sample87.0ms (0.5%)

Algorithm
intervals
Results
29.0ms256×body128valid
19.0ms33×body1024nan
9.0ms52×body128overflowed
9.0ms23×body512nan
4.0ms17×body256nan
2.0ms25×body128nan
1.0msbody128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify48.0ms (0.3%)

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%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.3b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.4b
(/.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
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)

series567.0ms (3.3%)

Counts
3 → 48
Calls

3 calls:

303.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
260.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite20.0ms (0.1%)

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

3 calls:

5.0ms
(/.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)

simplify126.0ms (0.7%)

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

prune215.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1617168
Fresh101
Picked101
Done000
Total1637170
Error
0b
Counts
170 → 7
Alt Table
StatusErrorProgram
0.6b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
1.0b
(*.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))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
21.9b
(/.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))
0.5b
(/.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))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
Compiler

Compiled 4396 to 2772 computations (36.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series550.0ms (3.2%)

Counts
4 → 28
Calls

4 calls:

286.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
255.0ms
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
5.0ms
(sqrt.f64 (/.f64 1 k))
3.0ms
(*.f64 n (PI.f64))

rewrite27.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
32×sqrt-prod_binary64
26×*-un-lft-identity_binary64
24×times-frac_binary64
24×add-exp-log_binary64
Counts
4 → 119
Calls

4 calls:

11.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))
4.0ms
(pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 n (PI.f64))
2.0ms
(sqrt.f64 (/.f64 1 k))

simplify181.0ms (1%)

Algorithm
egg-herbie
Rules
405×*-commutative_binary64
393×distribute-rgt-in_binary64
385×distribute-lft-in_binary64
267×fma-neg_binary64
257×log-prod_binary64
Counts
147 → 170
Iterations

Useful iterations: 6 (0.0ms)

IterNodesCost
01823227
13762983
211512831
331622831
445952831
549042831
649532827
749302827

prune225.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1682170
Fresh246
Picked101
Done000
Total1716177
Error
0b
Counts
177 → 6
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.6b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))))
21.9b
(/.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))
0.5b
(/.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 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
Compiler

Compiled 4405 to 3094 computations (29.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
0.2b
(sqrt.f64 (/.f64 1 k))
0.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.3b
(*.f64 n (*.f64 2 (PI.f64)))

series91.0ms (0.5%)

Counts
3 → 12
Calls

3 calls:

75.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
12.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
3.0ms
(*.f64 n (*.f64 2 (PI.f64)))

rewrite25.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
27×add-exp-log_binary64
19×associate-*l*_binary64
17×prod-exp_binary64
16×pow1_binary64
14×sqrt-prod_binary64
Counts
3 → 71
Calls

3 calls:

14.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (*.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))))

simplify81.0ms (0.5%)

Algorithm
egg-herbie
Rules
683×associate-/r/_binary64
466×fma-def_binary64
450×*-commutative_binary64
420×unswap-sqr_binary64
296×associate-/l/_binary64
Counts
83 → 105
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01151869
12281724
28441724
314451724
428511724
557311724

prune231.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1670167
Fresh055
Picked011
Done000
Total1676173
Error
0b
Counts
173 → 6
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.6b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))))
21.9b
(/.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))
0.5b
(/.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 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
Compiler

Compiled 5008 to 3518 computations (29.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k)))
0.2b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.3b
(*.f64 n (PI.f64))
0.4b
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k)))

series900.0ms (5.2%)

Counts
3 → 28
Calls

3 calls:

702.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k)))
111.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k)))
87.0ms
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))

rewrite212.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
244×sqrt-prod_binary64
207×times-frac_binary64
192×add-sqr-sqrt_binary64
103×*-un-lft-identity_binary64
103×add-cube-cbrt_binary64
Counts
3 → 288
Calls

3 calls:

100.0ms
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
12.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k)))
12.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k)))

simplify531.0ms (3.1%)

Algorithm
egg-herbie
Rules
609×times-frac_binary64
350×distribute-rgt-in_binary64
345×distribute-lft-in_binary64
246×associate-*l/_binary64
227×associate-*r/_binary64
Counts
316 → 379
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
033013430
178312515
2235712303
3497512303

prune1.1s (6.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New4230423
Fresh044
Picked011
Done011
Total4236429
Error
0b
Counts
429 → 6
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 (sqrt.f64 k))))
0.6b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))))
21.9b
(/.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))
0.5b
(/.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 (sqrt.f64 (/.f64 1 k)) (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
Compiler

Compiled 15631 to 7853 computations (49.8% saved)

regimes5.6s (32.3%)

Accuracy

Total 0.4b remaining (91.2%)

Threshold costs 0.4b (91.2%)

Counts
521 → 1
Compiler

Compiled 70029 to 49870 computations (28.8% saved)

simplify4.0ms (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)

sample5.8s (33.7%)

Algorithm
intervals
Results
1.6s1334×body1024nan
1.5s8000×body128valid
802.0ms2326×body128overflowed
556.0ms676×body512nan
141.0ms294×body256nan
134.0ms941×body128nan
44.0ms215×body128invalid
Compiler

Compiled 250 to 185 computations (26% saved)

Profiling

Loading profile data...