Details

Time bar (total: 7.2s)

analyze515.0ms (7.2%)

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)

sample164.0ms (2.3%)

Algorithm
intervals
Results
35.0ms53×body1024nan
23.0ms256×body128valid
19.0ms71×body128overflowed
8.0ms21×body512nan
2.0ms33×body128nan
2.0msbody256nan
1.0ms10×body128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify48.0ms (0.7%)

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
0.5b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.6b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.5b
(/.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)
0.3b
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))

series532.0ms (7.4%)

Counts
3 → 48
Calls

3 calls:

282.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
247.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite24.0ms (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))
5.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

simplify121.0ms (1.7%)

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

prune203.0ms (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
0.7b
(*.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))))
20.3b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 (sqrt.f64 2) k)) -1/2))) (sqrt.f64 k))
0.7b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
0.5b
(/.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))
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
1.0b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
0.6b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 4277 to 2788 computations (34.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series130.0ms (1.8%)

Counts
4 → 24
Calls

4 calls:

79.0ms
(/.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))
35.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
13.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
3.0ms
(*.f64 n (*.f64 2 (PI.f64)))

rewrite32.0ms (0.4%)

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:

10.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
10.0ms
(/.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))
4.0ms
(*.f64 n (*.f64 2 (PI.f64)))
3.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))

simplify126.0ms (1.8%)

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 → 152
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01753143
13882789
215522749
346982749
450002749
549782749

prune226.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1793182
Fresh347
Picked011
Done000
Total1828190
Error
0b
Counts
190 → 8
Alt Table
StatusErrorProgram
0.7b
(*.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))))
0.6b
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
0.6b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2)))) (sqrt.f64 k))
0.7b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
0.5b
(/.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))
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
0.7b
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 n)) (sqrt.f64 (*.f64 2 (PI.f64)))) (sqrt.f64 k))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 5183 to 3260 computations (37.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (*.f64 n (PI.f64)))
0.2b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2)))) (sqrt.f64 k))
0.2b
(*.f64 n (PI.f64))
0.5b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2))))

series138.0ms (1.9%)

Counts
4 → 12
Calls

4 calls:

88.0ms
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2)))) (sqrt.f64 k))
38.0ms
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2))))
10.0ms
(sqrt.f64 (*.f64 n (PI.f64)))
2.0ms
(*.f64 n (PI.f64))

rewrite32.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
52×add-exp-log_binary64
29×prod-exp_binary64
20×add-cbrt-cube_binary64
13×add-sqr-sqrt_binary64
11×*-un-lft-identity_binary64
Counts
4 → 92
Calls

4 calls:

12.0ms
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2)))) (sqrt.f64 k))
9.0ms
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2))))
3.0ms
(*.f64 n (PI.f64))
2.0ms
(sqrt.f64 (*.f64 n (PI.f64)))

simplify92.0ms (1.3%)

Algorithm
egg-herbie
Rules
433×associate-/r*_binary64
331×distribute-rgt-in_binary64
329×distribute-lft-in_binary64
295×associate-*l/_binary64
209×associate-/l/_binary64
Counts
104 → 121
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01733083
13912631
215002603
349902603

prune168.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1440144
Fresh066
Picked011
Done011
Total1448152
Error
0b
Counts
152 → 8
Alt Table
StatusErrorProgram
0.7b
(*.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))))
0.6b
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
0.6b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2)))) (sqrt.f64 k))
0.7b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
0.5b
(/.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))
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
0.7b
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 n)) (sqrt.f64 (*.f64 2 (PI.f64)))) (sqrt.f64 k))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 4345 to 2277 computations (47.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series96.0ms (1.3%)

Counts
2 → 0
Calls

2 calls:

81.0ms
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
15.0ms
(/.f64 1 (sqrt.f64 k))

rewrite31.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
88×add-exp-log_binary64
56×prod-exp_binary64
36×times-frac_binary64
30×*-un-lft-identity_binary64
30×add-sqr-sqrt_binary64
Counts
2 → 111
Calls

2 calls:

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

simplify108.0ms (1.5%)

Algorithm
egg-herbie
Rules
574×associate-/r*_binary64
505×unswap-sqr_binary64
501×fma-def_binary64
391×associate-/l/_binary64
343×associate-/r/_binary64
Counts
111 → 125
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01162714
12122475
27032475
316852475
440752475
553862475

prune305.0ms (4.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2390239
Fresh055
Picked011
Done022
Total2398247
Error
0b
Counts
247 → 8
Alt Table
StatusErrorProgram
0.7b
(*.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))))
0.6b
(*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
0.6b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2)))) (sqrt.f64 k))
0.7b
(/.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k)))
0.5b
(/.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))
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2))))
0.7b
(/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 n)) (sqrt.f64 (*.f64 2 (PI.f64)))) (sqrt.f64 k))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (sqrt.f64 (cbrt.f64 k))))
Compiler

Compiled 7037 to 4633 computations (34.2% saved)

regimes849.0ms (11.8%)

Accuracy

Total 0.4b remaining (88.8%)

Threshold costs 0.4b (88.8%)

Counts
153 → 1
Compiler

Compiled 15187 to 11615 computations (23.5% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01320
11520
21520

end1.0ms (0%)

Compiler

Compiled 15 to 12 computations (20% saved)

sample3.2s (44.6%)

Algorithm
intervals
Results
882.0ms1374×body1024nan
869.0ms8000×body128valid
413.0ms2192×body128overflowed
294.0ms665×body512nan
79.0ms317×body256nan
76.0ms966×body128nan
26.0ms226×body128invalid
Compiler

Compiled 226 to 172 computations (23.9% saved)

Profiling

Loading profile data...