Details

Time bar (total: 5.7s)

analyze335.0ms (5.8%)

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%25%57.9%7
18%20.3%61.8%8
18.3%16.4%65.3%9
18.5%13.7%67.8%10
18.6%11.5%69.9%11
18.7%10%71.3%12
18.7%8.9%72.4%13
18.7%8.2%73.1%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample3.0s (53.1%)

Results
1.3s8256×body128valid
1.1s1437×body1024invalid
361.0ms687×body512invalid
207.0ms1138×body128invalid
110.0ms335×body256invalid
Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify19.0ms (0.3%)

Algorithm
egg-herbie
Rules
664×associate-/l*_binary64
544×associate-/r*_binary64
257×associate-*l/_binary64
214×unswap-sqr_binary64
214×div-sub_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26822
314022
435422
595820
6218720
Stop Event
node limit
Counts
1 → 2

prune4.0ms (0.1%)

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

Compiled 97 to 77 computations (20.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series414.0ms (7.2%)

Counts
3 → 48
Calls

3 calls:

224.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
188.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
2.0ms
(*.f64 (PI.f64) n)

rewrite55.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
655×log-prod_binary64
233×expm1-udef_binary64
233×log1p-udef_binary64
222×log-pow_binary64
132×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01340
127440
2331940
Stop Event
node limit
Counts
3 → 82
Calls

3 calls:

52.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
52.0ms
(*.f64 (PI.f64) n)
52.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))

simplify41.0ms (0.7%)

Algorithm
egg-herbie
Rules
570×fma-neg_binary64
430×associate-*r*_binary64
373×associate-*l*_binary64
176×distribute-rgt-in_binary64
172×distribute-lft-in_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0671144
1183984
2587828
33439826
Stop Event
node limit
Counts
130 → 99

prune120.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New91899
Fresh101
Picked101
Done000
Total938101
Error
0.0b
Counts
101 → 8
Alt Table
StatusErrorProgram
0.5b
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
0.5b
(*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2)))
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))
0.5b
(/.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))
0.4b
(*.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2)))
25.7b
(/.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))
8.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
0.6b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
Compiler

Compiled 2567 to 1753 computations (31.7% saved)

localize10.0ms (0.2%)

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)))))
0.2b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
0.2b
(*.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))

series96.0ms (1.7%)

Counts
4 → 24
Calls

4 calls:

54.0ms
(/.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))
30.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
9.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
3.0ms
(*.f64 n (*.f64 2 (PI.f64)))

rewrite61.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
263×log-pow_binary64
256×expm1-udef_binary64
256×log1p-udef_binary64
144×add-sqr-sqrt_binary64
136×log1p-expm1-u_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01475
129857
2384153
Stop Event
node limit
Counts
4 → 103
Calls

4 calls:

59.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
59.0ms
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))
59.0ms
(*.f64 n (*.f64 2 (PI.f64)))
59.0ms
(/.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))

simplify38.0ms (0.7%)

Algorithm
egg-herbie
Rules
562×fma-neg_binary64
451×distribute-rgt-neg-in_binary64
449×distribute-lft-neg-in_binary64
438×associate-*r*_binary64
371×associate-*l*_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
042604
1127572
2460512
32920510
Stop Event
node limit
Counts
127 → 114

prune150.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1302132
Fresh257
Picked101
Done000
Total1337140
Error
0b
Counts
140 → 7
Alt Table
StatusErrorProgram
0.5b
(/.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))
25.7b
(/.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))
8.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
0.3b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))
8.4b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 (PI.f64) (*.f64 n 2))))))
0.5b
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
0.6b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
Compiler

Compiled 3298 to 2244 computations (32% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))
0.2b
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))
0.2b
(*.f64 (PI.f64) (*.f64 n 2))
0.4b
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))

series89.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

49.0ms
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))
28.0ms
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))
9.0ms
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))
3.0ms
(*.f64 (PI.f64) (*.f64 n 2))

rewrite58.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
787×log-prod_binary64
261×log-pow_binary64
255×expm1-udef_binary64
255×log1p-udef_binary64
145×add-sqr-sqrt_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01466
129857
2367155
Stop Event
node limit
Counts
4 → 86
Calls

4 calls:

56.0ms
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))
56.0ms
(sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2)))
56.0ms
(*.f64 (PI.f64) (*.f64 n 2))
56.0ms
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))

simplify9.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
associate-*r*_binary64
associate-*l*_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0696
11096
21796
31996
Stop Event
saturated
Counts
98 → 88

prune118.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1091110
Fresh246
Picked011
Done000
Total1116117
Error
0b
Counts
117 → 6
Alt Table
StatusErrorProgram
0.5b
(/.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))
25.7b
(/.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))
8.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
0.3b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))
0.4b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2) (pow.f64 k -1/2)))
0.5b
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
Compiler

Compiled 2964 to 1769 computations (40.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (PI.f64) (*.f64 n 2))
0.2b
(*.f64 (PI.f64) (+.f64 n n))
0.4b
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2) (pow.f64 k -1/2))
0.5b
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)

series216.0ms (3.8%)

Counts
3 → 24
Calls

3 calls:

190.0ms
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)
23.0ms
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2) (pow.f64 k -1/2))
3.0ms
(*.f64 (PI.f64) (+.f64 n n))

rewrite44.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
416×prod-diff_binary64
214×expm1-udef_binary64
214×log1p-udef_binary64
133×log1p-expm1-u_binary64
133×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01336
128934
2350634
Stop Event
node limit
Counts
3 → 71
Calls

3 calls:

43.0ms
(*.f64 (PI.f64) (+.f64 n n))
43.0ms
(*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2) (pow.f64 k -1/2))
43.0ms
(pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2)

simplify25.0ms (0.4%)

Algorithm
egg-herbie
Rules
539×fma-def_binary64
468×associate-*l*_binary64
411×associate-*r*_binary64
280×distribute-rgt-in_binary64
268×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
031336
177336
2166300
3505216
41779216
Stop Event
node limit
Counts
95 → 77

prune93.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New99099
Fresh044
Picked011
Done011
Total996105
Error
0b
Counts
105 → 6
Alt Table
StatusErrorProgram
0.5b
(/.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))
25.7b
(/.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))
8.9b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
0.3b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2)))
0.4b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (*.f64 (pow.f64 (pow.f64 (*.f64 (PI.f64) (+.f64 n n)) 1/4) 2) (pow.f64 k -1/2)))
0.5b
(*.f64 (/.f64 1 (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k 1/4)))
Compiler

Compiled 2787 to 1660 computations (40.4% saved)

regimes512.0ms (8.9%)

Accuracy

Total 0.3b remaining (92%)

Threshold costs 0.3b (92%)

Counts
113 → 1
Compiler

Compiled 10514 to 8214 computations (21.9% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01431
11831
Stop Event
saturated

end141.0ms (2.5%)

Compiler

Compiled 225 to 167 computations (25.8% saved)

Profiling

Loading profile data...