Details

Time bar (total: 7.2s)

analyze359.0ms (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%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)

sample3.4s (46.6%)

Results
1.5s8256×body128valid
1.2s1393×body1024invalid
373.0ms674×body512invalid
224.0ms1179×body128invalid
121.0ms338×body256invalid
Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess34.0ms (0.5%)

Algorithm
egg-herbie
Rules
421×div-sub_binary64
418×associate-/l*_binary64
293×associate-*l*_binary64
268×associate-/r*_binary64
224×associate-/l/_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02150
15244
211944
325644
466844
5183640
6416340
022
Stop Event
saturated
node limit
Compiler

Compiled 18 to 15 computations (16.7% 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

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.7b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.7b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.8b
(*.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)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series390.0ms (5.4%)

Counts
3 → 48
Calls

15 calls:

62.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
n
0
62.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
inf
60.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
0
60.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
-inf
59.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
n
-inf

rewrite54.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01340
127440
2330640
01340
Stop Event
saturated
node limit
Counts
3 → 82

simplify46.0ms (0.6%)

Algorithm
egg-herbie
Rules
570×fma-neg_binary64
433×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
33443826
Stop Event
node limit
Counts
130 → 99

prune130.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New891099
Fresh101
Picked101
Done000
Total9110101
Error
0.0b
Counts
101 → 10
Alt Table
StatusErrorProgram
25.5b
(cbrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 3) (pow.f64 k 3/2)))
0.9b
(*.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)))
8.9b
(sqrt.f64 (/.f64 (pow.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) 2) k))
0.8b
(*.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)))
0.7b
(/.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))
1.2b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (cbrt.f64 (sqrt.f64 k))))
22.5b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 (*.f64 1/2 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (sqrt.f64 k))
0.8b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
22.6b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (+.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (fma.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k)) (*.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) (*.f64 k -1/2)))))) (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))
Compiler

Compiled 2649 to 1844 computations (30.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series234.0ms (3.3%)

Counts
4 → 36
Calls

18 calls:

57.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
n
-inf
56.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
n
0
55.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
n
inf
14.0ms
(/.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))
k
-inf
11.0ms
(/.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))
k
0

rewrite63.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
256×expm1-udef_binary64
256×log1p-udef_binary64
251×log-pow_binary64
146×add-sqr-sqrt_binary64
142×pow1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01463
129854
2381052
01463
Stop Event
saturated
node limit
Counts
4 → 107

simplify33.0ms (0.5%)

Algorithm
egg-herbie
Rules
711×cancel-sign-sub-inv_binary64
282×fma-neg_binary64
184×associate-*r*_binary64
182×associate-*l*_binary64
179×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054632
1148600
2456532
32587528
Stop Event
node limit
Counts
143 → 122

prune175.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1382140
Fresh459
Picked101
Done000
Total1437150
Error
0.0b
Counts
150 → 7
Alt Table
StatusErrorProgram
0.5b
(*.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)))
0.9b
(*.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)))
7.8b
(*.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))))))
0.8b
(*.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)))
22.5b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 (*.f64 1/2 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (sqrt.f64 k))
0.8b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
0.7b
(/.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))
Compiler

Compiled 3526 to 2441 computations (30.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series205.0ms (2.9%)

Counts
4 → 36
Calls

18 calls:

56.0ms
(pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2))
n
-inf
56.0ms
(pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2))
n
0
55.0ms
(pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2))
n
inf
5.0ms
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))
n
inf
4.0ms
(*.f64 (sqrt.f64 (*.f64 (PI.f64) (*.f64 n 2))) (pow.f64 k -1/2))
k
-inf

rewrite55.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
695×log-prod_binary64
235×expm1-udef_binary64
235×log1p-udef_binary64
231×log-pow_binary64
135×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01348
127648
2329448
01348
Stop Event
saturated
node limit
Counts
4 → 92

simplify31.0ms (0.4%)

Algorithm
egg-herbie
Rules
711×cancel-sign-sub-inv_binary64
282×fma-neg_binary64
184×associate-*r*_binary64
182×associate-*l*_binary64
179×unswap-sqr_binary64
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
054632
1148600
2456532
32587528
Stop Event
node limit
Counts
128 → 107

prune149.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1281129
Fresh156
Picked011
Done000
Total1297136
Error
0.0b
Counts
136 → 7
Alt Table
StatusErrorProgram
0.5b
(*.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)))
0.9b
(*.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)))
0.8b
(*.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)))
22.5b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 (*.f64 1/2 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (sqrt.f64 k))
0.8b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
8.6b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (+.f64 n n)) (pow.f64 k -1))))
0.7b
(/.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))
Compiler

Compiled 3609 to 2215 computations (38.6% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.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))
0.3b
(pow.f64 n (fma.f64 k -1/2 1/2))
0.4b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
0.6b
(pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2))

series484.0ms (6.7%)

Counts
4 → 56
Calls

21 calls:

68.0ms
(/.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))
n
0
68.0ms
(/.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))
n
-inf
67.0ms
(/.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))
n
inf
66.0ms
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
n
-inf
64.0ms
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (pow.f64 n (fma.f64 k -1/2 1/2)))
n
0

rewrite61.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
253×expm1-udef_binary64
253×log1p-udef_binary64
246×log-pow_binary64
147×add-sqr-sqrt_binary64
143×pow1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01455
129955
2370055
01469
Stop Event
saturated
node limit
Counts
4 → 100

simplify46.0ms (0.6%)

Algorithm
egg-herbie
Rules
872×fma-def_binary64
392×cancel-sign-sub-inv_binary64
225×associate-*l*_binary64
207×associate-*r*_binary64
201×distribute-rgt-in_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01351829
14511629
218341497
Stop Event
node limit
Counts
156 → 135

prune157.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1332135
Fresh145
Picked101
Done101
Total1366142
Error
0.0b
Counts
142 → 6
Alt Table
StatusErrorProgram
2.1b
(/.f64 (*.f64 (*.f64 (sqrt.f64 (PI.f64)) (sqrt.f64 2)) (pow.f64 n (fma.f64 k -1/2 1/2))) (sqrt.f64 k))
0.8b
(*.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)))
0.4b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (*.f64 (pow.f64 n (*.f64 k -1/2)) (sqrt.f64 n))) (sqrt.f64 k))
22.5b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (-.f64 (*.f64 (+.f64 (*.f64 1/8 (*.f64 (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 2) (*.f64 k k))) 1) (sqrt.f64 2)) (*.f64 (sqrt.f64 2) (+.f64 (*.f64 (*.f64 1/48 (pow.f64 k 3)) (pow.f64 (log.f64 (*.f64 n (*.f64 2 (PI.f64)))) 3)) (*.f64 (*.f64 1/2 k) (log.f64 (*.f64 n (*.f64 2 (PI.f64))))))))) (sqrt.f64 k))
0.8b
(pow.f64 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) -1)
8.6b
(*.f64 (pow.f64 (*.f64 (PI.f64) (*.f64 n 2)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 (*.f64 (PI.f64) (+.f64 n n)) (pow.f64 k -1))))
Compiler

Compiled 3644 to 2454 computations (32.7% saved)

regimes930.0ms (12.9%)

Accuracy

Total 0.6b remaining (96.4%)

Threshold costs 0.6b (96.4%)

Counts
204 → 1
Compiler

Compiled 17974 to 14310 computations (20.4% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01731
12131
Stop Event
saturated

end135.0ms (1.9%)

Stop Event
fuel
Compiler

Compiled 201 to 158 computations (21.4% saved)

Profiling

Loading profile data...