Details

Time bar (total: 6.7s)

analyze345.0ms (5.2%)

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%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)

sample3.2s (48.5%)

Results
1.4s8256×body128valid
1.1s1335×body1024invalid
438.0ms705×body512invalid
182.0ms1199×body128invalid
116.0ms358×body256invalid
Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess35.0ms (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

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.6b
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))
0.7b
(*.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)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series437.0ms (6.6%)

Counts
3 → 48
Calls

15 calls:

72.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
n
0
70.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
0
67.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
-inf
67.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
inf
65.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
n
inf

rewrite53.0ms (0.8%)

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

simplify42.0ms (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

prune117.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New92799
Fresh011
Picked101
Done000
Total938101
Error
0.0b
Counts
101 → 8
Alt Table
StatusErrorProgram
0.7b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 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))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.9b
(/.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))
0.7b
(*.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 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (-.f64 1 k) 2)))
0.8b
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
0.8b
(/.f64 (pow.f64 (*.f64 2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 2437 to 1680 computations (31.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series267.0ms (4%)

Counts
4 → 36
Calls

18 calls:

64.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
n
-inf
64.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
n
inf
64.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2))
n
0
15.0ms
(/.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
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
0

rewrite63.0ms (0.9%)

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
01463
129854
2384152
Stop Event
node limit
Counts
4 → 107

simplify32.0ms (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 (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1373140
Fresh257
Picked011
Done000
Total1399148
Error
0b
Counts
148 → 9
Alt Table
StatusErrorProgram
0.8b
(/.f64 (*.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)))) 1) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.7b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 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))
0.9b
(/.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))
0.8b
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
0.8b
(/.f64 (pow.f64 (*.f64 2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))
0.5b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Compiler

Compiled 3531 to 2304 computations (34.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series256.0ms (3.8%)

Counts
3 → 24
Calls

15 calls:

65.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2))
n
0
64.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2))
n
-inf
64.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2))
n
inf
15.0ms
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
k
0
9.0ms
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
n
inf

rewrite53.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
784×log-prod_binary64
263×log-pow_binary64
255×expm1-udef_binary64
255×log1p-udef_binary64
145×associate-*r*_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01456
129847
2366747
Stop Event
node limit
Counts
3 → 72

simplify30.0ms (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
054536
1148504
2456436
32587432
Stop Event
node limit
Counts
96 → 85

prune157.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1230123
Fresh077
Picked011
Done011
Total1239132
Error
0b
Counts
132 → 9
Alt Table
StatusErrorProgram
0.8b
(/.f64 (*.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)))) 1) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.7b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 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))
0.9b
(/.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))
0.8b
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
0.8b
(/.f64 (pow.f64 (*.f64 2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))
0.5b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Compiler

Compiled 3404 to 2339 computations (31.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2))
0.3b
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))
0.4b
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4))
0.4b
(sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))

series98.0ms (1.5%)

Counts
2 → 12
Calls

12 calls:

13.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))
k
0
11.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4))
k
-inf
10.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4))
k
0
10.0ms
(/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4))
k
inf
8.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))
n
-inf

rewrite65.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
295×log1p-udef_binary64
167×add-sqr-sqrt_binary64
161×log1p-expm1-u_binary64
161×expm1-log1p-u_binary64
158×add-cbrt-cube_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01654
135237
2465037
Stop Event
node limit
Counts
2 → 85

simplify30.0ms (0.4%)

Algorithm
egg-herbie
Rules
942×unswap-sqr_binary64
371×associate-*l*_binary64
330×*-commutative_binary64
273×associate-*r*_binary64
220×div-sub_binary64
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
023252
150252
296252
3205252
4520252
51575216
62785216
Stop Event
node limit
Counts
97 → 88

prune223.0ms (3.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1550155
Fresh066
Picked011
Done022
Total1559164
Error
0b
Counts
164 → 9
Alt Table
StatusErrorProgram
0.8b
(/.f64 (*.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)))) 1) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))) (sqrt.f64 k))
0.8b
(*.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))) (sqrt.f64 k)))
0.7b
(*.f64 (/.f64 (pow.f64 2 (fma.f64 k -1/2 1/2)) 1) (/.f64 (pow.f64 (*.f64 (PI.f64) n) (fma.f64 k -1/2 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))
0.9b
(/.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))
0.8b
(pow.f64 (sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) 2)
0.8b
(/.f64 (pow.f64 (*.f64 2 (pow.f64 (sqrt.f64 (*.f64 (PI.f64) n)) 2)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.7b
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (pow.f64 k 1/4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k 1/4)))
0.5b
(*.f64 (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n))) (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (pow.f64 k -1/2)))
Compiler

Compiled 4419 to 3079 computations (30.3% saved)

regimes720.0ms (10.8%)

Accuracy

Total 0.4b remaining (94.2%)

Threshold costs 0.4b (94.2%)

Counts
162 → 1
Compiler

Compiled 14338 to 11442 computations (20.2% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01431
11831
Stop Event
saturated

end161.0ms (2.4%)

Stop Event
fuel
Compiler

Compiled 244 to 191 computations (21.7% saved)

Profiling

Loading profile data...