Details

Time bar (total: 6.1s)

analyze326.0ms (5.3%)

Algorithm
1×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 (49%)

Results
1.3s8256×body128valid
994.0ms1302×body1024invalid
376.0ms668×body512invalid
187.0ms1115×body128invalid
112.0ms345×body256invalid
Compiler

Compiled 38 to 32 computations (15.8% saved)

preprocess36.0ms (0.6%)

Algorithm
2×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
1×saturated
1×node limit
Compiler

Compiled 18 to 15 computations (16.7% saved)

simplify20.0ms (0.3%)

Algorithm
1×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
1×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
0.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
▶0.5b
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.5b
(*.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)

localize9.0ms (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))
✓0.3b
(*.f64 (PI.f64) n)
✓0.3b
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))

series464.0ms (7.5%)

Counts
3 → 48
Calls

15 calls:

78.0ms
(/.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
n
-inf
73.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
n
-inf
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
69.0ms
(pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (fma.f64 k -1/2 1/2))
n
inf

rewrite59.0ms (1%)

Algorithm
1×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
1×node limit
Counts
3 → 82

simplify44.0ms (0.7%)

Algorithm
1×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
1×node limit
Counts
130 → 99

prune112.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New93699
Fresh101
Picked101
Done000
Total956101
Error
0.0b
Counts
101 → 6
Alt Table
StatusErrorProgram
10.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
21.3b
(/.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))
0.7b
(*.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 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
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))
0.7b
(*.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)))
Compiler

Compiled 2393 to 1640 computations (31.5% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series442.0ms (7.2%)

Counts
3 → 48
Calls

15 calls:

78.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
n
0
76.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
n
-inf
72.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2)) (pow.f64 k -1/2))
n
inf
64.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
n
-inf
63.0ms
(pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (fma.f64 k -1/2 1/2))
n
inf

rewrite50.0ms (0.8%)

Algorithm
1×batch-egg-rewrite
Rules
641×log-prod_binary64
232×expm1-udef_binary64
232×log1p-udef_binary64
221×log-pow_binary64
133×add-sqr-sqrt_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01344
127444
2321244
Stop Event
1×node limit
Counts
3 → 60

simplify45.0ms (0.7%)

Algorithm
1×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
0671180
11831020
2587864
33443862
Stop Event
1×node limit
Counts
108 → 78

prune86.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New76278
Fresh235
Picked101
Done000
Total79584
Error
0.0b
Counts
84 → 5
Alt Table
StatusErrorProgram
10.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
21.3b
(/.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 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2))
0.8b
(*.f64 (*.f64 (pow.f64 (*.f64 n 2) (fma.f64 k -1/2 1/2)) (pow.f64 (PI.f64) (fma.f64 k -1/2 1/2))) (pow.f64 k -1/2))
▶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 1934 to 1381 computations (28.6% saved)

localize11.0ms (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
(/.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))
0.3b
(*.f64 n (*.f64 2 (PI.f64)))
✓0.4b
(sqrt.f64 (*.f64 n (*.f64 2 (PI.f64))))

series98.0ms (1.6%)

Counts
3 → 12
Calls

15 calls:

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
9.0ms
(*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))))
k
-inf
8.0ms
(/.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))
n
0
7.0ms
(/.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))
n
-inf

rewrite58.0ms (0.9%)

Algorithm
1×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
01467
129849
2384145
Stop Event
1×node limit
Counts
3 → 87

simplify32.0ms (0.5%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
042508
1127476
2460416
32920414
Stop Event
1×node limit
Counts
99 → 96

prune142.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1333136
Fresh224
Picked011
Done000
Total1356141
Error
0.0b
Counts
141 → 6
Alt Table
StatusErrorProgram
10.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 2 (fma.f64 k -1/2 1/2))) k))
9.8b
(*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (/.f64 1 (sqrt.f64 (/.f64 k (*.f64 2 (*.f64 (PI.f64) n))))))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2))
▶0.4b
(/.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))
✓0.5b
(/.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 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 2)) (sqrt.f64 k))
Compiler

Compiled 3259 to 2078 computations (36.2% saved)

localize13.0ms (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))
✓0.3b
(*.f64 n (PI.f64))
✓0.3b
(*.f64 (sqrt.f64 (*.f64 n (PI.f64))) (*.f64 (sqrt.f64 2) (pow.f64 (*.f64 (*.f64 n (PI.f64)) 2) (*.f64 k -1/2))))

series102.0ms (1.7%)

Counts
4 → 12
Calls

18 calls:

17.0ms
(/.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))
k
-inf
14.0ms
(/.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))
k
0
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))))
n
-inf
8.0ms
(/.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))
n
-inf
8.0ms
(/.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))
n
inf

rewrite67.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
286×expm1-udef_binary64
286×log1p-udef_binary64
161×add-sqr-sqrt_binary64
153×log1p-expm1-u_binary64
153×expm1-log1p-u_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01673
133967
2433467
Stop Event
1×node limit
Counts
4 → 103

simplify30.0ms (0.5%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
042508
1127476
2460416
32920414
Stop Event
1×node limit
Counts
115 → 112

prune117.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1262128
Fresh224
Picked011
Done101
Total1295134
Error
0b
Counts
134 → 5
Alt Table
StatusErrorProgram
0.6b
(/.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 (PI.f64))) (*.f64 k -1/2)) (pow.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) 1/4) 2)) (sqrt.f64 k))
0.2b
(/.f64 (sqrt.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 2 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k) -1)))) (sqrt.f64 k))
0.5b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 (PI.f64) n)) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (PI.f64) n)))) (pow.f64 k -1/2))
10.4b
(sqrt.f64 (/.f64 (*.f64 (*.f64 n (PI.f64)) (*.f64 2 (pow.f64 (pow.f64 (*.f64 n (*.f64 (PI.f64) 2)) k) -1))) k))
✓0.4b
(/.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))
Compiler

Compiled 3294 to 2027 computations (38.5% saved)

regimes651.0ms (10.6%)

Accuracy

Total 0.2b remaining (68.3%)

Threshold costs 0.2b (68.3%)

Counts
144 → 1
Compiler

Compiled 12570 to 10074 computations (19.9% saved)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Rules
5×*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01631
12131
Stop Event
1×saturated

end104.0ms (1.7%)

Stop Event
1×fuel
Compiler

Compiled 151 to 114 computations (24.5% saved)

Profiling

Loading profile data...