Details

Time bar (total: 8.0s)

analyze380.0ms (4.8%)

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)

sample3.3s (41.4%)

Results
1.4s8256×body128valid
1.1s1372×body1024invalid
398.0ms687×body512invalid
185.0ms1142×body128invalid
122.0ms332×body256invalid
Compiler

Compiled 56 to 47 computations (16.1% saved)

simplify46.0ms (0.6%)

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%)

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

series561.0ms (7%)

Counts
3 → 48
Calls

3 calls:

289.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
269.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite28.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
36×times-frac_binary64
26×*-un-lft-identity_binary64
26×add-sqr-sqrt_binary64
26×add-cube-cbrt_binary64
26×add-exp-log_binary64
Counts
3 → 108
Calls

3 calls:

6.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
4.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
4.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

simplify118.0ms (1.5%)

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

prune223.0ms (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
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
0.5b
(*.f64 (pow.f64 (*.f64 2 (PI.f64)) (fma.f64 k -1/2 1/2)) (/.f64 (pow.f64 n (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))
0.3b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.3b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
21.2b
(/.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 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.4b
(*.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (/.f64 1 (sqrt.f64 k)))
0.7b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
Compiler

Compiled 4348 to 2756 computations (36.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
0.1b
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))
0.2b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))
0.3b
(*.f64 n (PI.f64))

series135.0ms (1.7%)

Counts
4 → 12
Calls

4 calls:

80.0ms
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))
41.0ms
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
11.0ms
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))
2.0ms
(*.f64 n (PI.f64))

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
37×add-exp-log_binary64
18×pow1_binary64
17×add-sqr-sqrt_binary64
17×prod-exp_binary64
13×add-cbrt-cube_binary64
Counts
4 → 98
Calls

4 calls:

8.0ms
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (sqrt.f64 k))
7.0ms
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
6.0ms
(*.f64 n (PI.f64))
3.0ms
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))

simplify98.0ms (1.2%)

Algorithm
egg-herbie
Rules
875×fma-def_binary64
334×distribute-rgt-in_binary64
332×distribute-lft-in_binary64
280×associate-/r*_binary64
269×associate-*l/_binary64
Counts
110 → 143
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01692985
13652651
213732611
346792603
454782603

prune238.0ms (3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1632165
Fresh257
Picked101
Done000
Total1667173
Error
0b
Counts
173 → 7
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
0.7b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.3b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
21.2b
(/.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 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
0.4b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (sqrt.f64 k))
Compiler

Compiled 4826 to 2713 computations (43.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series97.0ms (1.2%)

Counts
2 → 0
Calls

2 calls:

83.0ms
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
14.0ms
(/.f64 1 (sqrt.f64 k))

rewrite33.0ms (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:

15.0ms
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
3.0ms
(/.f64 1 (sqrt.f64 k))

simplify97.0ms (1.2%)

Algorithm
egg-herbie
Rules
574×associate-/r*_binary64
505×unswap-sqr_binary64
501×fma-def_binary64
390×associate-/l/_binary64
343×associate-/r/_binary64
Counts
111 → 127
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01162714
12122475
27032475
316852475
440732475
553852475

prune256.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1891190
Fresh156
Picked011
Done000
Total1907197
Error
0b
Counts
197 → 7
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
0.7b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))))
21.2b
(/.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 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
0.4b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (sqrt.f64 k))
0.2b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))
Compiler

Compiled 5664 to 3313 computations (41.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))))
0.1b
(sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))
0.2b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))
0.3b
(*.f64 n (PI.f64))

series74.0ms (0.9%)

Counts
1 → 0
Calls

1 calls:

74.0ms
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))

rewrite19.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
52×add-exp-log_binary64
42×prod-exp_binary64
15×pow-exp_binary64
pow-to-exp_binary64
associate-*r*_binary64
Counts
1 → 38
Calls

1 calls:

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

simplify67.0ms (0.8%)

Algorithm
egg-herbie
Rules
824×fma-def_binary64
764×associate-/l*_binary64
349×*-commutative_binary64
243×unswap-sqr_binary64
239×associate-+l+_binary64
Counts
38 → 35
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0861372
11691276
26351272
311901215
427171215
552521215

prune209.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1520152
Fresh055
Picked011
Done011
Total1527159
Error
0b
Counts
159 → 7
Alt Table
StatusErrorProgram
0.3b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (/.f64 1 (sqrt.f64 k)))
0.7b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n)) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (cbrt.f64 (*.f64 (*.f64 2 (PI.f64)) n))) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))))
21.2b
(/.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 1/2 (*.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n (PI.f64)))) (sqrt.f64 2))) (sqrt.f64 (*.f64 n (PI.f64)))))) (sqrt.f64 k))
0.4b
(*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (/.f64 (fma.f64 k -1/2 1/2) 2)) (sqrt.f64 k)))
0.4b
(/.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 (*.f64 n (sqrt.f64 (PI.f64))) (sqrt.f64 (PI.f64)))))) (sqrt.f64 k))
0.2b
(*.f64 (*.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64))))) (pow.f64 k -1/2))
Compiler

Compiled 4439 to 2729 computations (38.5% saved)

regimes1.7s (21.8%)

Accuracy

Total 0.3b remaining (66.8%)

Threshold costs 0.3b (66.8%)

Counts
329 → 1
Compiler

Compiled 35187 to 25969 computations (26.2% saved)

simplify2.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01743
12343
22343

end162.0ms (2%)

Compiler

Compiled 271 to 195 computations (28% saved)

Profiling

Loading profile data...