Details

Time bar (total: 8.3s)

analyze619.0ms (7.4%)

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%26.5%56.3%7
18%22.6%59.4%8
18.3%19.9%61.8%9
18.5%17.8%63.7%10
18.6%16.3%65.1%11
18.7%15.2%66.1%12
18.7%14.4%66.9%13
18.7%13.8%67.4%14
Compiler

Compiled 19 to 16 computations (15.8% saved)

sample93.0ms (1.1%)

Algorithm
intervals
Results
28.0ms256×body128valid
23.0ms38×body1024nan
14.0ms78×body128overflowed
7.0ms16×body512nan
2.0ms29×body128nan
1.0msbody256nan
1.0msbody128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify53.0ms (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 (0.1%)

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 (*.f64 2 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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
72×add-exp-log_binary64
72×add-sqr-sqrt_binary64
62×times-frac_binary64
57×*-un-lft-identity_binary64
44×add-cube-cbrt_binary64
Counts
4 → 180
Calls

4 calls:

9.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
4.0ms
(*.f64 (*.f64 2 PI.f64) n)
3.0ms
(/.f64 1 (sqrt.f64 k))

series739.0ms (8.9%)

Counts
4 → 48
Calls

4 calls:

350.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
328.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
51.0ms
(*.f64 (*.f64 2 PI.f64) n)
9.0ms
(/.f64 1 (sqrt.f64 k))

simplify189.0ms (2.3%)

Algorithm
egg-herbie
Rules
512×distribute-rgt-in_binary64
508×distribute-lft-in_binary64
227×associate-*l*_binary64
200×associate-*r*_binary64
196×fma-def_binary64
Counts
228 → 429
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02444819
15354574
217134299
348304299
449404299

prune313.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New4227429
Fresh101
Picked101
Done000
Total4247431
Error
0b
Counts
431 → 7
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
21.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 2))) (sqrt.f64 2)) (fma.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 2))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 3))))))))
0.9b
(*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1 k))) (sqrt.f64 (sqrt.f64 k))))
0.5b
(*.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))))
1.3b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1 k))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1 k))) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1 k))) (sqrt.f64 k))))
0.3b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.9b
(*.f64 (/.f64 (pow.f64 (*.f64 2 PI.f64) (*.f64 1/2 (-.f64 1 k))) (sqrt.f64 k)) (pow.f64 n (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 6435 to 4502 computations (30% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
54×add-exp-log_binary64
34×add-sqr-sqrt_binary64
32×prod-exp_binary64
26×times-frac_binary64
22×associate-*l*_binary64
Counts
1 → 70
Calls

1 calls:

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

series28.0ms (0.3%)

Counts
1 → 0
Calls

1 calls:

28.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)))

simplify90.0ms (1.1%)

Algorithm
egg-herbie
Rules
846×times-frac_binary64
646×associate-/r*_binary64
528×associate-*l/_binary64
352×associate-*l*_binary64
336×fma-def_binary64
Counts
70 → 137
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0961527
11691398
24591376
315171376
446451376
550151376

prune264.0ms (3.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3884392
Fresh426
Picked101
Done000
Total3936399
Error
0b
Counts
399 → 6
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
21.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 2))) (sqrt.f64 2)) (fma.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 2))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 3))))))))
0.3b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.4b
(/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.3b
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) 1/4) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.8b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
Compiler

Compiled 6272 to 4396 computations (29.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 n (*.f64 2 PI.f64))
0.3b
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k))

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
24×times-frac_binary64
23×sqrt-prod_binary64
21×*-un-lft-identity_binary64
21×add-sqr-sqrt_binary64
21×add-cube-cbrt_binary64
Counts
3 → 83
Calls

3 calls:

5.0ms
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k))
3.0ms
(*.f64 n (*.f64 2 PI.f64))
2.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))

series59.0ms (0.7%)

Counts
3 → 12
Calls

3 calls:

39.0ms
(/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k))
12.0ms
(*.f64 n (*.f64 2 PI.f64))
7.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))

simplify131.0ms (1.6%)

Algorithm
egg-herbie
Rules
835×times-frac_binary64
753×fma-def_binary64
560×associate-*l*_binary64
550×associate-/l/_binary64
373×associate-*r*_binary64
Counts
95 → 164
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01211739
12121628
25981628
318661628
436191628
537901628
649341628
752881628

prune187.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4000400
Fresh055
Picked011
Done000
Total4006406
Error
0b
Counts
406 → 6
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
21.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 2))) (sqrt.f64 2)) (fma.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 2))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 3))))))))
0.3b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.4b
(/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.3b
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) 1/4) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.8b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
Compiler

Compiled 4294 to 2719 computations (36.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
91×add-exp-log_binary64
57×prod-exp_binary64
40×add-sqr-sqrt_binary64
26×times-frac_binary64
25×*-un-lft-identity_binary64
Counts
3 → 123
Calls

3 calls:

9.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)))
6.0ms
(*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
4.0ms
(*.f64 (*.f64 2 PI.f64) (sqrt.f64 n))

series68.0ms (0.8%)

Counts
3 → 8
Calls

3 calls:

52.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2)))
9.0ms
(*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n))
6.0ms
(*.f64 (*.f64 2 PI.f64) (sqrt.f64 n))

simplify122.0ms (1.5%)

Algorithm
egg-herbie
Rules
613×associate-/l*_binary64
517×fma-def_binary64
438×times-frac_binary64
401×*-commutative_binary64
337×associate-/r*_binary64
Counts
131 → 230
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01552304
13132086
210272064
318602064
446882064
550622064

prune243.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New7020702
Fresh044
Picked011
Done011
Total7026708
Error
0b
Counts
708 → 6
Alt Table
StatusErrorProgram
0.3b
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
21.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (-.f64 (fma.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 2))) (sqrt.f64 2)) (fma.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 2))) (*.f64 1/48 (*.f64 (pow.f64 k 3) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) 3))))))))
0.3b
(/.f64 (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (sqrt.f64 n)) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.4b
(/.f64 (*.f64 (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.3b
(/.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) 1/4) (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
0.8b
(/.f64 (*.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (sqrt.f64 k)))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2)))
Compiler

Compiled 6254 to 3998 computations (36.1% saved)

regimes1.9s (22.3%)

Accuracy

Total 0.2b remaining (46.1%)

Threshold costs 0.2b (46.1%)

Compiler

Compiled 44069 to 33528 computations (23.9% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01833
12333
22033

end1.0ms (0%)

Compiler

Compiled 23 to 18 computations (21.7% saved)

sample3.1s (37.5%)

Algorithm
intervals
Results
829.0ms8000×body128valid
810.0ms1269×body1024nan
436.0ms2329×body128overflowed
285.0ms661×body512nan
88.0ms337×body256nan
75.0ms983×body128nan
31.0ms244×body128invalid
Compiler

Compiled 265 to 205 computations (22.6% saved)

Profiling

Loading profile data...