Details

Time bar (total: 8.0s)

analyze603.0ms (7.6%)

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)

sample82.0ms (1%)

Algorithm
intervals
Results
29.0ms256×body128valid
15.0ms26×body1024nan
12.0ms51×body128overflowed
6.0ms15×body512nan
3.0ms38×body128nan
3.0ms11×body256nan
1.0msbody128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify51.0ms (0.6%)

Algorithm
egg-herbie
Rules
788×neg-mul-1_binary64
672×associate-/l*_binary64
625×associate-/r*_binary64
480×div-sub_binary64
445×distribute-frac-neg_binary64
Counts
1 → 1
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01425
13222
26522
312822
427722
562322
6129622
7302422
8469122
9493322

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 2
Alt Table
StatusErrorProgram
0.3b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 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 84 to 69 computations (17.9% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite174.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
48×times-frac_binary64
42×*-un-lft-identity_binary64
42×add-sqr-sqrt_binary64
33×add-cube-cbrt_binary64
26×add-exp-log_binary64
Counts
3 → 115
Calls

3 calls:

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

Compiled 2467 to 1670 computations (32.3% saved)

series81.0ms (1%)

Error
0.1b
Counts
3 → 18
Calls

3 calls:

34.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
29.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
Compiler

Compiled 1081 to 812 computations (24.9% saved)

simplify224.0ms (2.8%)

Algorithm
egg-herbie
Rules
504×distribute-rgt-in_binary64
500×distribute-lft-in_binary64
219×associate-/l*_binary64
207×associate-/l/_binary64
169×associate-*l*_binary64
Counts
133 → 118
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02383741
15153560
216133374
347263370
449613370
549423370

prune104.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1099118
Fresh011
Picked101
Done000
Total11010120
Error
0.0b
Counts
120 → 10
Alt Table
StatusErrorProgram
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n PI.f64))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.2b
(/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
0.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
0.4b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
0.8b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 (cbrt.f64 k))))
24.6b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (-.f64 (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) 2))))) (*.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 2)))))) (sqrt.f64 k))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.5b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))
0.5b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
0.5b
(/.f64 (*.f64 (pow.f64 (*.f64 2 PI.f64) (*.f64 1/2 (-.f64 1 k))) (pow.f64 n (*.f64 1/2 (-.f64 1 k)))) (sqrt.f64 k))
Compiler

Compiled 2284 to 1490 computations (34.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite186.0ms (2.3%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
124×add-exp-log_binary64
65×prod-exp_binary64
36×pow-exp_binary64
30×div-exp_binary64
18×add-sqr-sqrt_binary64
Counts
4 → 118
Calls

4 calls:

7.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
5.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
4.0ms
(*.f64 (*.f64 2 PI.f64) n)
3.0ms
(*.f64 n PI.f64)
Compiler

Compiled 2954 to 1959 computations (33.7% saved)

series70.0ms (0.9%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

29.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
19.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
7.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 n PI.f64)
Compiler

Compiled 969 to 737 computations (23.9% saved)

simplify116.0ms (1.5%)

Algorithm
egg-herbie
Rules
603×associate-/r*_binary64
277×associate-*l/_binary64
236×associate-*r/_binary64
219×associate-/l/_binary64
194×associate-*l*_binary64
Counts
133 → 105
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02143002
14312716
216272471
347122471
449712471

prune83.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1032105
Fresh369
Picked011
Done000
Total1069115
Error
0.0b
Counts
115 → 9
Alt Table
StatusErrorProgram
0.3b
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.5b
(*.f64 (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (sqrt.f64 k))))
0.8b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 (cbrt.f64 k))))
24.6b
(/.f64 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (-.f64 (+.f64 (sqrt.f64 2) (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (pow.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) 2))))) (*.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 (*.f64 n PI.f64))) (sqrt.f64 2)))))) (sqrt.f64 k))
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n PI.f64))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.9b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (-.f64 1 k)) (cbrt.f64 (sqrt.f64 k))))
0.5b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
0.4b
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
Compiler

Compiled 1763 to 1152 computations (34.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite378.0ms (4.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
94×add-exp-log_binary64
91×add-sqr-sqrt_binary64
78×times-frac_binary64
52×*-un-lft-identity_binary64
46×add-cube-cbrt_binary64
Counts
4 → 182
Calls

4 calls:

21.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
5.0ms
(/.f64 1 (sqrt.f64 k))
3.0ms
(*.f64 n PI.f64)
3.0ms
(*.f64 n PI.f64)
Compiler

Compiled 4922 to 2887 computations (41.3% saved)

series50.0ms (0.6%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

32.0ms
(*.f64 (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
7.0ms
(*.f64 n PI.f64)
6.0ms
(*.f64 n PI.f64)
5.0ms
(/.f64 1 (sqrt.f64 k))
Compiler

Compiled 895 to 681 computations (23.9% saved)

simplify195.0ms (2.4%)

Algorithm
egg-herbie
Rules
544×associate-/r*_binary64
478×associate-/l/_binary64
403×*-commutative_binary64
267×associate-/r/_binary64
163×associate-*r*_binary64
Counts
197 → 150
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02405309
15574803
217974726
340104726
449824726
549604726

prune159.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1464150
Fresh437
Picked101
Done101
Total1527159
Error
0b
Counts
159 → 7
Alt Table
StatusErrorProgram
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n PI.f64))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) (cbrt.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (pow.f64 (*.f64 (*.f64 n PI.f64) 2) (/.f64 k 2)))))
0.2b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (sqrt.f64 k)) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.4b
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.5b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
0.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.3b
(*.f64 (/.f64 (/.f64 (sqrt.f64 2) (pow.f64 2 (/.f64 k 2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))))
Compiler

Compiled 2748 to 1666 computations (39.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(sqrt.f64 (*.f64 (*.f64 n PI.f64) 2))
0.2b
(*.f64 n PI.f64)
0.2b
(*.f64 n PI.f64)
0.3b
(/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (sqrt.f64 k))

rewrite137.0ms (1.7%)

Algorithm
rewrite-expression-head
Error
0b
Rules
29×add-sqr-sqrt_binary64
25×*-un-lft-identity_binary64
25×add-cube-cbrt_binary64
24×times-frac_binary64
23×sqrt-prod_binary64
Counts
4 → 95
Calls

4 calls:

6.0ms
(/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (sqrt.f64 k))
4.0ms
(*.f64 n PI.f64)
3.0ms
(*.f64 n PI.f64)
3.0ms
(sqrt.f64 (*.f64 (*.f64 n PI.f64) 2))
Compiler

Compiled 2355 to 1310 computations (44.4% saved)

series40.0ms (0.5%)

Error
0b
Counts
4 → 15
Calls

4 calls:

19.0ms
(/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (sqrt.f64 k))
7.0ms
(*.f64 n PI.f64)
7.0ms
(sqrt.f64 (*.f64 (*.f64 n PI.f64) 2))
6.0ms
(*.f64 n PI.f64)
Compiler

Compiled 846 to 653 computations (22.8% saved)

simplify162.0ms (2%)

Algorithm
egg-herbie
Rules
510×associate-/r/_binary64
412×associate-*l/_binary64
379×div-sub_binary64
377×distribute-rgt-in_binary64
317×associate-*r/_binary64
Counts
110 → 60
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01201817
12101704
25401704
314681704
426301704
526671704
632471704
738751704
845611704
947251704

prune66.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New59160
Fresh156
Picked011
Done000
Total60767
Error
0b
Counts
67 → 7
Alt Table
StatusErrorProgram
0.6b
(/.f64 (pow.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 n PI.f64))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (cbrt.f64 (*.f64 2 (*.f64 n PI.f64)))) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
0.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 1 (sqrt.f64 k))) (cbrt.f64 (/.f64 1 (sqrt.f64 k)))) (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 k))) (/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (pow.f64 (*.f64 (*.f64 n PI.f64) 2) (/.f64 k 2)))))
0.2b
(*.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 n PI.f64) 2)) (sqrt.f64 k)) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.4b
(/.f64 (*.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 n)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.3b
(*.f64 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (/.f64 (sqrt.f64 2) (sqrt.f64 k))) (/.f64 1 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
0.5b
(*.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 (-.f64 1 k) 4)) (sqrt.f64 k)))
0.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
Compiler

Compiled 1424 to 844 computations (40.7% saved)

regimes1.6s (20.3%)

Accuracy

Total 0.3b remaining (77.2%)

Threshold costs 0.3b (77.2%)

Compiler

Compiled 25470 to 19066 computations (25.1% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01331
11631
21631

end1.0ms (0%)

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.3s (41.7%)

Algorithm
intervals
Results
914.0ms1358×body1024nan
809.0ms8000×body128valid
412.0ms2247×body128overflowed
313.0ms682×body512nan
81.0ms1008×body128nan
79.0ms318×body256nan
28.0ms232×body128invalid
Compiler

Compiled 229 to 172 computations (24.9% saved)

Profiling

Loading profile data...