Details

Time bar (total: 13.7s)

analyze509.0ms (3.7%)

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)

sample141.0ms (1%)

Algorithm
intervals
Results
26.0ms256×body128valid
15.0ms27×body1024nan
9.0ms57×body128overflowed
7.0ms19×body512nan
2.0ms11×body256nan
2.0ms28×body128nan
1.0ms12×body128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify47.0ms (0.3%)

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

series534.0ms (3.9%)

Counts
3 → 48
Calls

3 calls:

276.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
255.0ms
(pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2))
3.0ms
(*.f64 (*.f64 2 (PI.f64)) n)

rewrite21.0ms (0.2%)

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:

5.0ms
(/.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)

simplify115.0ms (0.8%)

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

prune211.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1626168
Fresh101
Picked011
Done000
Total1637170
Error
0b
Counts
170 → 7
Alt Table
StatusErrorProgram
0.5b
(/.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)))))
0.5b
(*.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)))
22.6b
(/.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)) (sqrt.f64 k))
0.9b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (*.f64 k -1/2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n (PI.f64)))) (cbrt.f64 (sqrt.f64 k))))
Compiler

Compiled 4319 to 2718 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 k))
0.2b
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
0.2b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
0.4b
(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

series521.0ms (3.8%)

Counts
4 → 48
Calls

4 calls:

278.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
234.0ms
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
5.0ms
(sqrt.f64 (/.f64 1 k))
3.0ms
(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))

rewrite47.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
101×times-frac_binary64
78×add-sqr-sqrt_binary64
55×*-un-lft-identity_binary64
51×add-cube-cbrt_binary64
50×add-exp-log_binary64
Counts
4 → 187
Calls

4 calls:

15.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
11.0ms
(pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2))
5.0ms
(/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n))
2.0ms
(sqrt.f64 (/.f64 1 k))

simplify128.0ms (0.9%)

Algorithm
egg-herbie
Rules
519×times-frac_binary64
329×distribute-rgt-in_binary64
320×distribute-lft-in_binary64
220×associate-*l*_binary64
202×associate-*r*_binary64
Counts
235 → 289
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03125342
16864831
222194803
349474803

prune368.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2872289
Fresh235
Picked011
Done011
Total2897296
Error
0b
Counts
296 → 7
Alt Table
StatusErrorProgram
0.5b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 -2 (/.f64 -1 (sqrt.f64 n))) (fma.f64 k -1/2 1/2)))
0.4b
(/.f64 (pow.f64 (*.f64 (*.f64 2 (PI.f64)) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
0.9b
(*.f64 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (/.f64 1 k))) (cbrt.f64 (sqrt.f64 (/.f64 1 k)))) (cbrt.f64 (sqrt.f64 (/.f64 1 k)))) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
0.5b
(/.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)))))
0.5b
(*.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)))
22.6b
(/.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))
Compiler

Compiled 7755 to 5778 computations (25.5% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.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 (*.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 n (PI.f64))
0.3b
(*.f64 (*.f64 2 (PI.f64)) n)

series1.0s (7.5%)

Counts
3 → 24
Calls

3 calls:

631.0ms
(/.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)))))
395.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))))
2.0ms
(*.f64 n (PI.f64))

rewrite123.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
668×times-frac_binary64
450×sqrt-prod_binary64
289×add-sqr-sqrt_binary64
284×*-un-lft-identity_binary64
284×add-cube-cbrt_binary64
Counts
3 → 484
Calls

3 calls:

17.0ms
(/.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)))))
5.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2))))
3.0ms
(*.f64 n (PI.f64))

simplify776.0ms (5.7%)

Algorithm
egg-herbie
Rules
485×associate-/r/_binary64
441×associate-/l/_binary64
372×fma-def_binary64
350×*-commutative_binary64
348×associate-*l/_binary64
Counts
508 → 578
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
057434133
1114033523
2398328349
3380827667
4488127667
5497827667

prune995.0ms (7.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New6051606
Fresh134
Picked011
Done112
Total6076613
Error
0b
Counts
613 → 6
Alt Table
StatusErrorProgram
0.5b
(/.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)))))
0.5b
(*.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)))
22.6b
(/.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))
0.5b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 -2 (/.f64 -1 (sqrt.f64 n))) (fma.f64 k -1/2 1/2)))
0.7b
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (cbrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
Compiler

Compiled 29354 to 19851 computations (32.4% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series215.0ms (1.6%)

Counts
4 → 0
Calls

4 calls:

185.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 -2 (/.f64 -1 (sqrt.f64 n))) (fma.f64 k -1/2 1/2)))
16.0ms
(/.f64 -1 (sqrt.f64 n))
7.0ms
(*.f64 (PI.f64) (sqrt.f64 n))
7.0ms
(/.f64 -2 (/.f64 -1 (sqrt.f64 n)))

rewrite75.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
276×times-frac_binary64
164×add-sqr-sqrt_binary64
160×*-un-lft-identity_binary64
160×add-cube-cbrt_binary64
93×add-exp-log_binary64
Counts
4 → 288
Calls

4 calls:

26.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 -2 (/.f64 -1 (sqrt.f64 n))) (fma.f64 k -1/2 1/2)))
8.0ms
(/.f64 -2 (/.f64 -1 (sqrt.f64 n)))
4.0ms
(*.f64 (PI.f64) (sqrt.f64 n))
3.0ms
(/.f64 -1 (sqrt.f64 n))

simplify255.0ms (1.9%)

Algorithm
egg-herbie
Rules
580×associate-*l*_binary64
450×associate-*r*_binary64
343×unswap-sqr_binary64
298×*-commutative_binary64
281×associate-/l/_binary64
Counts
288 → 360
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03907926
18907596
233547544
347187544
449897544
550027544

prune539.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New3600360
Fresh033
Picked011
Done022
Total3606366
Error
0b
Counts
366 → 6
Alt Table
StatusErrorProgram
0.5b
(/.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)))))
0.5b
(*.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)))
22.6b
(/.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))
0.5b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (*.f64 (PI.f64) (sqrt.f64 n)) (fma.f64 k -1/2 1/2))) (pow.f64 (/.f64 -2 (/.f64 -1 (sqrt.f64 n))) (fma.f64 k -1/2 1/2)))
0.7b
(/.f64 (/.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 (PI.f64)))) (fma.f64 k -1/2 1/2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (cbrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 2 (*.f64 n (PI.f64))) (fma.f64 k -1/2 1/2)))))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (/.f64 (*.f64 (PI.f64) -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)))
Compiler

Compiled 13481 to 9083 computations (32.6% saved)

regimes4.0s (29.3%)

Accuracy

Total 0.4b remaining (79.6%)

Threshold costs 0.4b (79.6%)

Counts
520 → 1
Compiler

Compiled 72950 to 56790 computations (22.2% saved)

simplify2.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
01634
12334
22234

end1.0ms (0%)

Compiler

Compiled 23 to 17 computations (26.1% saved)

sample3.0s (21.8%)

Algorithm
intervals
Results
805.0ms1327×body1024nan
777.0ms8000×body128valid
396.0ms2294×body128overflowed
264.0ms689×body512nan
82.0ms347×body256nan
71.0ms944×body128nan
27.0ms231×body128invalid
Compiler

Compiled 227 to 173 computations (23.8% saved)

Profiling

Loading profile data...