Details

Time bar (total: 7.0s)

analyze602.0ms (8.6%)

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)

sample95.0ms (1.4%)

Algorithm
intervals
Results
24.0ms256×body128valid
21.0ms36×body1024nan
14.0ms79×body128overflowed
13.0ms25×body512nan
3.0ms15×body256nan
3.0ms36×body128nan
1.0msbody128invalid
Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify54.0ms (0.8%)

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 → 1
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01425
13222
26522
312922
428022
563420
6133220
7312120
8491420
9455020

prune4.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.4b
Counts
2 → 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))
0.5b
(*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))
Compiler

Compiled 81 to 66 computations (18.5% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite156.0ms (2.2%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
25×pow1_binary64
20×add-cube-cbrt_binary64
17×add-exp-log_binary64
16×add-sqr-sqrt_binary64
15×add-cbrt-cube_binary64
Counts
3 → 120
Calls

3 calls:

18.0ms
(*.f64 (*.f64 2 PI.f64) n)
13.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
13.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
Compiler

Compiled 1974 to 1295 computations (34.4% saved)

series72.0ms (1%)

Error
0.2b
Counts
3 → 18
Calls

3 calls:

30.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
28.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (fma.f64 k -1/2 1/2))
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
Compiler

Compiled 1028 to 765 computations (25.6% saved)

simplify98.0ms (1.4%)

Algorithm
egg-herbie
Rules
495×times-frac_binary64
431×distribute-rgt-in_binary64
425×distribute-lft-in_binary64
199×fma-def_binary64
158×associate-*l*_binary64
Counts
138 → 84
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01802216
13902013
213821972
349611972
450191972

prune75.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New76884
Fresh101
Picked101
Done000
Total78886
Error
0.0b
Counts
86 → 8
Alt Table
StatusErrorProgram
19.3b
(/.f64 (*.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)) (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 k (sqrt.f64 2)))))) (sqrt.f64 k))
11.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k))
0.5b
(/.f64 (pow.f64 (/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
11.9b
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.5b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.3b
(/.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))
0.5b
(/.f64 1 (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2))))
Compiler

Compiled 1545 to 1089 computations (29.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b
(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))
0.2b
(*.f64 n (*.f64 2 PI.f64))
0.2b
(*.f64 n (*.f64 2 PI.f64))

rewrite277.0ms (4%)

Algorithm
rewrite-expression-head
Error
0b
Rules
42×pow1_binary64
26×add-sqr-sqrt_binary64
24×add-exp-log_binary64
24×add-cube-cbrt_binary64
22×pow-prod-down_binary64
Counts
4 → 154
Calls

4 calls:

20.0ms
(/.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))
19.0ms
(*.f64 n (*.f64 2 PI.f64))
14.0ms
(*.f64 n (*.f64 2 PI.f64))
11.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
Compiler

Compiled 3136 to 2052 computations (34.6% saved)

series51.0ms (0.7%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

29.0ms
(/.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))
7.0ms
(*.f64 n (*.f64 2 PI.f64))
6.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
6.0ms
(*.f64 n (*.f64 2 PI.f64))
Compiler

Compiled 904 to 698 computations (22.8% saved)

simplify78.0ms (1.1%)

Algorithm
egg-herbie
Rules
761×associate-/l*_binary64
498×associate-/r*_binary64
228×unswap-sqr_binary64
180×associate-*r*_binary64
165×associate-*l*_binary64
Counts
169 → 94
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01672504
13512207
213652026
350302026

prune113.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New92294
Fresh167
Picked011
Done000
Total939102
Error
0b
Counts
102 → 9
Alt Table
StatusErrorProgram
19.3b
(/.f64 (*.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)) (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 k (sqrt.f64 2)))))) (sqrt.f64 k))
11.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k))
0.5b
(/.f64 (pow.f64 (/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
11.9b
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.5b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.3b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))))
1.0b
(*.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (*.f64 -1/2 k)) (*.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))))
0.3b
(/.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 1997 to 1306 computations (34.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite241.0ms (3.5%)

Algorithm
rewrite-expression-head
Error
0b
Rules
36×add-cube-cbrt_binary64
35×pow1_binary64
30×add-sqr-sqrt_binary64
26×add-exp-log_binary64
24×add-cbrt-cube_binary64
Counts
4 → 170
Calls

4 calls:

19.0ms
(/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))))
15.0ms
(*.f64 n (*.f64 2 PI.f64))
14.0ms
(*.f64 n PI.f64)
13.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))))
Compiler

Compiled 3746 to 2238 computations (40.3% saved)

series59.0ms (0.8%)

Error
0b
Counts
4 → 18
Calls

4 calls:

28.0ms
(/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))))
18.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))))
6.0ms
(*.f64 n PI.f64)
5.0ms
(*.f64 n (*.f64 2 PI.f64))
Compiler

Compiled 1091 to 836 computations (23.4% saved)

simplify134.0ms (1.9%)

Algorithm
egg-herbie
Rules
415×associate-/l/_binary64
323×unswap-sqr_binary64
236×fma-neg_binary64
232×associate-*r*_binary64
214×associate-*l*_binary64
Counts
188 → 83
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02313095
14932747
220662634
349582634
451242634

prune73.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New82183
Fresh167
Picked101
Done011
Total84892
Error
0b
Counts
92 → 8
Alt Table
StatusErrorProgram
19.3b
(/.f64 (*.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)) (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 k (sqrt.f64 2)))))) (sqrt.f64 k))
11.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k))
0.5b
(/.f64 (pow.f64 (/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
11.9b
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.5b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.4b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64)))))))
0.3b
(/.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 1809 to 1159 computations (35.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(*.f64 n PI.f64)
0.2b
(*.f64 n (*.f64 2 PI.f64))
0.3b
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64))))))
0.6b
(*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64)))

rewrite220.0ms (3.2%)

Algorithm
rewrite-expression-head
Error
0b
Rules
39×add-sqr-sqrt_binary64
33×pow1_binary64
32×add-cube-cbrt_binary64
26×add-exp-log_binary64
22×add-cbrt-cube_binary64
Counts
4 → 175
Calls

4 calls:

16.0ms
(*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64)))
15.0ms
(*.f64 n PI.f64)
14.0ms
(*.f64 n (*.f64 2 PI.f64))
13.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64))))))
Compiler

Compiled 4390 to 2040 computations (53.5% saved)

series41.0ms (0.6%)

Error
0b
Counts
4 → 15
Calls

4 calls:

22.0ms
(/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64))))))
6.0ms
(*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64)))
6.0ms
(*.f64 n (*.f64 2 PI.f64))
5.0ms
(*.f64 n PI.f64)
Compiler

Compiled 899 to 645 computations (28.3% saved)

simplify105.0ms (1.5%)

Algorithm
egg-herbie
Rules
768×associate-/r*_binary64
497×unswap-sqr_binary64
387×fma-def_binary64
211×associate-*l/_binary64
203×associate-/l/_binary64
Counts
190 → 103
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01781910
13551716
214501698
347331698
450871698

prune88.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1030103
Fresh066
Picked011
Done011
Total1038111
Error
0b
Counts
111 → 8
Alt Table
StatusErrorProgram
19.3b
(/.f64 (*.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)) (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 k (sqrt.f64 2)))))) (sqrt.f64 k))
11.6b
(sqrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k))
0.5b
(/.f64 (pow.f64 (/.f64 (*.f64 PI.f64 -2) (/.f64 -1 n)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))
11.9b
(*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 2 (*.f64 k -1/2) 1)) k)) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.5b
(*.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 (/.f64 1 k)))
1.0b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (fma.f64 k -1/2 1/2)) (sqrt.f64 k))))
0.4b
(/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 k -1/2)) (/.f64 (sqrt.f64 k) (sqrt.f64 (*.f64 2 (*.f64 (sqrt.f64 (*.f64 n PI.f64)) (sqrt.f64 (*.f64 n PI.f64)))))))
0.3b
(/.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 1969 to 1100 computations (44.1% saved)

regimes1.2s (16.5%)

Accuracy

Total 0.3b remaining (71.5%)

Threshold costs 0.3b (71.5%)

Compiler

Compiled 22326 to 16644 computations (25.5% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01631
12231
22231

end1.0ms (0%)

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample3.1s (44.9%)

Algorithm
intervals
Results
854.0ms1342×body1024nan
810.0ms8000×body128valid
403.0ms2216×body128overflowed
276.0ms661×body512nan
90.0ms355×body256nan
75.0ms1006×body128nan
25.0ms230×body128invalid
Compiler

Compiled 262 to 202 computations (22.9% saved)

Profiling

Loading profile data...