Details

Time bar (total: 14.1s)

analyze414.0ms (2.9%)

Algorithm
1×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 17 to 16 computations (5.9% saved)

sample87.0ms (0.6%)

Algorithm
1×intervals
Results
27.0ms256×body128valid
21.0ms42×body1024nan
9.0ms27×body512nan
9.0ms62×body128overflowed
2.0ms29×body128nan
2.0ms8×body256nan
1.0ms10×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify137.0ms (1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0493322
1493322

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.3b
Counts
2 → 2
Compiler

Compiled 44 to 41 computations (6.8% saved)

localize11.0ms (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))
0.3b
(*.f64 (*.f64 2 PI.f64) n)

rewrite202.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Error
0.0b
Rules
48×times-frac_binary64_766
42×add-sqr-sqrt_binary64_782 *-un-lft-identity_binary64_760
33×add-cube-cbrt_binary64_795
26×add-exp-log_binary64_798
22×pow-unpow_binary64_837
18×sqrt-prod_binary64_776
14×pow1_binary64_821
10×add-cbrt-cube_binary64_796
9×prod-exp_binary64_809
8×unpow-prod-down_binary64_839 sqr-pow_binary64_732
6×pow-prod-down_binary64_831 pow-exp_binary64_828 associate-/r*_binary64_704 difference-of-squares_binary64_729
5×div-exp_binary64_811 associate-/l*_binary64_705
3×add-log-exp_binary64_799 cbrt-unprod_binary64_793 associate-*r*_binary64_700 distribute-lft-out--_binary64_712 pow-pow_binary64_832
2×pow-to-exp_binary64_829 div-inv_binary64_757 div-sub_binary64_765 pow-sub_binary64_836
1×associate-*l*_binary64_701 *-commutative_binary64_691 cbrt-undiv_binary64_794 frac-2neg_binary64_771 clear-num_binary64_759 associate-/l/_binary64_707
Counts
3 → 115
Calls

3 calls:

10.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
6.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
Compiler

Compiled 2834 to 1916 computations (32.4% saved)

series427.0ms (3%)

Error
0.2b
Counts
3 → 18
Calls

3 calls:

201.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
175.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
29.0ms
(*.f64 (*.f64 2 PI.f64) n)
Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify96.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049693385
149693385

prune177.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1249133
Fresh101
Picked101
Done000
Total1269135
Error
0.0b
Counts
135 → 9
Compiler

Compiled 3026 to 1902 computations (37.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite529.0ms (3.8%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
284×times-frac_binary64_766
132×add-sqr-sqrt_binary64_782
128×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
111×sqrt-prod_binary64_776
28×unpow-prod-down_binary64_839 sqr-pow_binary64_732
27×add-exp-log_binary64_798
24×associate-/l*_binary64_705
14×pow1_binary64_821
13×add-cbrt-cube_binary64_796
11×div-exp_binary64_811
8×div-inv_binary64_757
6×associate-*l*_binary64_701 associate-*r*_binary64_700 associate-/r*_binary64_704
5×pow-prod-down_binary64_831 prod-exp_binary64_809
4×add-log-exp_binary64_799
3×pow-exp_binary64_828 cbrt-undiv_binary64_794 sqrt-pow1_binary64_778
2×cbrt-unprod_binary64_793 unswap-sqr_binary64_728 *-commutative_binary64_691
1×pow-to-exp_binary64_829 frac-2neg_binary64_771 clear-num_binary64_759 associate-/l/_binary64_707 pow1/2_binary64_840
Counts
4 → 241
Calls

4 calls:

20.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
4.0ms
(*.f64 n PI.f64)
4.0ms
(*.f64 n PI.f64)
4.0ms
(sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))
Compiler

Compiled 8806 to 4891 computations (44.5% saved)

series224.0ms (1.6%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

144.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
23.0ms
(sqrt.f64 (*.f64 2 (*.f64 n PI.f64)))
23.0ms
(*.f64 n PI.f64)
21.0ms
(*.f64 n PI.f64)
Compiler

Compiled 1094 to 837 computations (23.5% saved)

simplify140.0ms (1%)

Algorithm
1×egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0500411439

prune489.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2542256
Fresh178
Picked011
Done000
Total25510265
Error
0b
Counts
265 → 10
Compiler

Compiled 8716 to 5380 computations (38.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite968.0ms (6.9%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
441×times-frac_binary64_766
235×add-sqr-sqrt_binary64_782
207×*-un-lft-identity_binary64_760
203×add-cube-cbrt_binary64_795
123×sqrt-prod_binary64_776
120×associate-*r*_binary64_700
118×add-exp-log_binary64_798
52×div-exp_binary64_811
43×sqr-pow_binary64_732
41×prod-exp_binary64_809
39×unpow-prod-down_binary64_839
28×add-cbrt-cube_binary64_796
19×associate-/l*_binary64_705
18×pow-exp_binary64_828
16×pow1_binary64_821
15×div-inv_binary64_757
11×unswap-sqr_binary64_728
10×associate-*l*_binary64_701 1-exp_binary64_804 rec-exp_binary64_810
9×cbrt-unprod_binary64_793
7×pow-prod-down_binary64_831
6×pow-to-exp_binary64_829 cbrt-undiv_binary64_794 associate-/r*_binary64_704
4×add-log-exp_binary64_799
3×*-commutative_binary64_691
1×associate-*r/_binary64_702 frac-2neg_binary64_771 clear-num_binary64_759 associate-/l/_binary64_707
Counts
4 → 367
Calls

4 calls:

40.0ms
(*.f64 (sqrt.f64 (*.f64 n (*.f64 PI.f64 2))) (/.f64 (/.f64 1 (pow.f64 (*.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k)))
12.0ms
(/.f64 (/.f64 1 (pow.f64 (*.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
7.0ms
(*.f64 n (*.f64 PI.f64 2))
5.0ms
(*.f64 n (*.f64 PI.f64 2))
Compiler

Compiled 13674 to 9235 computations (32.5% saved)

series441.0ms (3.1%)

Error
0b
Counts
4 → 18
Calls

4 calls:

229.0ms
(/.f64 (/.f64 1 (pow.f64 (*.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k))
140.0ms
(*.f64 (sqrt.f64 (*.f64 n (*.f64 PI.f64 2))) (/.f64 (/.f64 1 (pow.f64 (*.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k)))
29.0ms
(*.f64 n (*.f64 PI.f64 2))
25.0ms
(*.f64 n (*.f64 PI.f64 2))
Compiler

Compiled 1381 to 1110 computations (19.6% saved)

simplify163.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
385 → 385
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
0519813376

prune871.0ms (6.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3850385
Fresh088
Picked011
Done011
Total38510395
Error
0b
Counts
395 → 10
Compiler

Compiled 12865 to 7984 computations (37.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.6s (11.2%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
702×times-frac_binary64_766
450×add-sqr-sqrt_binary64_782
275×sqrt-prod_binary64_776
264×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
154×associate-*r*_binary64_700
118×add-exp-log_binary64_798
86×sqr-pow_binary64_732
84×unpow-prod-down_binary64_839
63×div-exp_binary64_811
52×associate-*l*_binary64_701
51×unswap-sqr_binary64_728
34×add-cbrt-cube_binary64_796
31×prod-exp_binary64_809
24×associate-/l*_binary64_705
16×pow-exp_binary64_828 div-inv_binary64_757
12×cbrt-undiv_binary64_794
11×pow-to-exp_binary64_829
10×pow1_binary64_821
8×cbrt-unprod_binary64_793
6×associate-/r*_binary64_704
4×add-log-exp_binary64_799
3×pow-prod-down_binary64_831 *-commutative_binary64_691
1×frac-times_binary64_770 associate-*l/_binary64_703 associate-*r/_binary64_702 frac-2neg_binary64_771 clear-num_binary64_759 associate-/l/_binary64_707
Counts
4 → 513
Calls

4 calls:

115.0ms
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 2 (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))) (sqrt.f64 k)))
14.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))) (sqrt.f64 k))
4.0ms
(*.f64 n PI.f64)
4.0ms
(*.f64 n PI.f64)
Compiler

Compiled 21748 to 11480 computations (47.2% saved)

series393.0ms (2.8%)

Error
0b
Counts
4 → 18
Calls

4 calls:

201.0ms
(*.f64 (/.f64 (sqrt.f64 2) (pow.f64 2 (/.f64 k 2))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))) (sqrt.f64 k)))
124.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))) (sqrt.f64 k))
23.0ms
(*.f64 n PI.f64)
22.0ms
(*.f64 n PI.f64)
Compiler

Compiled 1749 to 1327 computations (24.1% saved)

simplify235.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
531 → 531
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
0499523732
1499523732

prune1.3s (9.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New5310531
Fresh077
Picked011
Done022
Total53110541
Error
0b
Counts
541 → 10
Compiler

Compiled 20756 to 10720 computations (48.4% saved)

regimes642.0ms (4.6%)

Accuracy

Total 0.4b remaining (99.6%)

Threshold costs 0.4b (99.6%)

Compiler

Compiled 8238 to 6718 computations (18.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02522
12522

end0.0ms (0%)

sample4.5s (32.1%)

Algorithm
1×intervals
Results
805.0ms8000×body128valid
653.0ms1321×body1024nan
354.0ms2309×body128overflowed
224.0ms627×body512nan
68.0ms336×body256nan
59.0ms971×body128nan
23.0ms228×body128invalid
Compiler

Compiled 2079 to 1698 computations (18.3% saved)

Profiling

Loading profile data...