Details

Time bar (total: 14.7s)

analyze614.0ms (4.2%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0494244
1494244
022
122
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)

sample83.0ms (0.6%)

Algorithm
1×intervals
Results
25.0ms256×body128valid
21.0ms40×body1024nan
10.0ms72×body128overflowed
6.0ms19×body512nan
1.0ms7×body256nan
1.0ms20×body128nan
1.0ms10×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify70.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0493322
1493322

prune8.0ms (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)

localize13.0ms (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 (*.f64 2 PI.f64) n)
0.2b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))

rewrite268.0ms (1.8%)

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-exp_binary64_828 associate-/r*_binary64_704 pow-prod-down_binary64_831 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×cbrt-undiv_binary64_794 frac-2neg_binary64_771 clear-num_binary64_759 associate-/l/_binary64_707 associate-*l*_binary64_701 *-commutative_binary64_691
Counts
3 → 115
Calls

3 calls:

21.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
7.0ms
(/.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)

series466.0ms (3.2%)

Error
0.2b
Counts
3 → 18
Calls

3 calls:

212.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
201.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
33.0ms
(*.f64 (*.f64 2 PI.f64) n)
Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify108.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
049693385
149693385

prune203.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1267133
Fresh101
Picked101
Done000
Total1287135
Error
0.0b
Counts
135 → 7
Compiler

Compiled 3009 to 2033 computations (32.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite649.0ms (4.4%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
284×times-frac_binary64_766
126×add-cube-cbrt_binary64_795 add-sqr-sqrt_binary64_782 *-un-lft-identity_binary64_760
111×sqrt-prod_binary64_776
33×add-exp-log_binary64_798
28×unpow-prod-down_binary64_839 sqr-pow_binary64_732
24×associate-/l*_binary64_705
20×pow1_binary64_821
19×add-cbrt-cube_binary64_796
11×div-exp_binary64_811
9×prod-exp_binary64_809 pow-prod-down_binary64_831
8×div-inv_binary64_757
6×associate-/r*_binary64_704 cbrt-unprod_binary64_793 associate-*l*_binary64_701
4×add-log-exp_binary64_799
3×pow-exp_binary64_828 cbrt-undiv_binary64_794 sqrt-pow1_binary64_778
2×associate-*r*_binary64_700 *-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:

24.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
5.0ms
(*.f64 n (*.f64 2 PI.f64))
5.0ms
(*.f64 n (*.f64 2 PI.f64))
4.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
Compiler

Compiled 8830 to 5718 computations (35.2% saved)

series346.0ms (2.4%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

214.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))
54.0ms
(*.f64 n (*.f64 2 PI.f64))
37.0ms
(*.f64 n (*.f64 2 PI.f64))
27.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
Compiler

Compiled 1094 to 858 computations (21.6% saved)

simplify179.0ms (1.2%)

Algorithm
1×egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0507011529

prune592.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2551256
Fresh156
Picked011
Done000
Total2567263
Error
0b
Counts
263 → 7
Compiler

Compiled 8668 to 5595 computations (35.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite200.0ms (1.4%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
50×add-sqr-sqrt_binary64_782
37×sqrt-prod_binary64_776
27×*-un-lft-identity_binary64_760
26×times-frac_binary64_766
23×add-cube-cbrt_binary64_795
19×associate-*l*_binary64_701
17×pow1_binary64_821
14×add-exp-log_binary64_798
13×associate-*r*_binary64_700
12×unswap-sqr_binary64_728
11×add-cbrt-cube_binary64_796
8×unpow-prod-down_binary64_839
6×pow-prod-down_binary64_831 prod-exp_binary64_809 sqrt-pow1_binary64_778
5×sqr-pow_binary64_732
4×add-log-exp_binary64_799 cbrt-unprod_binary64_793 unpow-prod-up_binary64_838
3×sqrt-div_binary64_777 cancel-sign-sub-inv_binary64_726 rem-sqrt-square_binary64_773
2×*-commutative_binary64_691 pow-sub_binary64_836 div-inv_binary64_757 pow1/2_binary64_840
1×pow-to-exp_binary64_829 pow-exp_binary64_828 frac-times_binary64_770 associate-*l/_binary64_703 associate-*r/_binary64_702 sub-neg_binary64_753 inv-pow_binary64_845 pow-flip_binary64_834
Counts
4 → 113
Calls

4 calls:

15.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)))
5.0ms
(*.f64 n (*.f64 2 PI.f64))
5.0ms
(sqrt.f64 (/.f64 1 k))
4.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
Compiler

Compiled 2697 to 2008 computations (25.5% saved)

series258.0ms (1.8%)

Error
0b
Counts
4 → 15
Calls

4 calls:

171.0ms
(*.f64 (sqrt.f64 (/.f64 1 k)) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)))
33.0ms
(*.f64 n (*.f64 2 PI.f64))
28.0ms
(sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))
13.0ms
(sqrt.f64 (/.f64 1 k))
Compiler

Compiled 958 to 777 computations (18.9% saved)

simplify84.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049382495
149382495

prune185.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1271128
Fresh145
Picked011
Done011
Total1287135
Error
0b
Counts
135 → 7
Compiler

Compiled 2825 to 2001 computations (29.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite1.8s (12.6%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
480×times-frac_binary64_766
301×sqrt-prod_binary64_776
268×add-sqr-sqrt_binary64_782
241×associate-*r*_binary64_700
196×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
50×sqr-pow_binary64_732
46×add-exp-log_binary64_798
42×unpow-prod-down_binary64_839
28×add-cbrt-cube_binary64_796
22×unswap-sqr_binary64_728
21×pow1_binary64_821
19×prod-exp_binary64_809
16×associate-*l*_binary64_701
12×cbrt-unprod_binary64_793
11×div-exp_binary64_811
10×pow-prod-down_binary64_831
7×div-inv_binary64_757
4×add-log-exp_binary64_799 *-commutative_binary64_691
3×pow-exp_binary64_828 cbrt-undiv_binary64_794
1×pow-to-exp_binary64_829 associate-*r/_binary64_702
Counts
4 → 341
Calls

4 calls:

116.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 PI.f64 2)))) (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 PI.f64 2)))) (pow.f64 (*.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k)))
5.0ms
(*.f64 n (*.f64 PI.f64 2))
5.0ms
(*.f64 n (*.f64 PI.f64 2))
5.0ms
(*.f64 n (*.f64 PI.f64 2))
Compiler

Compiled 17009 to 11516 computations (32.3% saved)

series323.0ms (2.2%)

Error
0b
Counts
4 → 15
Calls

4 calls:

182.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 PI.f64 2)))) (/.f64 (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 PI.f64 2)))) (pow.f64 (*.f64 n (*.f64 PI.f64 2)) (/.f64 k 2))) (sqrt.f64 k)))
45.0ms
(*.f64 n (*.f64 PI.f64 2))
40.0ms
(*.f64 n (*.f64 PI.f64 2))
32.0ms
(*.f64 n (*.f64 PI.f64 2))
Compiler

Compiled 1302 to 1016 computations (22% saved)

simplify195.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
356 → 356
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
0499814347
1499814347

prune1.1s (7.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New3560356
Fresh044
Picked011
Done022
Total3567363
Error
0b
Counts
363 → 7
Compiler

Compiled 15523 to 10337 computations (33.4% saved)

regimes1.1s (7.3%)

Accuracy

Total 0.4b remaining (99.4%)

Threshold costs 0.4b (99.4%)

Compiler

Compiled 11922 to 9846 computations (17.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01531
11531

end0.0ms (0%)

sample5.8s (39.6%)

Algorithm
1×intervals
Results
845.0ms1411×body1024nan
771.0ms8000×body128valid
410.0ms2368×body128overflowed
254.0ms666×body512nan
73.0ms317×body256nan
69.0ms968×body128nan
29.0ms244×body128invalid
Compiler

Compiled 2736 to 2262 computations (17.3% saved)

Profiling

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