Details

Time bar (total: 2.5min)

analyze523.0ms (0.3%)

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)

sample74.0ms (0%)

Algorithm
1×intervals
Results
18.0ms256×body128valid
17.0ms39×body1024nan
10.0ms77×body128overflowed
8.0ms26×body512nan
2.0ms33×body128nan
2.0ms9×body256nan
1.0ms9×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify50.0ms (0%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0493322
1493322

prune8.0ms (0%)

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%)

Local error

Found 3 expressions with local error:

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

rewrite205.0ms (0.1%)

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 difference-of-squares_binary64_729 pow-exp_binary64_828 associate-/r*_binary64_704
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×div-inv_binary64_757 div-sub_binary64_765 pow-sub_binary64_836 pow-to-exp_binary64_829
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))
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)

series418.0ms (0.3%)

Error
0.2b
Counts
3 → 18
Calls

3 calls:

204.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
163.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
28.0ms
(*.f64 (*.f64 2 PI.f64) n)
Compiler

Compiled 1100 to 864 computations (21.5% saved)

simplify89.0ms (0.1%)

Algorithm
1×egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049693385
149693385

prune182.0ms (0.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

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

Compiled 3107 to 1959 computations (36.9% saved)

localize16.0ms (0%)

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

rewrite198.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
124×add-exp-log_binary64_798
65×prod-exp_binary64_809
36×pow-exp_binary64_828
30×div-exp_binary64_811
18×add-sqr-sqrt_binary64_782
17×pow1_binary64_821
16×add-cbrt-cube_binary64_796 add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
14×times-frac_binary64_766
13×pow-unpow_binary64_837
12×pow-to-exp_binary64_829
7×pow-prod-down_binary64_831
6×associate-*r*_binary64_700
5×cbrt-unprod_binary64_793 associate-/l*_binary64_705
4×add-log-exp_binary64_799 associate-*l*_binary64_701
3×unpow-prod-down_binary64_839 sqr-pow_binary64_732 pow-pow_binary64_832
2×*-commutative_binary64_691 cbrt-undiv_binary64_794 div-inv_binary64_757
1×unswap-sqr_binary64_728 frac-2neg_binary64_771 clear-num_binary64_759 associate-/r*_binary64_704
Counts
4 → 118
Calls

4 calls:

9.0ms
(/.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))))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
4.0ms
(*.f64 n PI.f64)
Compiler

Compiled 3457 to 2289 computations (33.8% saved)

series305.0ms (0.2%)

Error
0.0b
Counts
4 → 15
Calls

4 calls:

142.0ms
(/.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))))
95.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
30.0ms
(*.f64 (*.f64 2 PI.f64) n)
24.0ms
(*.f64 n PI.f64)
Compiler

Compiled 1100 to 849 computations (22.8% saved)

simplify68.0ms (0%)

Algorithm
1×egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049992500
149992500

prune162.0ms (0.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1312133
Fresh178
Picked101
Done000
Total1339142
Error
0.0b
Counts
142 → 9
Compiler

Compiled 3316 to 2076 computations (37.4% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite3.5s (2.3%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
1787×times-frac_binary64_766
718×add-sqr-sqrt_binary64_782
714×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
518×sqrt-prod_binary64_776
173×associate-/r*_binary64_704
124×unpow-prod-down_binary64_839 sqr-pow_binary64_732
94×add-exp-log_binary64_798
58×div-exp_binary64_811
37×div-inv_binary64_757
22×add-cbrt-cube_binary64_796
14×prod-exp_binary64_809
12×pow-exp_binary64_828
9×pow1_binary64_821 cbrt-undiv_binary64_794 associate-/l*_binary64_705
7×1-exp_binary64_804 rec-exp_binary64_810
6×associate-*l*_binary64_701 associate-*r*_binary64_700 associate-/r/_binary64_706
4×add-log-exp_binary64_799 pow-to-exp_binary64_829
2×pow-prod-down_binary64_831 cbrt-unprod_binary64_793 unswap-sqr_binary64_728 *-commutative_binary64_691 frac-2neg_binary64_771 clear-num_binary64_759
1×inv-pow_binary64_845 pow-flip_binary64_834
Counts
4 → 865
Calls

4 calls:

38.0ms
(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
20.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
4.0ms
(*.f64 n PI.f64)
4.0ms
(*.f64 n PI.f64)
Compiler

Compiled 38180 to 22883 computations (40.1% saved)

series353.0ms (0.2%)

Error
0.0b
Counts
4 → 18
Calls

4 calls:

150.0ms
(/.f64 1 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2)))))
140.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 2 (*.f64 n PI.f64))) (pow.f64 (*.f64 2 (*.f64 n PI.f64)) (/.f64 k 2))))
24.0ms
(*.f64 n PI.f64)
22.0ms
(*.f64 n PI.f64)
Compiler

Compiled 1504 to 1180 computations (21.5% saved)

simplify411.0ms (0.3%)

Algorithm
1×egg-herbie
Counts
883 → 883
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0548048568

prune2.8s (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New8812883
Fresh448
Picked011
Done000
Total8857892
Error
0b
Counts
892 → 7
Compiler

Compiled 35048 to 20128 computations (42.6% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite2.1min (84%)

Algorithm
1×rewrite-expression-head
Error
0b
Rules
25846×times-frac_binary64_766
9305×add-sqr-sqrt_binary64_782
9301×add-cube-cbrt_binary64_795 *-un-lft-identity_binary64_760
8054×sqrt-prod_binary64_776
3856×unpow-prod-down_binary64_839
2056×sqr-pow_binary64_732
488×div-inv_binary64_757
173×associate-/r*_binary64_704
118×add-exp-log_binary64_798
87×div-exp_binary64_811
52×associate-/l*_binary64_705
49×associate-/r/_binary64_706
34×add-cbrt-cube_binary64_796
18×cbrt-undiv_binary64_794
16×pow-exp_binary64_828
11×pow-to-exp_binary64_829
8×pow1_binary64_821
7×prod-exp_binary64_809
6×associate-*l*_binary64_701 associate-*r*_binary64_700
4×add-log-exp_binary64_799
2×frac-2neg_binary64_771 clear-num_binary64_759 pow-prod-down_binary64_831 cbrt-unprod_binary64_793 unswap-sqr_binary64_728 *-commutative_binary64_691
1×associate-/l/_binary64_707
Counts
4 → 7319
Calls

4 calls:

212.0ms
(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2)))))
13.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))))
4.0ms
(*.f64 n PI.f64)
4.0ms
(*.f64 n PI.f64)
Compiler

Compiled 410601 to 243309 computations (40.7% saved)

series345.0ms (0.2%)

Error
0b
Counts
4 → 18
Calls

4 calls:

180.0ms
(/.f64 (/.f64 (sqrt.f64 2) (pow.f64 2 (/.f64 k 2))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2)))))
107.0ms
(/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n PI.f64)) (pow.f64 (*.f64 n PI.f64) (/.f64 k 2))))
20.0ms
(*.f64 n PI.f64)
18.0ms
(*.f64 n PI.f64)
Compiler

Compiled 1741 to 1323 computations (24% saved)

simplify4.6s (3%)

Algorithm
1×egg-herbie
Counts
7337 → 7337
Iterations

Useful iterations: 0 (263.0ms)

IterNodesCost
06185652112

prune9.7s (6.5%)

Profiling

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