Details

Time bar (total: 6.9s)

analyze382.0ms (5.5%)

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)

sample80.0ms (1.2%)

Algorithm
1×intervals
Results
24.0ms256×body128valid
21.0ms35×body1024nan
10.0ms73×body128overflowed
9.0ms28×body512nan
2.0ms32×body128nan
1.0ms8×body256nan
0.0ms2×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify208.0ms (3%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
0490822
1490822

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.3b

Counts
2 → 2
Compiler

Compiled 44 to 41 computations (6.8% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite36.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
48×times-frac_binary64_757
42×*-un-lft-identity_binary64_751 add-sqr-sqrt_binary64_772
33×add-cube-cbrt_binary64_783
26×add-exp-log_binary64_786
22×pow-unpow_binary64_825
18×sqrt-prod_binary64_766
14×pow1_binary64_809
10×add-cbrt-cube_binary64_784
9×prod-exp_binary64_797
8×sqr-pow_binary64_723 unpow-prod-down_binary64_827
6×pow-exp_binary64_816 associate-/r*_binary64_697 pow-prod-down_binary64_819 difference-of-squares_binary64_720
5×associate-/l*_binary64_698 div-exp_binary64_799
3×distribute-lft-out--_binary64_705 add-log-exp_binary64_787 pow-pow_binary64_820 associate-*r*_binary64_693 cbrt-unprod_binary64_781
2×pow-to-exp_binary64_817 div-sub_binary64_756 div-inv_binary64_748 pow-sub_binary64_824
1×associate-/l/_binary64_700 *-commutative_binary64_684 cbrt-undiv_binary64_782 frac-2neg_binary64_762 associate-*l*_binary64_694 clear-num_binary64_750
Counts
3 → 115
Calls

3 calls:

11.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
8.0ms
(/.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)

series501.0ms (7.2%)

Counts
3 → 9
Calls

3 calls:

309.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
154.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
38.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify65.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
052413540

prune208.0ms (3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11311124
Fresh011
Picked101
Done000
Total11412126

Merged error: 0.0b

Counts
126 → 12
Compiler

Compiled 3298 to 2256 computations (31.6% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))

rewrite43.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
127×add-exp-log_binary64_786
67×prod-exp_binary64_797
36×pow-exp_binary64_816
30×div-exp_binary64_799
20×pow1_binary64_809
19×add-cbrt-cube_binary64_784
15×add-cube-cbrt_binary64_783 *-un-lft-identity_binary64_751 add-sqr-sqrt_binary64_772
14×times-frac_binary64_757
13×pow-unpow_binary64_825
12×pow-to-exp_binary64_817
9×pow-prod-down_binary64_819
7×cbrt-unprod_binary64_781
6×associate-*r*_binary64_693
5×associate-/l*_binary64_698
4×add-log-exp_binary64_787
3×sqr-pow_binary64_723 unpow-prod-down_binary64_827 pow-pow_binary64_820
2×*-commutative_binary64_684 div-inv_binary64_748 cbrt-undiv_binary64_782 associate-*l*_binary64_694
1×associate-/r*_binary64_697 frac-2neg_binary64_762 clear-num_binary64_750
Counts
4 → 118
Calls

4 calls:

11.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
7.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
5.0ms
(*.f64 (*.f64 2 PI.f64) n)
5.0ms
(*.f64 (*.f64 2 PI.f64) n)

series720.0ms (10.4%)

Counts
4 → 12
Calls

4 calls:

435.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2)) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
208.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 1 2))
40.0ms
(*.f64 (*.f64 2 PI.f64) n)
36.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify59.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
054372652

prune188.0ms (2.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1264130
Fresh3811
Picked011
Done000
Total12913142

Merged error: 0b

Counts
142 → 13
Compiler

Compiled 3459 to 2402 computations (30.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.4b
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))) (sqrt.f64 k))

rewrite42.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
59×sqrt-prod_binary64_766
42×times-frac_binary64_757
37×add-cube-cbrt_binary64_783 *-un-lft-identity_binary64_751 add-sqr-sqrt_binary64_772
21×add-cbrt-cube_binary64_784 add-exp-log_binary64_786
19×pow1_binary64_809
9×prod-exp_binary64_797 pow-prod-down_binary64_819 associate-*r*_binary64_693 cbrt-unprod_binary64_781
7×associate-/l*_binary64_698
6×associate-/r*_binary64_697
4×add-log-exp_binary64_787
3×*-commutative_binary64_684 associate-*l*_binary64_694
1×sqrt-undiv_binary64_771 div-inv_binary64_748 cbrt-undiv_binary64_782 frac-2neg_binary64_762 clear-num_binary64_750 div-exp_binary64_799
Counts
4 → 122
Calls

4 calls:

10.0ms
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))) (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series320.0ms (4.6%)

Counts
4 → 12
Calls

4 calls:

207.0ms
(/.f64 (sqrt.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))) (sqrt.f64 k))
38.0ms
(*.f64 (*.f64 2 PI.f64) n)
38.0ms
(*.f64 (*.f64 2 PI.f64) n)
38.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify59.0ms (0.9%)

Algorithm
1×egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
054832757

prune242.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1331134
Fresh4711
Picked011
Done011
Total13710147

Merged error: 0b

Counts
147 → 10
Compiler

Compiled 4833 to 3274 computations (32.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
0.3b
(*.f64 (*.f64 2 PI.f64) n)
0.4b
(/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k))
1.0b
(sqrt.f64 (*.f64 2 PI.f64))

rewrite73.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Rules
100×times-frac_binary64_757 add-sqr-sqrt_binary64_772
67×sqrt-prod_binary64_766
55×add-exp-log_binary64_786
54×add-cube-cbrt_binary64_783 *-un-lft-identity_binary64_751
37×associate-*r*_binary64_693
29×associate-*l*_binary64_694
23×add-cbrt-cube_binary64_784
21×prod-exp_binary64_797
17×div-exp_binary64_799
15×unswap-sqr_binary64_719
14×pow1_binary64_809
12×sqr-pow_binary64_723
7×cbrt-unprod_binary64_781
6×pow-exp_binary64_816 associate-/r*_binary64_697 unpow-prod-down_binary64_827
5×pow-prod-down_binary64_819 cbrt-undiv_binary64_782
4×add-log-exp_binary64_787 associate-/l*_binary64_698
3×div-inv_binary64_748
2×pow-to-exp_binary64_817 *-commutative_binary64_684 sqrt-pow1_binary64_768
1×frac-times_binary64_761 pow1/2_binary64_828 sqrt-undiv_binary64_771 associate-*r/_binary64_695 frac-2neg_binary64_762 clear-num_binary64_750 associate-*l/_binary64_696
Counts
4 → 181
Calls

4 calls:

35.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
6.0ms
(/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
3.0ms
(sqrt.f64 (*.f64 2 PI.f64))

series678.0ms (9.8%)

Counts
4 → 10
Calls

4 calls:

522.0ms
(*.f64 (/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))))
117.0ms
(/.f64 (sqrt.f64 (*.f64 2 PI.f64)) (sqrt.f64 k))
38.0ms
(*.f64 (*.f64 2 PI.f64) n)
0.0ms
(sqrt.f64 (*.f64 2 PI.f64))

simplify87.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050275941

prune294.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1901191
Fresh437
Picked011
Done112
Total1956201

Merged error: 0b

Counts
201 → 6
Compiler

Compiled 5699 to 3476 computations (39% saved)

regimes68.0ms (1%)

Compiler

Compiled 530 to 462 computations (12.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01932
11932

end0.0ms (0%)

sample2.5s (36.1%)

Algorithm
1×intervals
Results
749.0ms8000×body128valid
599.0ms1297×body1024nan
328.0ms2321×body128overflowed
211.0ms674×body512nan
56.0ms990×body128nan
53.0ms298×body256nan
22.0ms227×body128invalid
Compiler

Compiled 158 to 138 computations (12.7% saved)

Profiling

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