Details

Time bar (total: 11.6s)

analyze389.0ms (3.4%)

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)

sample79.0ms (0.7%)

Algorithm
1×intervals
Results
24.0ms256×body128valid
14.0ms28×body512nan
13.0ms29×body1024nan
10.0ms75×body128overflowed
2.0ms31×body128nan
1.0ms8×body256nan
1.0ms12×body128invalid
Compiler

Compiled 33 to 33 computations (0% saved)

simplify212.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
0490822
1490822

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.4b

Counts
2 → 2
Compiler

Compiled 74 to 69 computations (6.8% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite36.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
48×times-frac_binary64_773
42×add-sqr-sqrt_binary64_789 *-un-lft-identity_binary64_767
33×add-cube-cbrt_binary64_802
26×add-exp-log_binary64_805
22×pow-unpow_binary64_844
18×sqrt-prod_binary64_783
14×pow1_binary64_828
10×add-cbrt-cube_binary64_803
9×prod-exp_binary64_816
8×sqr-pow_binary64_739 unpow-prod-down_binary64_846
6×associate-/r*_binary64_711 pow-exp_binary64_835 pow-prod-down_binary64_838 difference-of-squares_binary64_736
5×associate-/l*_binary64_712 div-exp_binary64_818
3×associate-*r*_binary64_707 cbrt-unprod_binary64_800 add-log-exp_binary64_806 distribute-lft-out--_binary64_719 pow-pow_binary64_839
2×pow-to-exp_binary64_836 div-sub_binary64_772 pow-sub_binary64_843 div-inv_binary64_764
1×associate-*l*_binary64_708 frac-2neg_binary64_778 associate-/l/_binary64_714 cbrt-undiv_binary64_801 *-commutative_binary64_698 clear-num_binary64_766
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))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)

series492.0ms (4.2%)

Counts
3 → 9
Calls

3 calls:

310.0ms
(/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))
146.0ms
(pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))
36.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify64.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
054003540

prune754.0ms (6.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11410124
Fresh011
Picked101
Done000
Total11511126

Merged error: 0.0b

Counts
126 → 11
Compiler

Compiled 13599 to 10813 computations (20.5% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite71.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
284×times-frac_binary64_773
126×add-sqr-sqrt_binary64_789 *-un-lft-identity_binary64_767 add-cube-cbrt_binary64_802
111×sqrt-prod_binary64_783
33×add-exp-log_binary64_805
28×sqr-pow_binary64_739 unpow-prod-down_binary64_846
24×associate-/l*_binary64_712
20×pow1_binary64_828
19×add-cbrt-cube_binary64_803
11×div-exp_binary64_818
9×prod-exp_binary64_816 pow-prod-down_binary64_838
8×div-inv_binary64_764
6×associate-*r*_binary64_707 associate-/r*_binary64_711 cbrt-unprod_binary64_800
4×add-log-exp_binary64_806
3×cbrt-undiv_binary64_801 pow-exp_binary64_835 sqrt-pow1_binary64_785
2×associate-*l*_binary64_708 *-commutative_binary64_698
1×frac-2neg_binary64_778 pow-to-exp_binary64_836 associate-/l/_binary64_714 pow1/2_binary64_847 clear-num_binary64_766
Counts
4 → 241
Calls

4 calls:

17.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
8.0ms
(*.f64 (*.f64 2 PI.f64) n)
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
4.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))

series583.0ms (5%)

Counts
4 → 12
Calls

4 calls:

462.0ms
(/.f64 (/.f64 (sqrt.f64 (*.f64 (*.f64 2 PI.f64) n)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
44.0ms
(sqrt.f64 (*.f64 (*.f64 2 PI.f64) n))
39.0ms
(*.f64 (*.f64 2 PI.f64) n)
38.0ms
(*.f64 (*.f64 2 PI.f64) n)

simplify128.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
253 → 253
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0509011746

prune913.0ms (7.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2503253
Fresh4610
Picked011
Done000
Total25410264

Merged error: 0b

Counts
264 → 10
Compiler

Compiled 15938 to 11376 computations (28.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (sqrt.f64 (*.f64 2 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
1.0b
(sqrt.f64 (*.f64 2 PI.f64))

rewrite207.0ms (1.8%)

Algorithm
1×rewrite-expression-head
Rules
816×times-frac_binary64_773
413×sqrt-prod_binary64_783
402×add-sqr-sqrt_binary64_789
366×*-un-lft-identity_binary64_767 add-cube-cbrt_binary64_802
211×associate-*r*_binary64_707
82×sqr-pow_binary64_739
78×unpow-prod-down_binary64_846
55×add-exp-log_binary64_805
34×associate-/l*_binary64_712
23×add-cbrt-cube_binary64_803
22×div-exp_binary64_818
16×prod-exp_binary64_816
15×div-inv_binary64_764
14×pow1_binary64_828
11×unswap-sqr_binary64_735
6×associate-/r*_binary64_711 cbrt-undiv_binary64_801 cbrt-unprod_binary64_800 pow-exp_binary64_835
5×associate-*l*_binary64_708 pow-prod-down_binary64_838
4×add-log-exp_binary64_806
2×pow-to-exp_binary64_836 *-commutative_binary64_698 sqrt-pow1_binary64_785
1×frac-2neg_binary64_778 associate-/l/_binary64_714 pow1/2_binary64_847 associate-*r/_binary64_709 clear-num_binary64_766
Counts
4 → 535
Calls

4 calls:

71.0ms
(*.f64 (sqrt.f64 (*.f64 2 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
22.0ms
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
2.0ms
(sqrt.f64 (*.f64 2 PI.f64))

series872.0ms (7.5%)

Counts
4 → 10
Calls

4 calls:

473.0ms
(*.f64 (sqrt.f64 (*.f64 2 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
360.0ms
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
39.0ms
(*.f64 (*.f64 2 PI.f64) n)
0.0ms
(sqrt.f64 (*.f64 2 PI.f64))

simplify202.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
545 → 545
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0504322200

prune1.3s (11.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New5441545
Fresh268
Picked011
Done011
Total5469555

Merged error: 0b

Counts
555 → 9
Compiler

Compiled 20331 to 11602 computations (42.9% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
0.2b
(*.f64 (*.f64 2 PI.f64) n)
0.3b
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
1.0b
(sqrt.f64 PI.f64)

rewrite192.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Rules
798×times-frac_binary64_773
405×sqrt-prod_binary64_783
367×add-sqr-sqrt_binary64_789
366×*-un-lft-identity_binary64_767 add-cube-cbrt_binary64_802
211×associate-*r*_binary64_707
89×add-exp-log_binary64_805
78×sqr-pow_binary64_739 unpow-prod-down_binary64_846
35×add-cbrt-cube_binary64_803
34×associate-/l*_binary64_712
33×prod-exp_binary64_816 div-exp_binary64_818
15×pow1_binary64_828 div-inv_binary64_764
12×cbrt-unprod_binary64_800
9×cbrt-undiv_binary64_801 pow-exp_binary64_835
6×associate-/r*_binary64_711 pow-prod-down_binary64_838
4×add-log-exp_binary64_806
3×pow-to-exp_binary64_836
2×associate-*l*_binary64_708 *-commutative_binary64_698
1×frac-2neg_binary64_778 rem-sqrt-square_binary64_780 associate-/l/_binary64_714 pow1/2_binary64_847 associate-*r/_binary64_709 sqrt-pow1_binary64_785 clear-num_binary64_766
Counts
4 → 534
Calls

4 calls:

56.0ms
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
22.0ms
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
6.0ms
(*.f64 (*.f64 2 PI.f64) n)
1.0ms
(sqrt.f64 PI.f64)

series896.0ms (7.7%)

Counts
4 → 10
Calls

4 calls:

491.0ms
(*.f64 (*.f64 (sqrt.f64 2) (sqrt.f64 PI.f64)) (/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k)))
366.0ms
(/.f64 (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 k 2))) (sqrt.f64 k))
39.0ms
(*.f64 (*.f64 2 PI.f64) n)
0.0ms
(sqrt.f64 PI.f64)

simplify200.0ms (1.7%)

Algorithm
1×egg-herbie
Counts
544 → 544
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0536422083

prune1.3s (10.9%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New5440544
Fresh066
Picked011
Done022
Total5449553

Merged error: 0b

Counts
553 → 9
Compiler

Compiled 20292 to 11183 computations (44.9% saved)

regimes74.0ms (0.6%)

Compiler

Compiled 752 to 617 computations (18% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01531
11531

end0.0ms (0%)

sample2.6s (22.6%)

Algorithm
1×intervals
Results
758.0ms8000×body128valid
589.0ms1275×body1024nan
337.0ms2377×body128overflowed
227.0ms728×body512nan
61.0ms340×body256nan
60.0ms1001×body128nan
24.0ms236×body128invalid
Compiler

Compiled 282 to 233 computations (17.4% saved)

Profiling

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