Details

Time bar (total: 24.9s)

analyze785.0ms (3.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
3.1%96.8%0.1%6
15.6%81.2%3.2%7
23.4%72.6%4%8
32.4%56.2%11.4%9
36.3%51.7%12%10
40.7%42.9%16.4%11
42.6%40.3%17.1%12
44.5%35.7%19.8%13
45.5%34.4%20.1%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample154.0ms (0.6%)

Algorithm
intervals
Results
62.0ms53×body2048valid
49.0ms90×body1024valid
8.0ms34×body512valid
5.0msbody4096valid
5.0msbody1024invalid
3.0ms57×body128valid
3.0ms20×body256valid
2.0msbody512invalid
2.0ms17×body128invalid
1.0msbody256invalid
0.0msbody128nan
Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify166.0ms (0.7%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
0503622

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
47.2b
Counts
2 → 1
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

8.7b
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
8.0b
(pow.f64 (+.f64 1 (/.f64 i n)) n)
1.6b
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
0.0b
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
0.0b
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.6b
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.0b
(pow.f64 (+.f64 1 (/.f64 i n)) n)
8.7b
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite324.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
584×times-frac_binary64_2741
486×add-sqr-sqrt_binary64_2757
367×*-un-lft-identity_binary64_2735
225×add-cube-cbrt_binary64_2770
174×associate-*r*_binary64_2675
168×difference-of-squares_binary64_2704
88×unpow-prod-down_binary64_2814
85×sqr-pow_binary64_2707
84×difference-of-sqr-1_binary64_2705
29×div-inv_binary64_2732
28×distribute-lft-out--_binary64_2687
19×add-exp-log_binary64_2773
18×add-cbrt-cube_binary64_2771
13×associate-/l*_binary64_2680 associate-/r*_binary64_2679
pow1_binary64_2796
cbrt-undiv_binary64_2769 div-exp_binary64_2786 add-log-exp_binary64_2774
pow-unpow_binary64_2812 associate-*l*_binary64_2676 unswap-sqr_binary64_2703 cancel-sign-sub-inv_binary64_2701 prod-exp_binary64_2784 cbrt-unprod_binary64_2768
associate-/l/_binary64_2682 flip3--_binary64_2739 flip--_binary64_2710 associate-/r/_binary64_2681
div-sub_binary64_2740 pow-to-exp_binary64_2804 clear-num_binary64_2734 sub-neg_binary64_2728 pow-prod-down_binary64_2806 diff-log_binary64_2827 pow-exp_binary64_2803 *-commutative_binary64_2666 distribute-lft-out_binary64_2686 frac-2neg_binary64_2746 associate-*r/_binary64_2677 pow-pow_binary64_2807
Counts
4 → 451
Calls

8 calls:

60.0ms
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
20.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms
(pow.f64 (+.f64 1 (/.f64 i n)) n)
0.0ms
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))

series1.6s (6.4%)

Counts
4 → 60
Calls

4 calls:

605.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
567.0ms
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
281.0ms
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
150.0ms
(pow.f64 (+.f64 1 (/.f64 i n)) n)
Compiler

Compiled 4342 to 3245 computations (25.3% saved)

simplify219.0ms (0.9%)

Algorithm
egg-herbie
Counts
511 → 511
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
0494018028
1494018028

prune1.2s (4.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New49912511
Fresh000
Picked101
Done000
Total50012512
Error
0.6b
Counts
512 → 12
Compiler

Compiled 16701 to 8949 computations (46.4% saved)

localize23.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i)))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))
0.0b
(+.f64 i (*.f64 i i))
0.0b
(+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i)))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.2b
(*.f64 1/6 (*.f64 i i))
0.3b
(*.f64 1/3 (/.f64 i (/.f64 n i)))
2.8b
(+.f64 (+.f64 (*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i)))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))) (*.f64 -1/2 (+.f64 i (*.f64 i i))))
4.3b
(*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i))))

rewrite67.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
69×times-frac_binary64_2741
55×add-sqr-sqrt_binary64_2757
48×associate-*r*_binary64_2675
43×*-un-lft-identity_binary64_2735 add-cube-cbrt_binary64_2770
23×associate-*r/_binary64_2677
20×frac-add_binary64_2743 add-cbrt-cube_binary64_2771 add-exp-log_binary64_2773
18×flip-+_binary64_2709 flip3-+_binary64_2738
13×pow1_binary64_2796 add-log-exp_binary64_2774
associate-*l*_binary64_2676
prod-exp_binary64_2784 cbrt-unprod_binary64_2768
sum-log_binary64_2826
pow-prod-down_binary64_2806 unswap-sqr_binary64_2703
div-inv_binary64_2732
cbrt-undiv_binary64_2769 div-exp_binary64_2786 *-commutative_binary64_2666
distribute-rgt-in_binary64_2685 distribute-lft-in_binary64_2684 associate-+r+_binary64_2667
associate-+l+_binary64_2668 associate-/r/_binary64_2681 +-commutative_binary64_2665
Counts
4 → 135
Calls

8 calls:

16.0ms
(*.f64 1/3 (/.f64 i (/.f64 n i)))
14.0ms
(+.f64 (+.f64 (*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i)))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))) (*.f64 -1/2 (+.f64 i (*.f64 i i))))
7.0ms
(*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i))))
6.0ms
(*.f64 1/6 (*.f64 i i))
0.0ms
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))

series677.0ms (2.7%)

Counts
4 → 36
Calls

4 calls:

432.0ms
(+.f64 (+.f64 (*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i)))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))) (*.f64 -1/2 (+.f64 i (*.f64 i i))))
138.0ms
(*.f64 n (+.f64 (*.f64 i 1/2) (*.f64 1/6 (*.f64 i i))))
82.0ms
(*.f64 1/3 (/.f64 i (/.f64 n i)))
26.0ms
(*.f64 1/6 (*.f64 i i))
Compiler

Compiled 1669 to 1277 computations (23.5% saved)

simplify71.0ms (0.3%)

Algorithm
egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
050315453

prune365.0ms (1.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1692171
Fresh01111
Picked011
Done000
Total16914183
Error
0.6b
Counts
183 → 14
Compiler

Compiled 7884 to 4151 computations (47.3% saved)

localize33.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 1/2 (*.f64 i 1/6))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
4.3b
(*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))

rewrite92.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
100×associate-*r/_binary64_2677
60×frac-add_binary64_2743
52×flip-+_binary64_2709 flip3-+_binary64_2738
42×cbrt-div_binary64_2767
pow1_binary64_2796 add-cbrt-cube_binary64_2771 add-exp-log_binary64_2773 cbrt-prod_binary64_2766
*-un-lft-identity_binary64_2735 add-cube-cbrt_binary64_2770 add-sqr-sqrt_binary64_2757
distribute-rgt-in_binary64_2685 distribute-lft-in_binary64_2684 add-log-exp_binary64_2774
associate-*l*_binary64_2676 pow1/3_binary64_2817 pow-prod-down_binary64_2806 prod-exp_binary64_2784 cbrt-unprod_binary64_2768
*-commutative_binary64_2666 associate-*r*_binary64_2675
Counts
4 → 99
Calls

8 calls:

18.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
7.0ms
(*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6))))
0.0ms
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))

series3.6s (14.5%)

Counts
4 → 54
Calls

4 calls:

1.2s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.2s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
147.0ms
(*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6))))
Compiler

Compiled 14486 to 11066 computations (23.6% saved)

simplify140.0ms (0.6%)

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500014359

prune1.1s (4.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1521153
Fresh01212
Picked011
Done011
Total15215167
Error
0.6b
Counts
167 → 15
Compiler

Compiled 20294 to 11384 computations (43.9% saved)

localize50.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
0.0b
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
15.5b
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))

rewrite124.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
128×associate-*r/_binary64_2677
80×frac-add_binary64_2743
68×flip-+_binary64_2709 flip3-+_binary64_2738
56×cbrt-div_binary64_2767
12×cbrt-prod_binary64_2766
*-un-lft-identity_binary64_2735 add-cube-cbrt_binary64_2770 add-sqr-sqrt_binary64_2757
pow1_binary64_2796 pow1/3_binary64_2817 add-cbrt-cube_binary64_2771 add-log-exp_binary64_2774 add-exp-log_binary64_2773
Counts
4 → 100
Calls

8 calls:

16.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
16.0ms
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
0.0ms
(+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i))))

series4.6s (18.3%)

Counts
4 → 60
Calls

4 calls:

1.2s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
1.1s
(cbrt.f64 (+.f64 (*.f64 n (*.f64 i (+.f64 1/2 (*.f64 i 1/6)))) (+.f64 (*.f64 -1/2 (+.f64 i (*.f64 i i))) (+.f64 n (*.f64 1/3 (/.f64 i (/.f64 n i)))))))
Compiler

Compiled 22652 to 16464 computations (27.3% saved)

simplify163.0ms (0.7%)

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0519918528

prune2.0s (8.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1591160
Fresh01212
Picked101
Done022
Total16015175
Error
0.6b
Counts
175 → 15
Compiler

Compiled 32016 to 17817 computations (44.3% saved)

regimes774.0ms (3.1%)

Accuracy

Total 10.6b remaining (95.9%)

Threshold costs 0b (0%)

Compiler

Compiled 9686 to 6304 computations (34.9% saved)

bsearch236.0ms (0.9%)

Steps
ItersRangePoint
12
13.435813393928033
8.677803220342494e+40
13.565025160760564
9
-4.357261029441336
-7.481267210665203e-06
-0.00011156580364168401
Compiler

Compiled 1 to 2 computations (-100% saved)

simplify9.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0384306
1384306

end0.0ms (0%)

sample6.3s (25.2%)

Algorithm
intervals
Results
2.1s1744×body2048valid
1.4s2702×body1024valid
283.0ms1160×body512valid
110.0ms1806×body128valid
105.0ms179×body1024invalid
83.0ms228×body512invalid
79.0ms567×body256valid
43.0ms471×body128invalid
42.0ms21×body4096valid
33.0ms153×body256invalid
20.0ms22×body2048invalid
13.0ms288×body128nan
Compiler

Compiled 2632 to 1707 computations (35.1% saved)

Pareto

0

Profiling

Loading profile data...