Details

Time bar (total: 10.5s)

analyze803.0ms (7.6%)

Algorithm
1×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%36%19.4%13
45.5%34.5%20%14

sample200.0ms (1.9%)

Algorithm
1×intervals
Results
82.0ms37×body2560valid
72.0ms86×body1280valid
17.0ms46×body640valid
4.0ms20×body320valid
3.0ms7×body640invalid
3.0ms48×body80valid
2.0ms19×body160valid
2.0ms7×body320invalid
2.0ms3×body1280invalid
1.0ms12×body80invalid
1.0ms3×body160invalid
0.0ms5×body80nan

simplify43.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0528115

prune13.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 46.0b

Counts
2 → 1

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
2.4b
(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
5.6b
(pow.f64 (+.f64 1.0 (/.f64 i n)) n)
11.9b
(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))

rewrite94.0ms (0.9%)

Algorithm
1×rewrite-expression-head
Rules
320×times-frac_binary64
289×add-sqr-sqrt_binary64
198×*-un-lft-identity_binary64
140×add-cube-cbrt_binary64
96×associate-*r*_binary64
84×difference-of-squares_binary64
32×unpow-prod-down_binary64
29×sqr-pow_binary64
28×distribute-lft-out--_binary64
19×add-exp-log_binary64
18×add-cbrt-cube_binary64
17×div-inv_binary64
13×associate-/r*_binary64
7×pow1_binary64 associate-/l*_binary64
6×add-log-exp_binary64 cbrt-undiv_binary64 div-exp_binary64
3×pow-unpow_binary64 cbrt-unprod_binary64 associate-*l*_binary64 unswap-sqr_binary64 prod-exp_binary64
2×associate-/l/_binary64 flip3--_binary64 associate-/r/_binary64 flip--_binary64
1×pow-to-exp_binary64 pow-prod-down_binary64 sub-neg_binary64 diff-log_binary64 distribute-lft-out_binary64 associate-*r/_binary64 pow-pow_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 pow-exp_binary64 *-commutative_binary64
Counts
4 → 280
Calls

4 calls:

37.0ms
(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
21.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))
11.0ms
(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
8.0ms
(pow.f64 (+.f64 1.0 (/.f64 i n)) n)

series245.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

84.0ms
(*.f64 100.0 (/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n)))
80.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0) (/.f64 i n))
46.0ms
(-.f64 (pow.f64 (+.f64 1.0 (/.f64 i n)) n) 1.0)
34.0ms
(pow.f64 (+.f64 1.0 (/.f64 i n)) n)

simplify86.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049885853
149885853

prune507.0ms (4.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2848292
Fresh000
Picked101
Done000
Total2858293

Merged error: 20.4b

Counts
293 → 8

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5)))
0.1b
(*.f64 100.0 (/.f64 (-.f64 (+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5))) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))) (/.f64 i n)))
11.9b
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))
19.4b
(/.f64 (-.f64 (+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5))) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))) (/.f64 i n))

rewrite63.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
144×times-frac_binary64
92×add-sqr-sqrt_binary64
83×*-un-lft-identity_binary64 add-cube-cbrt_binary64
45×associate-*r*_binary64
27×add-exp-log_binary64 add-cbrt-cube_binary64
16×pow1_binary64
13×associate-/r*_binary64
9×add-log-exp_binary64 cbrt-unprod_binary64 prod-exp_binary64 div-inv_binary64
7×pow-prod-down_binary64 associate-*l*_binary64
6×cbrt-undiv_binary64 div-exp_binary64
3×unswap-sqr_binary64 associate-/l*_binary64 sum-log_binary64
2×associate-/l/_binary64 associate-/r/_binary64 *-commutative_binary64
1×flip3-+_binary64 flip3--_binary64 associate-*r/_binary64 log-pow_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 flip--_binary64 flip-+_binary64 associate-+r+_binary64
Counts
4 → 174
Calls

4 calls:

21.0ms
(*.f64 100.0 (/.f64 (-.f64 (+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5))) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))) (/.f64 i n)))
15.0ms
(/.f64 (-.f64 (+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5))) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))) (/.f64 i n))
10.0ms
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))
8.0ms
(+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5)))

series75.0ms (0.7%)

Counts
4 → 12
Calls

4 calls:

29.0ms
(*.f64 100.0 (/.f64 (-.f64 (+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5))) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))) (/.f64 i n)))
23.0ms
(/.f64 (-.f64 (+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5))) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))) (/.f64 i n))
15.0ms
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))
7.0ms
(+.f64 (*.f64 1.0 i) (+.f64 (*.f64 n (log.f64 1.0)) (*.f64 (*.f64 i i) 0.5)))

simplify58.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
058555678

prune486.0ms (4.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New17511186
Fresh167
Picked101
Done000
Total17717194

Merged error: 7.7b

Counts
194 → 17

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b
(*.f64 i (+.f64 1.0 (*.f64 i 0.5)))
0.1b
(*.f64 100.0 (*.f64 (/.f64 (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))) i) n))
11.2b
(/.f64 (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))) i)
11.9b
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))

rewrite48.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
26×add-exp-log_binary64 add-cbrt-cube_binary64
21×pow1_binary64
18×add-sqr-sqrt_binary64
16×*-un-lft-identity_binary64 add-cube-cbrt_binary64
12×cbrt-unprod_binary64 prod-exp_binary64
10×pow-prod-down_binary64 associate-*l*_binary64
9×times-frac_binary64
7×associate-*r/_binary64
6×associate-/l/_binary64
5×associate-*r*_binary64
4×flip3-+_binary64 add-log-exp_binary64 frac-add_binary64 flip-+_binary64
3×associate-/r*_binary64 associate-/l*_binary64 *-commutative_binary64
2×flip3--_binary64 cbrt-undiv_binary64 div-exp_binary64 flip--_binary64
1×associate-+r-_binary64 log-pow_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 div-sub_binary64 clear-num_binary64 frac-2neg_binary64 div-inv_binary64 associate-*l/_binary64
Counts
4 → 99
Calls

4 calls:

16.0ms
(*.f64 100.0 (*.f64 (/.f64 (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))) i) n))
13.0ms
(/.f64 (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))) i)
8.0ms
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))
6.0ms
(*.f64 i (+.f64 1.0 (*.f64 i 0.5)))

series68.0ms (0.6%)

Counts
4 → 12
Calls

4 calls:

26.0ms
(*.f64 100.0 (*.f64 (/.f64 (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))) i) n))
18.0ms
(/.f64 (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))) i)
16.0ms
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))
8.0ms
(*.f64 i (+.f64 1.0 (*.f64 i 0.5)))

simplify56.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049932061
149932061

prune236.0ms (2.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New1083111
Fresh31316
Picked011
Done000
Total11117128

Merged error: 7.7b

Counts
128 → 17

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b
(*.f64 100.0 (*.f64 (/.f64 1 i) (*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))))))
1.7b
(*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))))
11.9b
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))
12.6b
(*.f64 (/.f64 1 i) (*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))))))

rewrite70.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
75×associate-*r/_binary64
69×add-exp-log_binary64
45×add-cbrt-cube_binary64
40×prod-exp_binary64
30×pow1_binary64
24×cbrt-unprod_binary64
23×associate-*l*_binary64
20×frac-add_binary64
17×distribute-lft-in_binary64 distribute-rgt-in_binary64 add-sqr-sqrt_binary64
16×pow-prod-down_binary64
15×flip3-+_binary64 *-un-lft-identity_binary64 add-cube-cbrt_binary64 flip-+_binary64
12×frac-times_binary64
10×flip3--_binary64 flip--_binary64
9×times-frac_binary64
8×div-exp_binary64
6×associate-*r*_binary64
4×add-log-exp_binary64 1-exp_binary64 cbrt-undiv_binary64 rec-exp_binary64 *-commutative_binary64
2×associate-*l/_binary64
1×log-pow_binary64 unswap-sqr_binary64 div-inv_binary64
Counts
4 → 151
Calls

4 calls:

21.0ms
(*.f64 100.0 (*.f64 (/.f64 1 i) (*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))))))
20.0ms
(*.f64 (/.f64 1 i) (*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))))))
13.0ms
(*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))))
8.0ms
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))

series93.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

26.0ms
(*.f64 100.0 (*.f64 (/.f64 1 i) (*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))))))
24.0ms
(*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5)))))
23.0ms
(*.f64 (/.f64 1 i) (*.f64 n (+.f64 (*.f64 i (+.f64 1.0 (*.f64 i 0.5))) (-.f64 (*.f64 n (log.f64 1.0)) (*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))))))
19.0ms
(*.f64 (log.f64 1.0) (*.f64 (*.f64 i i) 0.5))

simplify57.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
052874644

prune356.0ms (3.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

PrunedKeptTotal
New1594163
Fresh21315
Picked101
Done011
Total16218180

Merged error: 7.7b

Counts
180 → 18

regimes380.0ms (3.6%)

Accuracy

Total 6.2b remaining (42.9%)

Threshold costs 0b (0%)

bsearch390.0ms (3.7%)

Steps
ItersRangePoint
11
247.1515610226138
4.661409735054298e+30
250.08617759702352
9
-4.9867238097996344e-148
-2.163157902216089e-155
-3.558185175373979e-154
10
-1.576312966337149e+32
-4.445638484546456e+21
-4.486060090746444e+21

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0150160
1150160

end0.0ms (0%)

sample6.0s (57.4%)

Algorithm
1×intervals
Results
2.4s2879×body1280valid
2.1s977×body2560valid
599.0ms1500×body640valid
159.0ms696×body320valid
124.0ms248×body640invalid
108.0ms1583×body80valid
84.0ms104×body1280invalid
61.0ms200×body320invalid
50.0ms358×body160valid
41.0ms438×body80invalid
31.0ms17×body2560invalid
28.0ms7×body5120valid
15.0ms83×body160invalid
14.0ms309×body80nan

Profiling

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