Details

Time bar (total: 9.5s)

analyze798.0ms

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%36%19.4%13
45.5%34.5%20%14

sample176.0ms

Algorithm
intervals
Results
67.0ms85×body1280valid
64.0ms29×body2560valid
16.0ms43×body640valid
5.0ms23×body320valid
4.0ms67×body80valid
3.0ms6×body640invalid
2.0ms3×body1280invalid
1.0ms5×body320invalid
1.0ms16×body80invalid
1.0ms9×body160valid
1.0ms5×body160invalid
0.0ms6×body80nan

simplify37.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
0492115
1492115

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 47.6b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.5b
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
8.7b
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
8.7b
(pow.f64 (+.f64 1 (/.f64 i n)) n)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
584×times-frac_binary64
485×add-sqr-sqrt_binary64
366×*-un-lft-identity_binary64
224×add-cube-cbrt_binary64
174×associate-*r*_binary64
168×difference-of-squares_binary64
88×unpow-prod-down_binary64
85×sqr-pow_binary64
84×difference-of-sqr-1_binary64
29×div-inv_binary64
28×distribute-lft-out--_binary64
19×add-exp-log_binary64
18×add-cbrt-cube_binary64
13×associate-/r*_binary64 associate-/l*_binary64
7×pow1_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 → 448
Calls
4 calls:
51.0ms
(*.f64 100 (/.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)
22.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
7.0ms
(pow.f64 (+.f64 1 (/.f64 i n)) n)

series205.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
36.0ms
(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
70.0ms
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
29.0ms
(pow.f64 (+.f64 1 (/.f64 i n)) n)

simplify95.0ms

Algorithm
egg-herbie
Counts
460 → 460
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
050739654

prune399.0ms

Filtered
264 candidates to 460 candidates (-74.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New45010460
Fresh000
Picked101
Done000
Total45110461

Merged error: 15.9b

Counts
461 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.f64 100 (/.f64 (+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2))) (/.f64 i n)))
0.1b
(*.f64 (pow.f64 i 3) 1/6)
7.5b
(+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2)))
17.9b
(/.f64 (+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2))) (/.f64 i n))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac_binary64
102×add-sqr-sqrt_binary64
86×*-un-lft-identity_binary64 add-cube-cbrt_binary64
47×associate-*r*_binary64
23×add-exp-log_binary64
20×add-cbrt-cube_binary64
15×associate-*l*_binary64
13×associate-/r*_binary64
9×add-log-exp_binary64 div-inv_binary64
7×unswap-sqr_binary64
6×pow1_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
4×cbrt-unprod_binary64 unpow-prod-down_binary64 cube-prod_binary64
3×associate-/l*_binary64 sum-log_binary64
2×flip3-+_binary64 associate-/l/_binary64 sqr-pow_binary64 associate-/r/_binary64 flip-+_binary64 *-commutative_binary64
1×pow-to-exp_binary64 pow-prod-down_binary64 associate-*r/_binary64 clear-num_binary64 frac-2neg_binary64 +-commutative_binary64 associate-+r+_binary64 pow-exp_binary64 unpow3_binary64 cube-mult_binary64
Counts
4 → 182
Calls
4 calls:
34.0ms
(*.f64 100 (/.f64 (+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2))) (/.f64 i n)))
13.0ms
(*.f64 (pow.f64 i 3) 1/6)
15.0ms
(+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2)))
19.0ms
(/.f64 (+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2))) (/.f64 i n))

series34.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(*.f64 100 (/.f64 (+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2))) (/.f64 i n)))
4.0ms
(*.f64 (pow.f64 i 3) 1/6)
4.0ms
(+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2)))
13.0ms
(/.f64 (+.f64 (*.f64 (pow.f64 i 3) 1/6) (+.f64 i (*.f64 (*.f64 i i) 1/2))) (/.f64 i n))

simplify52.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
054544116

prune246.0ms

Filtered
150 candidates to 194 candidates (-29.3%)
Pruning

24 alts after pruning (24 fresh and 0 done)

PrunedKeptTotal
New17915194
Fresh099
Picked101
Done000
Total18024204

Merged error: 6.7b

Counts
204 → 24

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.f64 100 (+.f64 (*.f64 1/2 (*.f64 i n)) (+.f64 n (*.f64 1/6 (*.f64 i (*.f64 i n))))))
0.1b
(*.f64 i (*.f64 i n))
0.2b
(*.f64 1/6 (*.f64 i (*.f64 i n)))
4.1b
(+.f64 (*.f64 1/2 (*.f64 i n)) (+.f64 n (*.f64 1/6 (*.f64 i (*.f64 i n)))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
10×pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64 add-sqr-sqrt_binary64
9×add-log-exp_binary64 associate-*l*_binary64
8×*-un-lft-identity_binary64 add-cube-cbrt_binary64
5×associate-*r*_binary64
3×sum-log_binary64 *-commutative_binary64
2×flip3-+_binary64 associate-*r/_binary64 flip-+_binary64
1×distribute-lft-in_binary64 distribute-rgt-in_binary64 unswap-sqr_binary64 +-commutative_binary64 associate-+r+_binary64
Counts
4 → 74
Calls
4 calls:
10.0ms
(*.f64 100 (+.f64 (*.f64 1/2 (*.f64 i n)) (+.f64 n (*.f64 1/6 (*.f64 i (*.f64 i n))))))
5.0ms
(*.f64 i (*.f64 i n))
7.0ms
(*.f64 1/6 (*.f64 i (*.f64 i n)))
9.0ms
(+.f64 (*.f64 1/2 (*.f64 i n)) (+.f64 n (*.f64 1/6 (*.f64 i (*.f64 i n)))))

series26.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(*.f64 100 (+.f64 (*.f64 1/2 (*.f64 i n)) (+.f64 n (*.f64 1/6 (*.f64 i (*.f64 i n))))))
4.0ms
(*.f64 i (*.f64 i n))
5.0ms
(*.f64 1/6 (*.f64 i (*.f64 i n)))
8.0ms
(+.f64 (*.f64 1/2 (*.f64 i n)) (+.f64 n (*.f64 1/6 (*.f64 i (*.f64 i n)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05228930

prune93.0ms

Filtered
53 candidates to 86 candidates (-62.3%)
Pruning

24 alts after pruning (23 fresh and 1 done)

PrunedKeptTotal
New85186
Fresh12223
Picked011
Done000
Total8624110

Merged error: 6.7b

Counts
110 → 24

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(*.f64 (+.f64 n (*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))) 10)
0.1b
(*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))
0.2b
(*.f64 (sqrt.f64 100) (*.f64 (+.f64 n (*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))) 10))
0.4b
(*.f64 i 1/6)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1_binary64 add-exp-log_binary64 add-cbrt-cube_binary64
15×add-sqr-sqrt_binary64
13×associate-*l*_binary64
11×*-un-lft-identity_binary64 add-cube-cbrt_binary64
10×associate-*r*_binary64
8×pow-prod-down_binary64 cbrt-unprod_binary64 prod-exp_binary64
4×add-log-exp_binary64 associate-*r/_binary64 associate-*l/_binary64 *-commutative_binary64
3×flip3-+_binary64 sqrt-prod_binary64 flip-+_binary64
2×unswap-sqr_binary64
1×distribute-lft-in_binary64 distribute-rgt-in_binary64
Counts
4 → 83
Calls
4 calls:
7.0ms
(*.f64 (+.f64 n (*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))) 10)
8.0ms
(*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))
11.0ms
(*.f64 (sqrt.f64 100) (*.f64 (+.f64 n (*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))) 10))
4.0ms
(*.f64 i 1/6)

series39.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(*.f64 (+.f64 n (*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))) 10)
7.0ms
(*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))
15.0ms
(*.f64 (sqrt.f64 100) (*.f64 (+.f64 n (*.f64 (*.f64 i n) (+.f64 1/2 (*.f64 i 1/6)))) 10))
3.0ms
(*.f64 i 1/6)

simplify46.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050341085

prune63.0ms

Filtered
65 candidates to 95 candidates (-46.2%)
Pruning

25 alts after pruning (24 fresh and 1 done)

PrunedKeptTotal
New90595
Fresh31922
Picked101
Done011
Total9425119

Merged error: 6.7b

Counts
119 → 25

regimes434.0ms

Accuracy

70.1% (6.0b remaining)

Error of 14.3b against oracle of 8.3b and baseline of 28.2b

bsearch314.0ms

Steps
ItersRangePoint
7
5.164866102278071e+227
4.0832018100559106e+229
6.755767338475522e+227
10
8.430388706160222e+156
6.485164529897893e+169
2.8968362884498612e+166
10
9.123958155951444e-16
16.72430715742968
0.014357544782884098
7
-6499532418.018426
-42258463.18468076
-43209245.05120845

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06075
16075

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.4s2804×body1280valid
2.2s1008×body2560valid
622.0ms1531×body640valid
162.0ms687×body320valid
116.0ms235×body640invalid
110.0ms1621×body80valid
75.0ms93×body1280invalid
54.0ms168×body320invalid
52.0ms345×body160valid
41.0ms454×body80invalid
16.0ms86×body160invalid
15.0ms4×body5120valid
14.0ms7×body2560invalid
13.0ms287×body80nan

Profiling

Loading profile data...