Details

Time bar (total: 14.2s)

sample27.0ms

Algorithm
intervals
Results
13.0ms93×body1280valid
4.0ms132×body80valid
2.0ms17×body640valid
1.0ms7×body320valid
1.0ms7×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
2.0b
(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 22
Calls
2 calls:
0.0ms
(atan (+ N 1.0))
2.0ms
(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
11.0ms
(- (atan (+ N 1.0)) (atan N))

simplify2.5s

Counts
28 → 28
Iterations

Useful iterations: 4 (81.0ms)

IterNodesCost
040271
176259
2144245
3238241
4457239
51155239
64314239
done5000239

prune54.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.4b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
3×associate-*r*
2×associate-*l/ add-log-exp
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
2 → 28
Calls
2 calls:
9.0ms
(* (+ N 1.0) N)
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series48.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(* (+ N 1.0) N)
6.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.6s

Counts
34 → 34
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
055317
1120312
2347264
31178264
43505264
done5001264

prune65.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt N) (cbrt N))
0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt N) (cbrt N))
0.0ms
(cbrt N)
0.0ms
(cbrt N)
1.0ms
(cbrt N)

series723.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(* (cbrt N) (cbrt N))
175.0ms
(cbrt N)
170.0ms
(cbrt N)
175.0ms
(cbrt N)

simplify2.7s

Counts
85 → 85
Iterations

Useful iterations: 4 (944.0ms)

IterNodesCost
061524
1115417
2327397
31169379
43701374
done5000374

prune181.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log pow1/3 add-cbrt-cube add-log-exp
Counts
4 → 44
Calls
4 calls:
0.0ms
(cbrt N)
0.0ms
(cbrt N)
0.0ms
(cbrt N)
1.0ms
(cbrt N)

series674.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(cbrt N)
168.0ms
(cbrt N)
171.0ms
(cbrt N)
168.0ms
(cbrt N)

simplify2.8s

Counts
56 → 56
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
024260
142244
283220
3161208
4369208
51062208
64130208
done5001208

prune147.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes17.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
079
1129
done129

end0.0ms

sample693.0ms

Algorithm
intervals
Results
360.0ms2764×body1280valid
119.0ms4044×body80valid
68.0ms657×body640valid
29.0ms355×body320valid
11.0ms180×body160valid