Details

Time bar (total: 8.0s)

sample28.0ms

Algorithm
intervals
Results
13.0ms93×body1280valid
4.0ms132×body80valid
2.0ms17×body640valid
1.0ms7×body320valid
0.0ms7×body160valid

simplify3.0ms

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))

rewrite4.0ms

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))
3.0ms
(- (atan (+ N 1.0)) (atan N))

series11.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify846.0ms

Counts
28 → 28
Iterations

Useful iterations: 4 (92.0ms)

IterNodesCost
040271
176259
2144245
3258241
4534239
51772239
done5000239

prune50.0ms

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:
10.0ms
(* (+ N 1.0) N)
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series46.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(* (+ N 1.0) N)
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify1.2s

Counts
34 → 34
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
055317
1122312
2415264
31676264
done5000264

prune60.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

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)

rewrite10.0ms

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)

series846.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(* (cbrt N) (cbrt N))
164.0ms
(cbrt N)
335.0ms
(cbrt N)
171.0ms
(cbrt N)

simplify1.4s

Counts
85 → 85
Iterations

Useful iterations: 3 (272.0ms)

IterNodesCost
061524
1118465
2446397
31994379
done5000379

prune176.0ms

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)

series663.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(cbrt N)
166.0ms
(cbrt N)
169.0ms
(cbrt N)
163.0ms
(cbrt N)

simplify1.8s

Counts
56 → 56
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
024260
142244
286220
3198208
4603208
53223208
done5001208

prune148.0ms

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

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1129
done129

end0.0ms

sample709.0ms

Algorithm
intervals
Results
365.0ms2764×body1280valid
122.0ms4044×body80valid
73.0ms657×body640valid
32.0ms355×body320valid
11.0ms180×body160valid