Details

Time bar (total: 1.9s)

sample26.0ms

Algorithm
intervals
Results
12.0ms93×body1280valid
4.0ms134×body80valid
2.0ms15×body640valid
1.0ms11×body320valid
0.0ms3×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
0.6b
(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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

simplify74.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42491142
55001142

prune75.0ms

Filtered
28 candidates to 19 candidates (67.9%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New26228
Fresh000
Picked101
Done000
Total27229

Merged error: 0.5b

Counts
29 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.5b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite12.0ms

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)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series60.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(* (+ N 1.0) N)
5.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune55.0ms

Filtered
34 candidates to 22 candidates (64.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh101
Picked011
Done000
Total31536

Merged error: 0.4b

Counts
36 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b
(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
15.3b
(cbrt (* (+ N 1.0) N))
15.3b
(cbrt (* (+ N 1.0) N))
15.3b
(cbrt (* (+ N 1.0) N))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div associate-*l/
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+
Counts
4 → 40
Calls
4 calls:
1.0ms
(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
4.0ms
(cbrt (* (+ N 1.0) N))
4.0ms
(cbrt (* (+ N 1.0) N))
4.0ms
(cbrt (* (+ N 1.0) N))

series305.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
105.0ms
(cbrt (* (+ N 1.0) N))
97.0ms
(cbrt (* (+ N 1.0) N))
97.0ms
(cbrt (* (+ N 1.0) N))

simplify68.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0208572
1609524
22244482
35002474

prune147.0ms

Filtered
52 candidates to 47 candidates (90.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New51152
Fresh033
Picked101
Done011
Total52557

Merged error: 0.4b

Counts
57 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
14.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 82
Calls
4 calls:
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
6.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series33.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
14.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify110.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune102.0ms

Filtered
94 candidates to 46 candidates (48.9%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New93194
Fresh033
Picked011
Done011
Total93699

Merged error: 0.4b

Counts
99 → 6

regimes24.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

sample709.0ms

Algorithm
intervals
Results
382.0ms2877×body1280valid
122.0ms4054×body80valid
65.0ms605×body640valid
25.0ms301×body320valid
10.0ms163×body160valid