Details

Time bar (total: 2.2s)

sample34.0ms

Algorithm
intervals
Results
14.0ms89×body1280valid
8.0ms133×body80valid
2.0ms18×body640valid
1.0ms11×body320valid
0.0ms5×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.3b
(- (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))

series4.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

simplify87.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42447142
55001142

prune49.0ms

Filtered
28 candidates to 19 candidates (32.1%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New27128
Fresh000
Picked011
Done000
Total27229

Merged error: 0.5b

Counts
29 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

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)))

series12.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(* (+ N 1.0) N)
4.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify64.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune58.0ms

Filtered
34 candidates to 22 candidates (35.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New31334
Fresh000
Picked011
Done101
Total32436

Merged error: 0.4b

Counts
36 → 4

localize18.0ms

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)))))
14.6b
(cbrt (* (+ N 1.0) N))
14.6b
(cbrt (* (+ N 1.0) N))
14.6b
(cbrt (* (+ N 1.0) N))

rewrite30.0ms

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)))))
9.0ms
(cbrt (* (+ N 1.0) N))
9.0ms
(cbrt (* (+ N 1.0) N))
9.0ms
(cbrt (* (+ N 1.0) N))

series35.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
9.0ms
(cbrt (* (+ N 1.0) N))
9.0ms
(cbrt (* (+ N 1.0) N))
11.0ms
(cbrt (* (+ N 1.0) N))

simplify74.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0207623
1572575
21929533
35001525

prune241.0ms

Filtered
52 candidates to 47 candidates (9.6%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New48452
Fresh112
Picked101
Done011
Total50656

Merged error: 0.4b

Counts
56 → 6

localize13.0ms

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)))))
13.8b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.8b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite12.0ms

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))))

series19.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
2.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
6.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
7.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify159.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune167.0ms

Filtered
94 candidates to 47 candidates (50.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New93194
Fresh044
Picked101
Done011
Total946100

Merged error: 0.4b

Counts
100 → 6

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

sample1.0s

Algorithm
intervals
Results
551.0ms2894×body1280valid
167.0ms4052×body80valid
85.0ms573×body640valid
40.0ms339×body320valid
12.0ms142×body160valid

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