Details

Time bar (total: 1.7s)

sample28.0ms

Algorithm
intervals
Results
14.0ms95×body1280valid
4.0ms127×body80valid
2.0ms19×body640valid
1.0ms9×body320valid
0.0ms6×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: 15.0b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log diff-atan add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 15
Calls
1 calls:
3.0ms
(- (atan (+ N 1.0)) (atan N))

series10.0ms

Counts
1 → 3
Calls
1 calls:
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify74.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune25.0ms

Filtered
18 candidates to 12 candidates (66.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New17118
Fresh000
Picked101
Done000
Total18119

Merged error: 0.3b

Counts
19 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.3b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite7.0ms

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:
6.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series43.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(* (+ N 1.0) N)
2.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify56.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune53.0ms

Filtered
34 candidates to 22 candidates (64.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh000
Picked011
Done000
Total30535

Merged error: 0.3b

Counts
35 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b
(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)))))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.3b
(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))))

series37.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(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)))))
15.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify115.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (105.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune112.0ms

Filtered
94 candidates to 46 candidates (48.9%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New92294
Fresh213
Picked011
Done011
Total94599

Merged error: 0.3b

Counts
99 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.3b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 40
Calls
4 calls:
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
1.0ms
(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))))

series32.0ms

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

simplify76.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
049332
179294
2159294
3330292
41184292
55001292

prune108.0ms

Filtered
52 candidates to 34 candidates (65.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New50252
Fresh112
Picked101
Done022
Total52557

Merged error: 0.3b

Counts
57 → 5

regimes20.0ms

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

sample793.0ms

Algorithm
intervals
Results
437.0ms2888×body1280valid
137.0ms4033×body80valid
74.0ms611×body640valid
31.0ms298×body320valid
12.0ms170×body160valid

Profiling

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