Details

Time bar (total: 1.6s)

sample28.0ms

Algorithm
intervals
Results
12.0ms79×body1280valid
4.0ms126×body80valid
4.0ms30×body640valid
1.0ms13×body320valid
1.0ms8×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: 18.0b

Counts
2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (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))

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(- (atan (+ N 1.0)) (atan N))

simplify68.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune24.0ms

Filtered
18 candidates to 12 candidates (33.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New17118
Fresh000
Picked011
Done000
Total17219

Merged error: 0.4b

Counts
19 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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:
5.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series6.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(* (+ N 1.0) N)
2.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify51.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune56.0ms

Filtered
34 candidates to 22 candidates (35.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh000
Picked011
Done101
Total31536

Merged error: 0.3b

Counts
36 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b
(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)))))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite10.0ms

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))))

series16.0ms

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

simplify102.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune129.0ms

Filtered
94 candidates to 46 candidates (51.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New92294
Fresh033
Picked011
Done011
Total92799

Merged error: 0.3b

Counts
99 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.4b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite6.0ms

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)))
2.0ms
(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))))

series16.0ms

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

simplify71.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
049332
179294
2159294
3330292
41184292
55001292

prune112.0ms

Filtered
52 candidates to 34 candidates (34.6%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New52052
Fresh044
Picked011
Done022
Total52759

Merged error: 0.3b

Counts
59 → 7

regimes44.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

sample822.0ms

Algorithm
intervals
Results
426.0ms2824×body1280valid
137.0ms4078×body80valid
79.0ms614×body640valid
30.0ms317×body320valid
11.0ms167×body160valid

Profiling

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