Details

Time bar (total: 1.8s)

sample32.0ms

Algorithm
intervals
Results
15.0ms100×body1280valid
4.0ms113×body80valid
3.0ms24×body640valid
1.0ms11×body320valid
1.0ms8×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 17.5b

Counts
2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

2.9b
(- (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))

series2.0ms

Counts
1 → 3
Calls
1 calls:
2.0ms
(- (atan (+ N 1.0)) (atan N))

simplify78.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (13.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune26.0ms

Filtered
18 candidates to 12 candidates (33.3%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New17118
Fresh000
Picked101
Done000
Total18119

Merged error: 0.3b

Counts
19 → 1

localize6.0ms

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)))

series7.0ms

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

simplify55.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune51.0ms

Filtered
34 candidates to 22 candidates (35.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh000
Picked011
Done000
Total30535

Merged error: 0.2b

Counts
35 → 5

localize9.0ms

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)))))
16.1b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.1b
(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))))

series17.0ms

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))))

simplify111.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (102.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune133.0ms

Filtered
94 candidates to 46 candidates (51.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New92294
Fresh033
Picked101
Done011
Total93699

Merged error: 0.2b

Counts
99 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
16.1b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.1b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.1b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
54×sqrt-pow1
45×pow1
30×pow1/2 pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
7×pow-prod-down
6×associate-*l* pow-sqr
4×add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod swap-sqr unswap-sqr
1×associate-*r* *-commutative
Counts
4 → 85
Calls
4 calls:
15.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (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))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
8.0ms
(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))))

simplify85.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0193630
1469496
21361484
35001484

prune146.0ms

Filtered
97 candidates to 47 candidates (51.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh044
Picked011
Done011
Total976103

Merged error: 0.2b

Counts
103 → 6

regimes41.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0124
1124

end0.0ms

sample863.0ms

Algorithm
intervals
Results
448.0ms2847×body1280valid
140.0ms4034×body80valid
83.0ms643×body640valid
34.0ms327×body320valid
11.0ms149×body160valid

Profiling

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