Details

Time bar (total: 1.7s)

analyze1.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 100%

sample32.0ms

Algorithm
intervals
Results
16.0ms86×body1280valid
5.0ms142×body80valid
2.0ms16×body640valid
1.0ms6×body320valid
0.0ms6×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 12.7b

Counts
2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

1.4b
(- (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))

simplify72.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune23.0ms

Filtered
12 candidates to 18 candidates (-50.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New17118
Fresh000
Picked101
Done000
Total18119

Merged error: 0.7b

Counts
19 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.7b
(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:
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)))

simplify56.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune41.0ms

Filtered
22 candidates to 34 candidates (-54.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New32234
Fresh000
Picked011
Done000
Total32335

Merged error: 0.7b

Counts
35 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.7b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.9b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.9b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

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))))

series18.0ms

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))))
8.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify73.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (8.0ms)

IterNodesCost
049332
179294
2159294
3330292
41184292
55001292

prune95.0ms

Filtered
34 candidates to 52 candidates (-52.9%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New51152
Fresh011
Picked011
Done011
Total51455

Merged error: 0.7b

Counts
55 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

13.9b
(sqrt (* (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
14.4b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
15×sqrt-pow1
12×pow1/3
9×cbrt-prod pow-prod-up
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 57
Calls
4 calls:
7.0ms
(sqrt (* (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series107.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(sqrt (* (* (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
33.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
34.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
33.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify95.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (88.0ms)

IterNodesCost
087542
1221480
21261461
35001432

prune160.0ms

Filtered
39 candidates to 69 candidates (-76.9%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New68169
Fresh011
Picked011
Done022
Total68573

Merged error: 0.7b

Counts
73 → 5

regimes40.0ms

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

analyze1.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 100%

sample810.0ms

Algorithm
intervals
Results
439.0ms2865×body1280valid
139.0ms3998×body80valid
83.0ms652×body640valid
35.0ms331×body320valid
11.0ms154×body160valid

Profiling

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