Details

Time bar (total: 3.4s)

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1

sample72.0ms

Algorithm
intervals
Results
13.0ms89×body1280valid
4.0ms126×body80valid
3.0ms25×body640valid
1.0ms9×body320valid
0.0ms7×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.1b

Counts
2 → 1

localize16.0ms

Local error

Found 1 expressions with local error:

15.1b
(- (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 → 14
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))

simplify64.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
05339182

prune27.0ms

Filtered
12 candidates to 17 candidates (-41.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New16117
Fresh000
Picked011
Done000
Total16218

Merged error: 0.3b

Counts
18 → 2

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-exp-log add-cube-cbrt associate-*r* add-cbrt-cube
3×associate-*l*
2×associate-*r/ add-log-exp
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
2 → 30
Calls
2 calls:
6.0ms
(* N (+ N 1.0))
1.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series7.0ms

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

simplify60.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04907272
14907272

prune63.0ms

Filtered
26 candidates to 36 candidates (-38.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New31536
Fresh000
Picked011
Done011
Total31738

Merged error: 0.2b

Counts
38 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
16.4b
(cbrt (* N (+ 1.0 N)))
16.4b
(cbrt (* N (+ 1.0 N)))
16.4b
(cbrt (* N (+ 1.0 N)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*r/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
6.0ms
(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
4.0ms
(cbrt (* N (+ 1.0 N)))
4.0ms
(cbrt (* N (+ 1.0 N)))
4.0ms
(cbrt (* N (+ 1.0 N)))

series38.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (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)))

simplify51.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
049501066
149501066

prune212.0ms

Filtered
71 candidates to 84 candidates (-18.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New83184
Fresh044
Picked011
Done022
Total83891

Merged error: 0.2b

Counts
91 → 8

localize17.0ms

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))))))
15.7b
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
15.7b
(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)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05253989

prune117.0ms

Filtered
47 candidates to 94 candidates (-100.0%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New92294
Fresh314
Picked011
Done123
Total966102

Merged error: 0.2b

Counts
102 → 6

regimes39.0ms

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
0119
1119

end0.0ms

sample2.4s

Algorithm
intervals
Results
399.0ms2826×body1280valid
118.0ms4091×body80valid
72.0ms619×body640valid
30.0ms314×body320valid
10.0ms150×body160valid

Profiling

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