Details

Time bar (total: 1.7s)

sample34.0ms

Algorithm
intervals
Results
19.0ms101×body1280valid
4.0ms124×body80valid
2.0ms17×body640valid
1.0ms11×body320valid
0.0ms3×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0107
1107

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.3b

Counts
2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

1.6b
(- (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))

simplify70.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
04926185
14926185

prune24.0ms

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: 0.2b

Counts
19 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* N (+ N 1.0))
0.2b
(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:
5.0ms
(* N (+ N 1.0))
1.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series8.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(* N (+ N 1.0))
2.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify58.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04879272
14879272

prune59.0ms

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

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New33336
Fresh000
Picked011
Done000
Total33437

Merged error: 0.2b

Counts
37 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(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))))))
17.3b
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
17.3b
(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)))))

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)))))

simplify45.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05253989

prune122.0ms

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

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New93194
Fresh022
Picked011
Done011
Total93598

Merged error: 0.2b

Counts
98 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
17.9b
(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
17.9b
(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
17.9b
(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
Counts
4 → 40
Calls
4 calls:
1.0ms
(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)))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
35.0ms
(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
33.0ms
(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
33.0ms
(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify48.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04909621
14909621

prune123.0ms

Filtered
37 candidates to 52 candidates (-40.5%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New52052
Fresh022
Picked011
Done022
Total52557

Merged error: 0.2b

Counts
57 → 5

regimes38.0ms

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
0119
1119

end0.0ms

sample869.0ms

Algorithm
intervals
Results
453.0ms2835×body1280valid
145.0ms4069×body80valid
81.0ms632×body640valid
31.0ms316×body320valid
11.0ms148×body160valid

Profiling

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