Details

Time bar (total: 1.6s)

analyze2.0ms

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

sample27.0ms

Algorithm
intervals
Results
12.0ms80×body1280valid
5.0ms135×body80valid
2.0ms19×body640valid
1.0ms13×body320valid
1.0ms9×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: 14.3b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
2.0b
(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 21
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

series3.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
2.0ms
(- (atan (+ N 1.0)) (atan N))

simplify65.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
05349236

prune39.0ms

Filtered
19 candidates to 27 candidates (-42.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New25227
Fresh000
Picked011
Done000
Total25328

Merged error: 0.2b

Counts
28 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt associate-+r+ *-un-lft-identity add-cbrt-cube
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log flip-+
Counts
2 → 20
Calls
2 calls:
3.0ms
(+ 1 (* N (+ N 1.0)))
1.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series5.0ms

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

simplify50.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04998258
14998258

prune49.0ms

Filtered
20 candidates to 26 candidates (-30.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New21526
Fresh101
Picked011
Done011
Total22729

Merged error: 0.2b

Counts
29 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(atan2 1.0 (* (* (cbrt (+ 1 (* N (+ 1.0 N)))) (cbrt (+ 1 (* N (+ 1.0 N))))) (cbrt (+ 1 (* N (+ 1.0 N))))))
14.2b
(cbrt (+ 1 (* N (+ 1.0 N))))
14.2b
(cbrt (+ 1 (* N (+ 1.0 N))))
14.2b
(cbrt (+ 1 (* N (+ 1.0 N))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ pow1/3 flip-+
Counts
4 → 46
Calls
4 calls:
1.0ms
(atan2 1.0 (* (* (cbrt (+ 1 (* N (+ 1.0 N)))) (cbrt (+ 1 (* N (+ 1.0 N))))) (cbrt (+ 1 (* N (+ 1.0 N))))))
2.0ms
(cbrt (+ 1 (* N (+ 1.0 N))))
2.0ms
(cbrt (+ 1 (* N (+ 1.0 N))))
2.0ms
(cbrt (+ 1 (* N (+ 1.0 N))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 1.0 (* (* (cbrt (+ 1 (* N (+ 1.0 N)))) (cbrt (+ 1 (* N (+ 1.0 N))))) (cbrt (+ 1 (* N (+ 1.0 N))))))
7.0ms
(cbrt (+ 1 (* N (+ 1.0 N))))
7.0ms
(cbrt (+ 1 (* N (+ 1.0 N))))
8.0ms
(cbrt (+ 1 (* N (+ 1.0 N))))

simplify56.0ms

Algorithm
egg-herbie
Counts
58 → 58
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
05047745

prune139.0ms

Filtered
52 candidates to 58 candidates (-11.5%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New58058
Fresh044
Picked011
Done022
Total58765

Merged error: 0.2b

Counts
65 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b
(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.7b
(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (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)))))

rewrite12.0ms

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)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
05253989

prune109.0ms

Filtered
46 candidates to 94 candidates (-104.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New91394
Fresh213
Picked101
Done123
Total956101

Merged error: 0.2b

Counts
101 → 6

regimes80.0ms

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

sample798.0ms

Algorithm
intervals
Results
436.0ms2880×body1280valid
138.0ms4014×body80valid
74.0ms590×body640valid
33.0ms344×body320valid
12.0ms172×body160valid

Profiling

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