Details

Time bar (total: 1.8s)

analyze1.0ms

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

sample27.0ms

Algorithm
intervals
Results
12.0ms78×body1280valid
5.0ms146×body80valid
3.0ms22×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0717
1717

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.2b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

simplify66.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
05349236

prune38.0ms

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

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New26127
Fresh000
Picked101
Done000
Total27128

Merged error: 0.1b

Counts
28 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
1 → 7
Calls
1 calls:
1.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series2.0ms

Counts
1 → 3
Calls
1 calls:
2.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify123.0ms

Algorithm
egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 0 (120.0ms)

IterNodesCost
04712109
14712109

prune18.0ms

Filtered
8 candidates to 10 candidates (-25.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New9110
Fresh000
Picked011
Done000
Total9211

Merged error: 0.0b

Counts
11 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(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))))))
11.9b
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
11.9b
(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)))))

series20.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
5.0ms
(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
7.0ms
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
7.0ms
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify46.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05253989

prune129.0ms

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

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New90494
Fresh000
Picked011
Done011
Total90696

Merged error: 0.0b

Counts
96 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))
0.3b
(pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3)
11.9b
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
11.9b
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
70×add-sqr-sqrt
27×unpow-prod-down cube-prod
24×associate-*l* unswap-sqr
23×add-cube-cbrt *-un-lft-identity
10×pow1 add-exp-log
9×associate-*r*
7×add-cbrt-cube
6×sqrt-pow1
5×pow-pow sqr-pow
4×pow1/2 add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp rem-sqrt-square unpow3 pow-exp
1×pow-plus *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 137
Calls
4 calls:
12.0ms
(* (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))
4.0ms
(pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3)
1.0ms
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series75.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3) (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))))
50.0ms
(pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3)
10.0ms
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
12.0ms
(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049152183
149152183

prune199.0ms

Filtered
62 candidates to 149 candidates (-140.3%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1481149
Fresh033
Picked011
Done022
Total1487155

Merged error: 0.0b

Counts
155 → 7

regimes49.0ms

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 (1.0ms)

IterNodesCost
0119
1119

end0.0ms

sample812.0ms

Algorithm
intervals
Results
445.0ms2846×body1280valid
142.0ms4052×body80valid
83.0ms657×body640valid
28.0ms288×body320valid
11.0ms157×body160valid

Profiling

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