Details

Time bar (total: 1.7s)

sample26.0ms

Algorithm
intervals
Results
11.0ms78×body1280valid
4.0ms133×body80valid
3.0ms22×body640valid
1.0ms13×body320valid
1.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
2.4b
(- (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 → 22
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

series11.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify83.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42491142
55001142

prune44.0ms

Filtered
28 candidates to 19 candidates (67.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New25328
Fresh000
Picked101
Done000
Total26329

Merged error: 0.2b

Counts
29 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.2b
(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:
6.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series47.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(* (+ N 1.0) N)
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune52.0ms

Filtered
34 candidates to 22 candidates (64.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New30434
Fresh112
Picked011
Done000
Total31637

Merged error: 0.2b

Counts
37 → 6

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)))))
13.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.3b
(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))))

series37.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
14.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify104.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune116.0ms

Filtered
94 candidates to 47 candidates (50.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New91394
Fresh224
Picked101
Done011
Total946100

Merged error: 0.2b

Counts
100 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
13.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
54×sqrt-pow1
45×pow1
30×pow1/2 pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
9×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
7×pow-prod-down
6×associate-*l* pow-sqr
4×add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod swap-sqr unswap-sqr
1×associate-*r* *-commutative
Counts
4 → 85
Calls
4 calls:
16.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (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))))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series50.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
15.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify93.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0193630
1469496
21361484
35001484

prune118.0ms

Filtered
97 candidates to 49 candidates (50.5%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh044
Picked011
Done011
Total976103

Merged error: 0.2b

Counts
103 → 6

regimes23.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

sample730.0ms

Algorithm
intervals
Results
386.0ms2831×body1280valid
132.0ms4055×body80valid
71.0ms640×body640valid
29.0ms334×body320valid
9.0ms140×body160valid

Profiling

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