Details

Time bar (total: 1.8s)

sample28.0ms

Algorithm
intervals
Results
13.0ms83×body1280valid
5.0ms141×body80valid
2.0ms13×body640valid
1.0ms14×body320valid
0.0ms5×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.5b
(- (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))

series3.0ms

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

simplify72.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42447142
55001142

prune40.0ms

Filtered
19 candidates to 28 candidates (-47.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New26228
Fresh000
Picked101
Done000
Total27229

Merged error: 0.1b

Counts
29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.1b
(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)))

series7.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(* (+ N 1.0) N)
2.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify53.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune56.0ms

Filtered
22 candidates to 34 candidates (-54.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New29534
Fresh011
Picked011
Done000
Total29736

Merged error: 0.0b

Counts
36 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(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)))))
14.0b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0b
(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))))

series19.0ms

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)))))
8.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
6.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify105.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune133.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New92294
Fresh145
Picked101
Done011
Total947101

Merged error: 0.0b

Counts
101 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
14.0b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity sqrt-prod
10×cbrt-prod
9×associate-*r*
7×pow1
6×add-exp-log add-cbrt-cube
4×add-log-exp
3×associate-*l* unswap-sqr
2×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 61
Calls
4 calls:
6.0ms
(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
3.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series117.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
6.0ms
(sqrt (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))))

simplify51.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0137815
1390742
21504732
35002724

prune183.0ms

Filtered
46 candidates to 73 candidates (-58.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New72173
Fresh055
Picked011
Done011
Total72880

Merged error: 0.0b

Counts
80 → 8

regimes47.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0124
1124

end0.0ms

sample851.0ms

Algorithm
intervals
Results
441.0ms2849×body1280valid
143.0ms4081×body80valid
79.0ms605×body640valid
30.0ms303×body320valid
14.0ms162×body160valid

Profiling

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