Details

Time bar (total: 2.4s)

sample29.0ms

Algorithm
intervals
Results
12.0ms78×body1280valid
5.0ms143×body80valid
3.0ms20×body640valid
1.0ms8×body320valid
0.0ms7×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.0b

Counts
2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

1.5b
(- (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))

series13.0ms

Counts
1 → 3
Calls
1 calls:
13.0ms
(- (atan (+ N 1.0)) (atan N))

simplify73.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune29.0ms

Filtered
18 candidates to 12 candidates (33.3%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New17118
Fresh000
Picked101
Done000
Total18119

Merged error: 0.5b

Counts
19 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.5b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

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 1.0) N)))

series3.0ms

Counts
1 → 3
Calls
1 calls:
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify314.0ms

Algorithm
egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03565
15053
211353
322453
466953
5428153
6500253

prune20.0ms

Filtered
10 candidates to 7 candidates (30.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New7310
Fresh000
Picked011
Done000
Total7411

Merged error: 0.5b

Counts
11 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b
(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)))))
11.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
11.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite15.0ms

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))))

series36.0ms

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)))))
15.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify108.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune122.0ms

Filtered
94 candidates to 46 candidates (51.1%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New90494
Fresh112
Picked011
Done011
Total91798

Merged error: 0.4b

Counts
98 → 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))))))
11.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.0b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.0b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

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))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series455.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))))
15.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
139.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
139.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify50.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (41.0ms)

IterNodesCost
0137815
1390742
21504732
35002724

prune165.0ms

Filtered
73 candidates to 46 candidates (37.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New71273
Fresh044
Picked101
Done022
Total72880

Merged error: 0.4b

Counts
80 → 8

regimes52.0ms

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
0124
1124

end0.0ms

sample812.0ms

Algorithm
intervals
Results
418.0ms2851×body1280valid
136.0ms4057×body80valid
76.0ms639×body640valid
27.0ms286×body320valid
11.0ms167×body160valid

Profiling

Loading profile data...