Details

Time bar (total: 2.1s)

sample29.0ms

Algorithm
intervals
Results
13.0ms86×body1280valid
5.0ms139×body80valid
2.0ms18×body640valid
1.0ms8×body320valid
0.0ms5×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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.0b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

1.6b
(- (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))

series10.0ms

Counts
1 → 3
Calls
1 calls:
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify73.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune43.0ms

Filtered
18 candidates to 12 candidates (66.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New17118
Fresh000
Picked011
Done000
Total17219

Merged error: 0.6b

Counts
19 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

0.6b
(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)))

series2.0ms

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

simplify312.0ms

Algorithm
egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03565
15053
211353
322453
466953
5428153
6500253

prune31.0ms

Filtered
10 candidates to 7 candidates (70.0%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New8210
Fresh000
Picked011
Done011
Total8412

Merged error: 0.6b

Counts
12 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b
(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)))))
14.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.7b
(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))))

series33.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(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))))

simplify107.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune170.0ms

Filtered
94 candidates to 46 candidates (48.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New92294
Fresh011
Picked011
Done022
Total92698

Merged error: 0.6b

Counts
98 → 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)))))))
14.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite22.0ms

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

series45.0ms

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)))))))
13.0ms
(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))))

simplify82.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0193630
1469496
21361484
35001484

prune172.0ms

Filtered
97 candidates to 47 candidates (48.5%)
Pruning

7 alts after pruning (3 fresh and 4 done)

PrunedKeptTotal
New96197
Fresh022
Picked011
Done033
Total967103

Merged error: 0.6b

Counts
103 → 7

regimes87.0ms

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

sample803.0ms

Algorithm
intervals
Results
413.0ms2849×body1280valid
135.0ms4057×body80valid
74.0ms633×body640valid
26.0ms287×body320valid
11.0ms174×body160valid

Profiling

Loading profile data...