Details

Time bar (total: 2.0s)

sample31.0ms

Algorithm
intervals
Results
16.0ms97×body1280valid
4.0ms127×body80valid
2.0ms15×body640valid
1.0ms13×body320valid
0.0ms4×body160valid

simplify5.0ms

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: 15.8b

Counts
2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.1b
(- (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))

series4.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

simplify73.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42447142
55001142

prune34.0ms

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

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New27128
Fresh000
Picked101
Done000
Total28129

Merged error: 0.1b

Counts
29 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b
(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)))

simplify309.0ms

Algorithm
egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03565
15053
211353
322453
466953
5428153
6500253

prune23.0ms

Filtered
7 candidates to 10 candidates (-42.9%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New8210
Fresh000
Picked011
Done000
Total8311

Merged error: 0.1b

Counts
11 → 3

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)))))
14.8b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.8b
(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))))

series17.0ms

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

simplify106.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune138.0ms

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

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New90494
Fresh011
Picked011
Done011
Total90797

Merged error: 0.0b

Counts
97 → 7

localize11.0ms

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)))))))
14.8b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.8b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.8b
(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))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* (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)))))))
6.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
6.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
6.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify83.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0193630
1469496
21361484
35001484

prune148.0ms

Filtered
46 candidates to 97 candidates (-110.9%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New96197
Fresh044
Picked011
Done022
Total968104

Merged error: 0.0b

Counts
104 → 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

sample862.0ms

Algorithm
intervals
Results
445.0ms2798×body1280valid
146.0ms4107×body80valid
79.0ms621×body640valid
34.0ms318×body320valid
11.0ms156×body160valid

Profiling

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