Details

Time bar (total: 2.1s)

sample28.0ms

Algorithm
intervals
Results
13.0ms82×body1280valid
5.0ms137×body80valid
3.0ms23×body640valid
1.0ms8×body320valid
0.0ms6×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 15.3b

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))

series12.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
11.0ms
(- (atan (+ N 1.0)) (atan N))

simplify73.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42447142
55001142

prune42.0ms

Filtered
28 candidates to 19 candidates (67.9%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New27128
Fresh000
Picked101
Done000
Total28129

Merged error: 0.1b

Counts
29 → 1

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:
5.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series44.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(* (+ N 1.0) N)
2.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify57.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune48.0ms

Filtered
34 candidates to 22 candidates (64.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New31334
Fresh000
Picked011
Done000
Total31435

Merged error: 0.0b

Counts
35 → 4

localize11.0ms

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)))))
13.2b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.2b
(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))))

series34.0ms

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))))

simplify106.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0110649
1391565
22248539
35001520

prune114.0ms

Filtered
94 candidates to 47 candidates (50.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New92294
Fresh022
Picked011
Done011
Total92698

Merged error: 0.0b

Counts
98 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
13.2b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.6b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.6b
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×pow1 sqrt-prod
6×add-exp-log cbrt-prod associate-*r* add-cbrt-cube
4×add-log-exp
3×associate-*l*
2×pow1/3 unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 57
Calls
4 calls:
5.0ms
(* (fabs (cbrt (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
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (fabs (cbrt (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))))
120.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
122.0ms
(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify191.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
0112717
1306638
21079625
34956623
45001623

prune130.0ms

Filtered
69 candidates to 42 candidates (60.9%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New67269
Fresh213
Picked101
Done022
Total70575

Merged error: 0.0b

Counts
75 → 5

regimes20.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

sample796.0ms

Algorithm
intervals
Results
429.0ms2873×body1280valid
137.0ms3985×body80valid
78.0ms656×body640valid
30.0ms325×body320valid
11.0ms161×body160valid

Profiling

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