Details

Time bar (total: 2.3s)

sample27.0ms

Algorithm
intervals
Results
11.0ms81×body1280valid
5.0ms138×body80valid
3.0ms22×body640valid
1.0ms11×body320valid
0.0ms4×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: 13.2b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.4b
(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
1×sub-neg flip3-- diff-atan flip--
Counts
2 → 5
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
2.0ms
(- (atan (+ N 1.0)) (atan N))

series13.0ms

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

simplify57.0ms

Algorithm
egg-herbie
Counts
11 → 11
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
05258
110658
219456
337055
4148255
5500255

prune12.0ms

Filtered
11 candidates to 4 candidates (36.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New10111
Fresh000
Picked011
Done000
Total10212

Merged error: 0.3b

Counts
12 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (* (+ N 1.0) N))
0.0b
(* (+ N 1.0) N)
0.4b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
2×flip3-+ associate-*l/ flip-+
1×+-commutative *-commutative
Counts
3 → 6
Calls
3 calls:
3.0ms
(+ 1 (* (+ N 1.0) N))
3.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series66.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(+ 1 (* (+ N 1.0) N))
44.0ms
(* (+ N 1.0) N)
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify58.0ms

Algorithm
egg-herbie
Counts
15 → 15
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
08664
134958
2193758
3500358

prune22.0ms

Filtered
15 candidates to 7 candidates (46.7%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New14115
Fresh000
Picked011
Done011
Total14317

Merged error: 0.3b

Counts
17 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* N N) (- (* 1.0 1.0) (* N 1.0)))
0.0b
(* (+ (pow N 3) (pow 1.0 3)) N)
0.4b
(atan2 1.0 (+ 1 (/ (* (+ (pow N 3) (pow 1.0 3)) N) (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))))
17.8b
(/ (* (+ (pow N 3) (pow 1.0 3)) N) (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
4×flip3-+ associate-*l/ flip-+
3×associate-/l*
2×associate-+r+ associate-*l* associate-/r/ sum-cubes *-commutative associate-/l/
1×+-commutative associate-+r- sub-neg frac-2neg clear-num div-inv
Counts
4 → 20
Calls
4 calls:
7.0ms
(+ (* N N) (- (* 1.0 1.0) (* N 1.0)))
5.0ms
(* (+ (pow N 3) (pow 1.0 3)) N)
1.0ms
(atan2 1.0 (+ 1 (/ (* (+ (pow N 3) (pow 1.0 3)) N) (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))))
11.0ms
(/ (* (+ (pow N 3) (pow 1.0 3)) N) (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(+ (* N N) (- (* 1.0 1.0) (* N 1.0)))
98.0ms
(* (+ (pow N 3) (pow 1.0 3)) N)
9.0ms
(atan2 1.0 (+ 1 (/ (* (+ (pow N 3) (pow 1.0 3)) N) (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))))
204.0ms
(/ (* (+ (pow N 3) (pow 1.0 3)) N) (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))

simplify103.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0184229
1673220
23268213
35002213

prune94.0ms

Filtered
32 candidates to 23 candidates (71.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New31132
Fresh000
Picked101
Done022
Total32335

Merged error: 0.3b

Counts
35 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3))))
0.4b
(atan2 1.0 (+ 1 (/ 1 (/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3))))))
3.4b
(/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3)))
15.0b
(/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
17×associate-/l/
14×associate-/r/
8×clear-num div-inv
6×frac-2neg associate-/r*
5×flip3-+ flip-+
4×sum-cubes
2×times-frac remove-double-div associate-/l*
1×inv-pow
Counts
4 → 38
Calls
4 calls:
11.0ms
(/ 1 (/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3))))
1.0ms
(atan2 1.0 (+ 1 (/ 1 (/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3))))))
10.0ms
(/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3)))
8.0ms
(/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N)

series341.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(/ 1 (/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3))))
8.0ms
(atan2 1.0 (+ 1 (/ 1 (/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3))))))
81.0ms
(/ (/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N) (+ (pow N 3) (pow 1.0 3)))
50.0ms
(/ (+ (* 1.0 (- 1.0 N)) (pow N 2)) N)

simplify42.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0251372
11003328
25001312

prune146.0ms

Filtered
50 candidates to 38 candidates (76.0%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New49150
Fresh000
Picked011
Done022
Total49453

Merged error: 0.3b

Counts
53 → 4

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

sample797.0ms

Algorithm
intervals
Results
438.0ms2874×body1280valid
130.0ms4015×body80valid
74.0ms607×body640valid
33.0ms324×body320valid
13.0ms180×body160valid