Details

Time bar (total: 2.8s)

sample26.0ms

Algorithm
intervals
Results
12.0ms89×body1280valid
4.0ms122×body80valid
2.0ms18×body640valid
2.0ms19×body320valid
0.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
2.5b
(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

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:
0.0ms
(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))
12.0ms
(- (atan (+ N 1.0)) (atan N))

simplify76.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42491142
55001142

prune51.0ms

Filtered
28 candidates to 19 candidates (67.9%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.2b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

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:
10.0ms
(* (+ N 1.0) N)
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series49.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(* (+ N 1.0) N)
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune61.0ms

Filtered
34 candidates to 22 candidates (64.7%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
14.7b
(cbrt (* (+ N 1.0) N))
14.7b
(cbrt (* (+ N 1.0) N))
14.7b
(cbrt (* (+ N 1.0) N))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
18×cbrt-div
11×pow1
10×add-sqr-sqrt
9×flip3-+ pow1/3 flip-+
8×add-cube-cbrt *-un-lft-identity
7×cbrt-prod
6×add-exp-log
4×frac-times swap-sqr associate-*r* associate-*l* add-cbrt-cube add-log-exp
2×associate-*r/ pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 72
Calls
4 calls:
9.0ms
(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
3.0ms
(cbrt (* (+ N 1.0) N))
3.0ms
(cbrt (* (+ N 1.0) N))
3.0ms
(cbrt (* (+ N 1.0) N))

series439.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
103.0ms
(cbrt (* (+ N 1.0) N))
104.0ms
(cbrt (* (+ N 1.0) N))
108.0ms
(cbrt (* (+ N 1.0) N))

simplify47.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0353803
11280743
25001669

prune245.0ms

Filtered
84 candidates to 67 candidates (79.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

14.7b
(cbrt (* (+ N 1.0) N))
14.7b
(cbrt (* (+ N 1.0) N))
14.7b
(cbrt (* (+ N 1.0) N))
14.7b
(cbrt (* (+ N 1.0) N))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-div associate-*l/
4×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 44
Calls
4 calls:
3.0ms
(cbrt (* (+ N 1.0) N))
3.0ms
(cbrt (* (+ N 1.0) N))
3.0ms
(cbrt (* (+ N 1.0) N))
3.0ms
(cbrt (* (+ N 1.0) N))

series412.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(cbrt (* (+ N 1.0) N))
100.0ms
(cbrt (* (+ N 1.0) N))
100.0ms
(cbrt (* (+ N 1.0) N))
110.0ms
(cbrt (* (+ N 1.0) N))

simplify68.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0190556
1580528
22211472
35001472

prune241.0ms

Filtered
56 candidates to 52 candidates (92.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes25.0ms

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

sample935.0ms

Algorithm
intervals
Results
596.0ms2911×body1280valid
128.0ms4026×body80valid
66.0ms590×body640valid
28.0ms310×body320valid
11.0ms163×body160valid