Details

Time bar (total: 2.9s)

sample27.0ms

Algorithm
intervals
Results
13.0ms99×body1280valid
4.0ms124×body80valid
2.0ms16×body640valid
1.0ms9×body320valid
1.0ms8×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: 13.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.6b
(- (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))

series12.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify77.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (12.0ms)

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)))

rewrite10.0ms

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:
9.0ms
(* (+ N 1.0) N)
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series49.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(* (+ N 1.0) N)
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify58.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt N) (cbrt N))
0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (cbrt N) (cbrt N))
0.0ms
(cbrt N)
0.0ms
(cbrt N)
1.0ms
(cbrt N)

series740.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (cbrt N) (cbrt N))
177.0ms
(cbrt N)
183.0ms
(cbrt N)
177.0ms
(cbrt N)

simplify90.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0115288
1472261
22959238
35003235

prune203.0ms

Filtered
85 candidates to 64 candidates (75.3%)
Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
0.2b
(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
0.6b
(cbrt N)
29.7b
(cbrt (pow N 2))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
9×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-*r* add-cbrt-cube
4×associate-*l/ add-log-exp
3×unpow-prod-down pow-prod-down prod-exp cbrt-unprod
2×pow1/3
1×flip3-+ associate-*l* *-commutative flip-+ unpow2 sqr-pow
Counts
4 → 57
Calls
4 calls:
0.0ms
(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
20.0ms
(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
0.0ms
(cbrt N)
1.0ms
(cbrt (pow N 2))

series424.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
55.0ms
(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
186.0ms
(cbrt N)
176.0ms
(cbrt (pow N 2))

simplify44.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0265418
11012368
25001342

prune177.0ms

Filtered
69 candidates to 52 candidates (75.4%)
Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes24.0ms

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

sample736.0ms

Algorithm
intervals
Results
390.0ms2829×body1280valid
124.0ms4035×body80valid
74.0ms649×body640valid
28.0ms315×body320valid
11.0ms172×body160valid