Details

Time bar (total: 2.8s)

sample27.0ms

Algorithm
intervals
Results
13.0ms86×body1280valid
5.0ms141×body80valid
2.0ms19×body640valid
1.0ms8×body320valid
0.0ms2×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 13.8b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.8b
(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log diff-atan add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 15
Calls
1 calls:
3.0ms
(- (atan (+ N 1.0)) (atan N))

series10.0ms

Counts
1 → 3
Calls
1 calls:
10.0ms
(- (atan (+ N 1.0)) (atan N))

simplify95.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune29.0ms

Filtered
18 candidates to 12 candidates (66.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New17118
Fresh000
Picked101
Done000
Total18119

Merged error: 0.4b

Counts
19 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.4b
(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:
6.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series42.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(* (+ N 1.0) N)
2.0ms
(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

prune49.0ms

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: 0.3b

Counts
35 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
14.3b
(cbrt (* (+ N 1.0) N))
14.3b
(cbrt (* (+ N 1.0) N))
14.3b
(cbrt (* (+ N 1.0) N))

rewrite25.0ms

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)))
5.0ms
(cbrt (* (+ N 1.0) N))
4.0ms
(cbrt (* (+ N 1.0) N))
4.0ms
(cbrt (* (+ N 1.0) N))

series403.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
93.0ms
(cbrt (* (+ N 1.0) N))
93.0ms
(cbrt (* (+ N 1.0) N))
95.0ms
(cbrt (* (+ N 1.0) N))

simplify43.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0353803
11280743
25001669

prune197.0ms

Filtered
84 candidates to 67 candidates (79.8%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh022
Picked011
Done011
Total84488

Merged error: 0.3b

Counts
88 → 4

localize9.0ms

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)

rewrite11.0ms

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:
5.0ms
(* (cbrt N) (cbrt N))
1.0ms
(cbrt N)
1.0ms
(cbrt N)
1.0ms
(cbrt N)

series720.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(* (cbrt N) (cbrt N))
172.0ms
(cbrt N)
178.0ms
(cbrt N)
170.0ms
(cbrt N)

simplify89.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0115288
1472261
22959238
35003235

prune155.0ms

Filtered
85 candidates to 64 candidates (75.3%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New85085
Fresh011
Picked011
Done022
Total85489

Merged error: 0.3b

Counts
89 → 4

regimes14.0ms

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

sample792.0ms

Algorithm
intervals
Results
443.0ms2926×body1280valid
136.0ms4033×body80valid
72.0ms599×body640valid
29.0ms308×body320valid
9.0ms134×body160valid

Profiling

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