Details

Time bar (total: 2.0s)

analyze1.0ms

Algorithm
search

sample29.0ms

Algorithm
intervals
Results
15.0ms97×body1280valid
4.0ms124×body80valid
3.0ms23×body640valid
1.0ms7×body320valid
0.0ms5×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 17.5b

Counts
2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

1.4b
(- (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))

series2.0ms

Counts
1 → 3
Calls
1 calls:
2.0ms
(- (atan (+ N 1.0)) (atan N))

simplify72.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (9.0ms)

IterNodesCost
072123
1142114
2286112
3678111
42444111
55002111

prune26.0ms

Filtered
12 candidates to 18 candidates (-50.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New17118
Fresh000
Picked011
Done000
Total17219

Merged error: 0.4b

Counts
19 → 2

localize6.0ms

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

series6.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(* (+ 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

prune54.0ms

Filtered
22 candidates to 34 candidates (-54.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New29534
Fresh000
Picked011
Done011
Total29736

Merged error: 0.4b

Counts
36 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ N 1.0))
0.3b
(cbrt (+ N 1.0))
0.3b
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.4b
(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 88
Calls
4 calls:
3.0ms
(cbrt (+ N 1.0))
3.0ms
(cbrt (+ N 1.0))
10.0ms
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
1.0ms
(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ N 1.0))
6.0ms
(cbrt (+ N 1.0))
9.0ms
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
2.0ms
(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify153.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0345866
11119805
24847721
35001721

prune206.0ms

Filtered
67 candidates to 100 candidates (-49.3%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New982100
Fresh134
Picked011
Done022
Total998107

Merged error: 0.4b

Counts
107 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(atan2 1.0 (+ 1 (* (/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
8.9b
(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
14.2b
(cbrt (- (* N N) (* 1.0 1.0)))
14.2b
(cbrt (- (* N N) (* 1.0 1.0)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-div
16×add-exp-log
14×flip3-- flip--
8×cbrt-prod frac-times associate-/r/ add-cbrt-cube associate-/l/
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 cbrt-undiv associate-*r/ div-exp associate-*l/ prod-exp cbrt-unprod add-log-exp
2×pow1/3 difference-of-squares
1×frac-2neg times-frac clear-num associate-/r* div-inv associate-/l*
Counts
4 → 72
Calls
4 calls:
1.0ms
(atan2 1.0 (+ 1 (* (/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
18.0ms
(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
3.0ms
(cbrt (- (* N N) (* 1.0 1.0)))
4.0ms
(cbrt (- (* N N) (* 1.0 1.0)))

series46.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(atan2 1.0 (+ 1 (* (/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
13.0ms
(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
15.0ms
(cbrt (- (* N N) (* 1.0 1.0)))
12.0ms
(cbrt (- (* N N) (* 1.0 1.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05791387
121261169
250011126

prune271.0ms

Filtered
71 candidates to 84 candidates (-18.3%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New84084
Fresh044
Picked011
Done033
Total84892

Merged error: 0.4b

Counts
92 → 8

regimes88.0ms

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

analyze1.0ms

Algorithm
search

sample795.0ms

Algorithm
intervals
Results
438.0ms2858×body1280valid
136.0ms4060×body80valid
81.0ms630×body640valid
30.0ms310×body320valid
10.0ms142×body160valid

Profiling

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