Details

Time bar (total: 1.7s)

analyze1.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
100%0%0%1

sample33.0ms

Algorithm
intervals
Results
18.0ms98×body1280valid
4.0ms116×body80valid
4.0ms29×body640valid
1.0ms6×body320valid
0.0ms7×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0777
1777

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.4b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
2.1b
(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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 → 21
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

series4.0ms

Counts
2 → 6
Calls
2 calls:
1.0ms
(atan (+ N 1.0))
3.0ms
(- (atan (+ N 1.0)) (atan N))

simplify44.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
05254236

prune43.0ms

Filtered
19 candidates to 27 candidates (-42.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New25227
Fresh000
Picked011
Done000
Total25328

Merged error: 0.3b

Counts
28 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (* N (+ N 1.0)))
0.0b
(* N (+ N 1.0))
0.3b
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
4×associate-*r*
3×associate-*l*
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ flip-+
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 43
Calls
3 calls:
3.0ms
(+ 1 (* N (+ N 1.0)))
6.0ms
(* N (+ N 1.0))
1.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series9.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(+ 1 (* N (+ N 1.0)))
4.0ms
(* N (+ N 1.0))
2.0ms
(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify49.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04965421
14965421

prune98.0ms

Filtered
38 candidates to 52 candidates (-36.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New44852
Fresh101
Picked101
Done011
Total46955

Merged error: 0.3b

Counts
55 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (+ (* N N) (* 1.0 N)))
0.0b
(+ (* N N) (* 1.0 N))
0.3b
(atan2 1.0 (+ 1 (+ (* N N) (* 1.0 N))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×*-un-lft-identity
4×sum-log
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube
2×+-commutative flip3-+ flip-+
1×associate-+r+ distribute-rgt-out distribute-lft-out
Counts
3 → 33
Calls
3 calls:
6.0ms
(+ 1 (+ (* N N) (* 1.0 N)))
4.0ms
(+ (* N N) (* 1.0 N))
1.0ms
(atan2 1.0 (+ 1 (+ (* N N) (* 1.0 N))))

series10.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(+ 1 (+ (* N N) (* 1.0 N)))
5.0ms
(+ (* N N) (* 1.0 N))
2.0ms
(atan2 1.0 (+ 1 (+ (* N N) (* 1.0 N))))

simplify50.0ms

Algorithm
egg-herbie
Counts
42 → 42
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
05059380

prune66.0ms

Filtered
25 candidates to 42 candidates (-68.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New42042
Fresh077
Picked011
Done011
Total42951

Merged error: 0.3b

Counts
51 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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 (+ 1.0 N))
3.0ms
(cbrt (+ 1.0 N))
1.0ms
(atan2 1.0 (+ 1 (* (* N (* (cbrt (+ 1.0 N)) (cbrt (+ 1.0 N)))) (cbrt (+ N 1.0)))))
12.0ms
(* (cbrt (+ 1.0 N)) (cbrt (+ 1.0 N)))

series21.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 N))
6.0ms
(cbrt (+ 1.0 N))
2.0ms
(atan2 1.0 (+ 1 (* (* N (* (cbrt (+ 1.0 N)) (cbrt (+ 1.0 N)))) (cbrt (+ N 1.0)))))
7.0ms
(* (cbrt (+ 1.0 N)) (cbrt (+ 1.0 N)))

simplify54.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04912998
14912998

prune170.0ms

Filtered
62 candidates to 100 candidates (-61.3%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New991100
Fresh156
Picked011
Done022
Total1009109

Merged error: 0.3b

Counts
109 → 9

regimes101.0ms

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 (1.0ms)

IterNodesCost
02811
12811

end0.0ms

sample812.0ms

Algorithm
intervals
Results
443.0ms2878×body1280valid
139.0ms4008×body80valid
84.0ms638×body640valid
31.0ms320×body320valid
11.0ms156×body160valid

Profiling

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