Details

Time bar (total: 2.0s)

analyze1.0ms

Algorithm
search

sample33.0ms

Algorithm
intervals
Results
19.0ms99×body1280valid
4.0ms115×body80valid
3.0ms22×body640valid
1.0ms14×body320valid
0.0ms6×body160valid

simplify5.0ms

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: 15.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
2.0b
(- (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 → 22
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))

simplify75.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
075154
1145145
2289143
3681142
42447142
55001142

prune41.0ms

Filtered
19 candidates to 28 candidates (-47.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New26228
Fresh000
Picked101
Done000
Total27229

Merged error: 0.3b

Counts
29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

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

series8.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(* (+ N 1.0) N)
2.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify56.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0121151
1432127
22321127
35002127

prune55.0ms

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

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New31334
Fresh011
Picked011
Done000
Total31536

Merged error: 0.3b

Counts
36 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

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

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))
1.0ms
(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))
10.0ms
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))

series22.0ms

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

simplify160.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0345866
11119805
24847721
35001721

prune214.0ms

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

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New973100
Fresh213
Picked101
Done011
Total1005105

Merged error: 0.3b

Counts
105 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(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))))
10.0b
(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
18.3b
(cbrt (- (* N N) (* 1.0 1.0)))
18.3b
(cbrt (- (* N N) (* 1.0 1.0)))

rewrite30.0ms

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))))
19.0ms
(/ (* (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)))

series47.0ms

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))))
15.0ms
(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
12.0ms
(cbrt (- (* N N) (* 1.0 1.0)))
13.0ms
(cbrt (- (* N N) (* 1.0 1.0)))

simplify58.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05791387
121261169
250011126

prune282.0ms

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

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh033
Picked011
Done011
Total84589

Merged error: 0.3b

Counts
89 → 5

regimes40.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0124
1124

end0.0ms

analyze1.0ms

Algorithm
search

sample794.0ms

Algorithm
intervals
Results
436.0ms2880×body1280valid
138.0ms3994×body80valid
79.0ms649×body640valid
29.0ms313×body320valid
11.0ms164×body160valid

Profiling

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