Details

Time bar (total: 3.4s)

sample49.0ms

Algorithm
intervals
Results
24.0ms88×body1280valid
9.0ms141×body80valid
4.0ms16×body640valid
1.0ms6×body320valid
1.0ms5×body160valid

simplify2.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize7.0ms

Local error

Found 1 expressions with local error:

1.2b
(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

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:
7.0ms
(- (atan (+ N 1.0)) (atan N))

series21.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(- (atan (+ N 1.0)) (atan N))

simplify60.0ms

Counts
18 → 18

prune79.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(* (+ N 1.0) N)
0.7b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite51.0ms

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:
49.0ms
(* (+ N 1.0) N)
1.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series69.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(* (+ N 1.0) N)
6.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify57.0ms

Counts
34 → 34

prune89.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
2.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series80.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
6.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
30.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
37.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify86.0ms

Counts
52 → 52

prune228.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.7b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.3b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 46
Calls
4 calls:
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
38.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
30.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
20.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify106.0ms

Counts
58 → 58

prune286.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.7b

regimes68.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.2s2871×body1280valid
280.0ms3986×body80valid
116.0ms640×body640valid
45.0ms328×body320valid
18.0ms175×body160valid