Details

Time bar (total: 10.7s)

sample42.0ms

Algorithm
intervals
Results
14.0ms86×body1280valid
14.0ms130×body80valid
4.0ms28×body640valid
1.0ms10×body320valid
0.0ms2×body160valid

simplify14.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize7.0ms

Local error

Found 1 expressions with local error:

0.8b
(- (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:
6.0ms
(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts
1 → 3
Calls
1 calls:
13.0ms
(- (atan (+ N 1.0)) (atan N))

simplify1.1s

Counts
18 → 18

prune44.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 1 expressions with local error:

0.6b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
Counts
1 → 7
Calls
1 calls:
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series4.0ms

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

simplify1.8s

Counts
10 → 10

prune30.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 82
Calls
4 calls:
0.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (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))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
4.0ms
(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
20.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
24.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify5.0s

Counts
94 → 94

prune223.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.7b
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite8.0ms

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))))
3.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
6.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
22.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
22.0ms
(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify563.0ms

Counts
52 → 52

prune197.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.5b

regimes62.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify31.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
697.0ms2845×body1280valid
170.0ms3987×body80valid
163.0ms676×body640valid
71.0ms317×body320valid
15.0ms175×body160valid