Details

Time bar (total: 6.9s)

sample67.0ms

Algorithm
intervals
Results
35.0ms89×body1280valid
11.0ms130×body80valid
6.0ms20×body640valid
4.0ms13×body320valid
1.0ms4×body160valid

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (atan (+ N 1)) (atan N))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize22.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
Slowest
4.0ms
(- (atan (+ N 1)) (atan N))
1.0ms
(atan (+ N 1))

series15.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
13.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

simplify224.0ms

Counts
12 → 30
Calls
12 calls:
Slowest
55.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))
21.0ms
(- (atan (+ N 1)) (atan N))
20.0ms
(- (atan (+ N 1)) (atan N))
19.0ms
(- (atan (+ N 1)) (atan N))
17.0ms
(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))

prune300.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 1 expressions with local error:

0.4b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
Counts
1 → 8
Calls
1 calls:
Slowest
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series3.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
3.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify98.0ms

Counts
3 → 11
Calls
3 calls:
Slowest
42.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
28.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
28.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune68.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize29.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.4b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×insert-posit16 add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 86
Calls
4 calls:
Slowest
12.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
2.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
2.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series47.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
23.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
5.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
5.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.2s

Counts
82 → 98
Calls
82 calls:
Slowest
187.0ms
(* (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
107.0ms
(* (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))))
50.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
46.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
41.0ms
(* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))

prune758.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

14.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.4b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 50
Calls
4 calls:
Slowest
1.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series60.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
21.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
20.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
4.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify734.0ms

Counts
27 → 62
Calls
27 calls:
Slowest
54.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
50.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
41.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
40.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
37.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))

prune583.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.4b

regimes81.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
890.0ms2886×body1280valid
375.0ms4027×body80valid
138.0ms618×body640valid
56.0ms331×body320valid
17.0ms138×body160valid