Details

Time bar (total: 10.5s)

sample71.0ms

Algorithm
intervals
Results
42.0ms108×body1280valid
10.0ms118×body80valid
5.0ms17×body640valid
1.0ms9×body160valid
1.0ms4×body320valid

simplify20.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize22.0ms

Local error

Found 2 expressions with local error:

2.7b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite11.0ms

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
8.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

series22.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
19.0ms
(- (atan (+ N 1)) (atan N))
3.0ms
(atan (+ N 1))

simplify2.3s

Counts
30 → 30

prune178.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
3×associate-*r*
2×associate-*l/ insert-posit16 add-log-exp
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Counts
2 → 30
Calls
2 calls:
Slowest
23.0ms
(* (+ N 1) N)
1.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series55.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
52.0ms
(* (+ N 1) N)
3.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.1s

Counts
36 → 36

prune353.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)
0.5b
(* (cbrt N) (cbrt N))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
11×pow1
9×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 77
Calls
4 calls:
Slowest
15.0ms
(* (cbrt N) (cbrt N))
1.0ms
(cbrt N)
1.0ms
(cbrt N)
1.0ms
(cbrt N)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
295.0ms
(cbrt N)
280.0ms
(* (cbrt N) (cbrt N))
278.0ms
(cbrt N)
265.0ms
(cbrt N)

simplify1.2s

Counts
89 → 89

prune722.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

35.3b
(cbrt (* N N))
0.6b
(cbrt N)
0.3b
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
0.2b
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log
7×cbrt-prod add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*r*
4×associate-*l/ insert-posit16 add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×pow1/3
1×flip3-+ associate-*l* *-commutative flip-+
Counts
4 → 54
Calls
4 calls:
Slowest
50.0ms
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
6.0ms
(cbrt (* N N))
1.0ms
(cbrt N)
0.0ms
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

series518.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
229.0ms
(cbrt N)
224.0ms
(cbrt (* N N))
59.0ms
(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
6.0ms
(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

simplify610.0ms

Counts
66 → 66

prune453.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s2874×body1280valid
188.0ms4061×body80valid
126.0ms625×body640valid
38.0ms285×body320valid
15.0ms155×body160valid