Details

Time bar (total: 9.2s)

sample57.0ms

Algorithm
intervals
Results
32.0ms95×body1280valid
10.0ms133×body80valid
4.0ms17×body640valid
1.0ms4×body320valid
1.0ms7×body160valid

simplify14.0ms

Calls
1 calls:
Slowest
14.0ms
(- (atan (+ N 1)) (atan N))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize11.0ms

Local error

Found 1 expressions with local error:

2.0b
(- (atan (+ N 1)) (atan N))

rewrite4.0ms

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

series11.0ms

Calls
1 calls:
Slowest
11.0ms
(- (atan (+ N 1)) (atan N))

simplify250.0ms

Calls
9 calls:
Slowest
63.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))
42.0ms
(+ 1 (* (+ N 1) N))
28.0ms
(- (+ N 1) N)
25.0ms
(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
23.0ms
(- (atan (+ N 1)) (atan N))

prune159.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.6b
(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b
(* (+ N 1) N)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
2×pow1 add-cbrt-cube associate-*l/ add-exp-log insert-posit16 add-log-exp
1×flip3-+ *-commutative flip-+
Calls
2 calls:
Slowest
3.0ms
(* (+ N 1) N)
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series21.0ms

Calls
2 calls:
Slowest
18.0ms
(* (+ N 1) N)
3.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify272.0ms

Calls
10 calls:
Slowest
58.0ms
(* (- (* N N) (* 1 1)) N)
41.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
41.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
35.0ms
(* (+ (pow N 3) (pow 1 3)) N)
34.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune232.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

16.0b
(cbrt (* (+ N 1) N))
16.0b
(cbrt (* (+ N 1) N))
16.0b
(cbrt (* (+ N 1) N))
0.6b
(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (cbrt (* (+ N 1) N)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×cbrt-div associate-*l/
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod flip3-+ pow1/3 flip-+
Calls
4 calls:
Slowest
4.0ms
(cbrt (* (+ N 1) N))
2.0ms
(cbrt (* (+ N 1) N))
2.0ms
(cbrt (* (+ N 1) N))
0.0ms
(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (cbrt (* (+ N 1) N)))))

series169.0ms

Calls
4 calls:
Slowest
58.0ms
(cbrt (* (+ N 1) N))
55.0ms
(cbrt (* (+ N 1) N))
51.0ms
(cbrt (* (+ N 1) N))
5.0ms
(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (cbrt (* (+ N 1) N)))))

simplify2.2s

Calls
21 calls:
Slowest
372.0ms
(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
340.0ms
(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
331.0ms
(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
116.0ms
(- (+ (* 1/3 (pow (/ 1 N) 1/3)) (pow (/ 1 N) -2/3)) (* 1/9 (pow (/ 1 (pow N 4)) 1/3)))
110.0ms
(- (+ (* 1/3 (pow (/ 1 N) 1/3)) (pow (/ 1 N) -2/3)) (* 1/9 (pow (/ 1 (pow N 4)) 1/3)))

prune626.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

16.0b
(cbrt (* (+ N 1) N))
16.0b
(cbrt (* (+ N 1) N))
0.6b
(cbrt N)
0.6b
(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (* (cbrt (+ N 1)) (cbrt N)))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 cbrt-div *-un-lft-identity add-cbrt-cube associate-*l/ add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×pow1/3
2×cbrt-prod flip3-+ flip-+
Calls
4 calls:
Slowest
2.0ms
(cbrt (* (+ N 1) N))
2.0ms
(cbrt (* (+ N 1) N))
0.0ms
(cbrt N)
0.0ms
(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (* (cbrt (+ N 1)) (cbrt N)))))

series391.0ms

Calls
4 calls:
Slowest
269.0ms
(cbrt N)
65.0ms
(cbrt (* (+ N 1) N))
51.0ms
(cbrt (* (+ N 1) N))
6.0ms
(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (* (cbrt (+ N 1)) (cbrt N)))))

simplify1.6s

Calls
18 calls:
Slowest
386.0ms
(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
345.0ms
(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
132.0ms
(- (+ (* 1/3 (pow (/ 1 N) 1/3)) (pow (/ 1 N) -2/3)) (* 1/9 (pow (/ 1 (pow N 4)) 1/3)))
116.0ms
(- (+ (pow N 1/3) (* 1/3 (pow (pow N 4) 1/3))) (* 1/9 (pow (pow N 7) 1/3)))
116.0ms
(- (+ (* 1/3 (pow (/ 1 N) 1/3)) (pow (/ 1 N) -2/3)) (* 1/9 (pow (/ 1 (pow N 4)) 1/3)))

prune727.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.5b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.6s2864×body1280valid
281.0ms4048×body80valid
168.0ms632×body640valid
60.0ms302×body320valid
22.0ms154×body160valid