Details

Time bar (total: 8.9s)

sample71.0ms

Algorithm
intervals
Results
41.0ms93×body1280valid
10.0ms125×body80valid
7.0ms24×body640valid
2.0ms8×body320valid
1.0ms6×body160valid

simplify10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize11.0ms

Local error

Found 1 expressions with local error:

1.3b
(- (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))

series13.0ms

Calls
1 calls:
Slowest
13.0ms
(- (atan (+ N 1)) (atan N))

simplify185.0ms

Calls
9 calls:
Slowest
49.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))
34.0ms
(+ 1 (* (+ N 1) N))
20.0ms
(- (atan (+ N 1)) (atan N))
19.0ms
(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))
15.0ms
(- (+ N 1) N)

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(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)))

series44.0ms

Calls
2 calls:
Slowest
41.0ms
(* (+ N 1) N)
3.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify264.0ms

Calls
10 calls:
Slowest
60.0ms
(* (- (* N N) (* 1 1)) N)
52.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
48.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
29.0ms
(* (+ (pow N 3) (pow 1 3)) N)
28.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune218.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

17.2b
(cbrt (* (+ N 1) N))
17.2b
(cbrt (* (+ N 1) N))
17.2b
(cbrt (* (+ N 1) N))
0.4b
(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-*l/
18×cbrt-div
9×pow1 flip3-+ flip-+
7×pow1/3
6×add-sqr-sqrt *-un-lft-identity add-exp-log add-cube-cbrt
5×cbrt-prod
4×frac-times add-cbrt-cube associate-*r* associate-*l* insert-posit16 add-log-exp
2×pow-prod-down associate-*r/ pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
11.0ms
(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
2.0ms
(cbrt (* (+ N 1) N))
2.0ms
(cbrt (* (+ N 1) N))
2.0ms
(cbrt (* (+ N 1) N))

series272.0ms

Calls
4 calls:
Slowest
79.0ms
(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
75.0ms
(cbrt (* (+ N 1) N))
68.0ms
(cbrt (* (+ N 1) N))
49.0ms
(cbrt (* (+ N 1) N))

simplify3.9s

Calls
49 calls:
Slowest
352.0ms
(- (+ (* (pow (pow N 4) 1/3) (pow (cbrt -1) 2)) (* 2/3 (* (pow N 1/3) (pow (cbrt -1) 2)))) (* 1/9 (* (pow (/ 1 (pow N 2)) 1/3) (pow (cbrt -1) 2))))
341.0ms
(- (+ (* (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))))
310.0ms
(- (+ (* (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))))
266.0ms
(- (+ (* (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))))
236.0ms
(* (* (+ N 1) N) (* (+ N 1) N))

prune712.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 4 expressions with local error:

16.7b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.7b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.2b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
10×*-un-lft-identity add-cube-cbrt
9×pow1
6×add-cbrt-cube pow1/2 associate-*r* associate-*l* add-exp-log
4×insert-posit16 add-log-exp
2×rem-sqrt-square pow-prod-down pow-prod-up
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (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)))

series37.0ms

Calls
4 calls:
Slowest
18.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
3.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
3.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.1s

Calls
42 calls:
Slowest
74.0ms
(* (* (* (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))))))
45.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
42.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
42.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
40.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))

prune505.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

regimes44.0ms

Accuracy

0% (0.1b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
742.0ms2837×body1280valid
330.0ms4085×body80valid
120.0ms616×body640valid
45.0ms305×body320valid
16.0ms157×body160valid