Details

Time bar (total: 10.7s)

sample68.0ms

Algorithm
intervals
Results
39.0ms104×body1280valid
10.0ms121×body80valid
6.0ms19×body640valid
2.0ms8×body320valid
1.0ms4×body160valid

simplify21.0ms

Calls
1 calls:
Slowest
21.0ms
(- (atan (+ N 1)) (atan N))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize21.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite10.0ms

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
Calls
2 calls:
Slowest
8.0ms
(- (atan (+ N 1)) (atan N))
1.0ms
(atan (+ N 1))

series14.0ms

Calls
2 calls:
Slowest
11.0ms
(- (atan (+ N 1)) (atan N))
3.0ms
(atan (+ N 1))

simplify189.0ms

Calls
12 calls:
Slowest
44.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))
28.0ms
(- (+ N 1) N)
19.0ms
(- (atan (+ N 1)) (atan N))
17.0ms
(- (atan (+ N 1)) (atan N))
14.0ms
(+ 1 (* (+ N 1) N))

prune232.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

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
6.0ms
(* (+ N 1) N)
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series35.0ms

Calls
2 calls:
Slowest
30.0ms
(* (+ N 1) N)
5.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify297.0ms

Calls
10 calls:
Slowest
79.0ms
(* (- (* N N) (* 1 1)) N)
43.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
40.0ms
(* (+ (pow N 3) (pow 1 3)) N)
39.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
29.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune200.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

18.4b
(cbrt (* (+ N 1) N))
18.4b
(cbrt (* (+ N 1) N))
18.4b
(cbrt (* (+ N 1) N))
0.5b
(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

rewrite37.0ms

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
22.0ms
(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
5.0ms
(cbrt (* (+ N 1) N))
4.0ms
(cbrt (* (+ N 1) N))
4.0ms
(cbrt (* (+ N 1) N))

series238.0ms

Calls
4 calls:
Slowest
67.0ms
(cbrt (* (+ N 1) N))
63.0ms
(cbrt (* (+ N 1) N))
59.0ms
(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
48.0ms
(cbrt (* (+ N 1) N))

simplify4.4s

Calls
49 calls:
Slowest
392.0ms
(- (+ (* (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))))
371.0ms
(- (+ (* (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))))
368.0ms
(- (+ (* (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))))
336.0ms
(- (+ (* (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))))
221.0ms
(* (* (+ N 1) N) (* (+ N 1) N))

prune975.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

17.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.5b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.3b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite16.0ms

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
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))))
1.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series58.0ms

Calls
4 calls:
Slowest
26.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
22.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
5.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
4.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.2s

Calls
42 calls:
Slowest
98.0ms
(* (* (* (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))))))
57.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
55.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
54.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
50.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune737.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes54.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s2797×body1280valid
321.0ms4120×body80valid
162.0ms626×body640valid
57.0ms303×body320valid
24.0ms154×body160valid