Details

sample70.0ms

Algorithm

intervals

Results

41.0ms	107×	body	1280	valid
10.0ms	121×	body	80	valid
5.0ms	16×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify20.0ms

Calls

1 calls:

Slowest

19.0ms

(- (atan (+ N 1)) (atan N))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize11.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1)) (atan N))

rewrite5.0ms

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))

series7.0ms

Calls

1 calls:

Slowest

7.0ms

(- (atan (+ N 1)) (atan N))

simplify152.0ms

Calls

9 calls:

Slowest

44.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
19.0ms	(- (atan (+ N 1)) (atan N))
16.0ms	(- (+ N 1) N)
15.0ms	(+ 1 (* (+ N 1) N))
13.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))

prune145.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite7.0ms

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)))

series36.0ms

Calls

2 calls:

Slowest

32.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify276.0ms

Calls

10 calls:

Slowest

88.0ms	(* (- (* N N) (* 1 1)) N)
55.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
36.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
32.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
25.0ms	(* (+ (pow N 3) (pow 1 3)) N)

prune220.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

17.8b	(cbrt (* (+ N 1) N))
17.8b	(cbrt (* (+ N 1) N))
17.8b	(cbrt (* (+ N 1) N))
0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

rewrite30.0ms

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

18.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
4.0ms	(cbrt (* (+ N 1) N))
4.0ms	(cbrt (* (+ N 1) N))
4.0ms	(cbrt (* (+ N 1) N))

series207.0ms

Calls

4 calls:

Slowest

73.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
47.0ms	(cbrt (* (+ N 1) N))
47.0ms	(cbrt (* (+ N 1) N))
41.0ms	(cbrt (* (+ N 1) N))

simplify4.1s

Calls

49 calls:

Slowest

377.0ms	(- (+ (* (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))))
364.0ms	(- (+ (* (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))))
332.0ms	(- (+ (* (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	(- (+ (* (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))))
199.0ms	(* (* (+ N 1) N) (* (+ N 1) N))

prune810.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

17.8b	(cbrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.8b	(cbrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.8b	(cbrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`

Calls

4 calls:

Slowest

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

series506.0ms

Calls

4 calls:

Slowest

181.0ms	(cbrt (atan2 1 (+ 1 (* (+ N 1) N))))
176.0ms	(cbrt (atan2 1 (+ 1 (* (+ N 1) N))))
145.0ms	(cbrt (atan2 1 (+ 1 (* (+ N 1) N))))
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify630.0ms

Calls

21 calls:

Slowest

46.0ms	(pow (atan2 1 (+ N (+ (pow N 2) 1))) 1/3)
44.0ms	(pow (atan2 1 (+ N (+ (pow N 2) 1))) 1/3)
43.0ms	(pow (atan2 1 (+ N (+ (pow N 2) 1))) 1/3)
39.0ms	(pow (atan2 1 (+ N (+ (pow N 2) 1))) 1/3)
37.0ms	(pow (atan2 1 (+ N (+ (pow N 2) 1))) 1/3)

prune550.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.2b

regimes41.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

891.0ms	2843×	body	1280	valid
260.0ms	4064×	body	80	valid
156.0ms	614×	body	640	valid
53.0ms	325×	body	320	valid
18.0ms	154×	body	160	valid