Details

sample44.0ms

Algorithm

intervals

Results

26.0ms	96×	body	1280	valid
7.0ms	131×	body	80	valid
4.0ms	19×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Counts

1 → 1

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: 14.1b

localize10.0ms

Local error

Found 1 expressions with local error:

0.9b	(- (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`

Counts

1 → 16

Calls

1 calls:

Slowest

4.0ms

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

series15.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

15.0ms

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

simplify184.0ms

Counts

9 → 19

Calls

9 calls:

Slowest

39.0ms	(+ 1 (* (+ N 1) N))
38.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
29.0ms	(- (+ N 1) N)
21.0ms	(- (atan (+ N 1)) (atan N))
12.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))

prune126.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite14.0ms

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

14.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series57.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

55.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify626.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

283.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
81.0ms	(* (+ (pow N 3) (pow 1 3)) N)
64.0ms	(* (- (* N N) (* 1 1)) N)
30.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
28.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune205.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.5b	(atan2 1 (+ 1 (* (* (+ N 1) (* (cbrt N) (cbrt N))) (cbrt 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`

Counts

4 → 44

Calls

4 calls:

Slowest

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

series600.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

202.0ms	(cbrt N)
198.0ms	(cbrt N)
193.0ms	(cbrt N)
7.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (* (cbrt N) (cbrt N))) (cbrt N))))

simplify464.0ms

Counts

21 → 56

Calls

21 calls:

Slowest

98.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
96.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
94.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
30.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
30.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune384.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))
0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 53

Calls

4 calls:

Slowest

3.0ms	(cbrt (+ N 1))
2.0ms	(cbrt (+ N 1))
2.0ms	(cbrt (+ N 1))
0.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

42.0ms	(cbrt (+ N 1))
40.0ms	(cbrt (+ N 1))
36.0ms	(cbrt (+ N 1))
3.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

simplify1.5s

Counts

30 → 65

Calls

30 calls:

Slowest

163.0ms	(- (+ (pow (/ 1 N) -1/3) (* 1/3 (pow (/ 1 (pow N 2)) 1/3))) (* 1/9 (pow (/ 1 (pow N 5)) 1/3)))
163.0ms	(- (+ (pow (/ 1 N) -1/3) (* 1/3 (pow (/ 1 (pow N 2)) 1/3))) (* 1/9 (pow (/ 1 (pow N 5)) 1/3)))
162.0ms	(- (+ (pow (/ 1 N) -1/3) (* 1/3 (pow (/ 1 (pow N 2)) 1/3))) (* 1/9 (pow (/ 1 (pow N 5)) 1/3)))
146.0ms	(- (+ (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 N))))) N)) (exp (* 1/3 (- (log -1) (log (/ -1 N)))))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 N))))) (pow N 2))))
145.0ms	(- (+ (* 1/3 (/ (exp (* 1/3 (- (log -1) (log (/ -1 N))))) N)) (exp (* 1/3 (- (log -1) (log (/ -1 N)))))) (* 1/9 (/ (exp (* 1/3 (- (log -1) (log (/ -1 N))))) (pow N 2))))

prune459.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

903.0ms	2783×	body	1280	valid
247.0ms	4111×	body	80	valid
106.0ms	629×	body	640	valid
77.0ms	322×	body	320	valid
14.0ms	155×	body	160	valid