Details

sample38.0ms

Algorithm

intervals

Results

21.0ms	103×	body	1280	valid
5.0ms	114×	body	80	valid
4.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

11.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize11.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite6.0ms

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`

Counts

2 → 24

Calls

2 calls:

Slowest

5.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series33.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

31.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify227.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

51.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
29.0ms	(- (+ N 1) N)
23.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))
21.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
18.0ms	(- (atan (+ N 1)) (atan N))

prune234.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)
0.0b	(+ 1 (* (+ N 1) N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`associate-l`
3×	`associate-r` `insert-posit16`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 42

Calls

3 calls:

Slowest

17.0ms	(* (+ N 1) N)
5.0ms	(+ 1 (* (+ N 1) N))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series84.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

67.0ms	(* (+ N 1) N)
15.0ms	(+ 1 (* (+ N 1) N))
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.1s

Counts

21 → 51

Calls

21 calls:

Slowest

351.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
176.0ms	(* (exp 1) (exp (* (+ N 1) N)))
106.0ms	(* (+ (pow N 3) (pow 1 3)) N)
104.0ms	(* (- (* N N) (* 1 1)) N)
52.0ms	(+ N (+ (pow N 2) 1))

prune457.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(atan2 1 (+ N (+ 1 (* N N))))
0.0b	(+ N (+ 1 (* N N)))
0.0b	(+ 1 (* N N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
5×	`*-un-lft-identity`
4×	`sum-log`
3×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

3 → 35

Calls

3 calls:

Slowest

10.0ms	(+ N (+ 1 (* N N)))
4.0ms	(+ 1 (* N N))
0.0ms	(atan2 1 (+ N (+ 1 (* N N))))

series66.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

40.0ms	(+ 1 (* N N))
24.0ms	(+ N (+ 1 (* N N)))
3.0ms	(atan2 1 (+ N (+ 1 (* N N))))

simplify841.0ms

Counts

14 → 44

Calls

14 calls:

Slowest

276.0ms	(* (exp N) (* (exp 1) (exp (* N N))))
160.0ms	(* (exp N) (exp (+ 1 (* N N))))
72.0ms	(* (exp 1) (exp (* N N)))
52.0ms	(+ N (+ (pow N 2) 1))
51.0ms	(+ N (+ 1 (* N N)))

prune358.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

16.7b	(cbrt (+ 1 (* (+ N 1) N)))
16.7b	(cbrt (+ 1 (* (+ N 1) N)))
16.7b	(cbrt (+ 1 (* (+ N 1) N)))
0.2b	(* (cbrt (+ 1 (* (+ N 1) N))) (cbrt (+ 1 (* (+ N 1) N))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 91

Calls

4 calls:

Slowest

18.0ms	(* (cbrt (+ 1 (* (+ N 1) N))) (cbrt (+ 1 (* (+ N 1) N))))
5.0ms	(cbrt (+ 1 (* (+ N 1) N)))
2.0ms	(cbrt (+ 1 (* (+ N 1) N)))
2.0ms	(cbrt (+ 1 (* (+ N 1) N)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

69.0ms	(* (cbrt (+ 1 (* (+ N 1) N))) (cbrt (+ 1 (* (+ N 1) N))))
51.0ms	(cbrt (+ 1 (* (+ N 1) N)))
45.0ms	(cbrt (+ 1 (* (+ N 1) N)))
40.0ms	(cbrt (+ 1 (* (+ N 1) N)))

simplify10.1s

Counts

83 → 103

Calls

83 calls:

Slowest

541.0ms	(cbrt (- (* 1 1) (* (* (+ N 1) N) (* (+ N 1) N))))
507.0ms	(cbrt (+ (pow 1 3) (pow (* (+ N 1) N) 3)))
477.0ms	(cbrt (+ (pow 1 3) (pow (* (+ N 1) N) 3)))
472.0ms	(* (cbrt (+ (pow 1 3) (pow (* (+ N 1) N) 3))) (cbrt (+ 1 (* (+ N 1) N))))
466.0ms	(* (cbrt (+ (pow 1 3) (pow (* (+ N 1) N) 3))) (cbrt (+ (pow 1 3) (pow (* (+ N 1) N) 3))))

prune928.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes142.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

928.0ms	2885×	body	1280	valid
302.0ms	4033×	body	80	valid
134.0ms	613×	body	640	valid
57.0ms	320×	body	320	valid
42.0ms	149×	body	160	valid