Details

sample50.0ms

Algorithm

intervals

Results

27.0ms	89×	body	1280	valid
8.0ms	134×	body	80	valid
4.0ms	17×	body	640	valid
2.0ms	12×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

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: 14.1b

localize22.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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

10.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

12.0ms

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

simplify1.2s

Counts

23 → 19

Calls

23 calls:

Slowest

362.0ms	(* (* (- (atan (+ N 1)) (atan N)) (- (atan (+ N 1)) (atan N))) (- (atan (+ N 1)) (atan N)))
234.0ms	(- (pow (atan (+ N 1)) 3) (pow (atan N) 3))
160.0ms	(- (* (atan (+ N 1)) (atan (+ N 1))) (* (atan N) (atan N)))
70.0ms	(exp (- (atan (+ N 1)) (atan N)))
59.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))

prune174.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite20.0ms

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

19.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series52.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

48.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.2s

Counts

36 → 36

Calls

36 calls:

Slowest

652.0ms	(* (* (* (+ N 1) N) (* (+ N 1) N)) (* (+ N 1) N))
281.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
136.0ms	(* (- (* N N) (* 1 1)) N)
125.0ms	(* (+ (pow N 3) (pow 1 3)) N)
92.0ms	(* (* (atan2 1 (+ 1 (* (+ N 1) N))) (atan2 1 (+ 1 (* (+ N 1) N)))) (atan2 1 (+ 1 (* (+ N 1) N))))

prune228.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.5b	(* (cbrt N) (cbrt N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

Slowest

11.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

337.0ms	(* (cbrt N) (cbrt N))
301.0ms	(cbrt N)
291.0ms	(cbrt N)
277.0ms	(cbrt N)

simplify1.2s

Counts

103 → 89

Calls

103 calls:

Slowest

153.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
142.0ms	(* (pow (pow N 2) 1/3) (pow (cbrt -1) 2))
139.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
119.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
98.0ms	(* (* (* (cbrt N) (cbrt N)) (* (cbrt N) (cbrt N))) (* (cbrt N) (cbrt N)))

prune824.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize36.0ms

Local error

Found 4 expressions with local error:

30.4b	(cbrt (* N N))
0.6b	(cbrt N)
0.4b	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
0.3b	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

Slowest

41.0ms	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
3.0ms	(cbrt (* N N))
1.0ms	(cbrt N)
0.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

306.0ms	(cbrt N)
284.0ms	(cbrt (* N N))
93.0ms	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
9.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

simplify5.4s

Counts

67 → 66

Calls

67 calls:

Slowest

620.0ms	(* (* (* (* (+ N 1) (cbrt (* N N))) (* (+ N 1) (cbrt (* N N)))) (* (+ N 1) (cbrt (* N N)))) N)
335.0ms	(* (* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* N N)) N)
277.0ms	(atan2 1 (- 1 (+ (* (pow N 2) (cbrt -1)) (* N (cbrt -1)))))
246.0ms	(exp (* (* (+ N 1) (cbrt (* N N))) (cbrt N)))
242.0ms	(* (* (+ N 1) (cbrt (* N N))) (* (cbrt (cbrt N)) (cbrt (cbrt N))))

prune660.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	2839×	body	1280	valid
284.0ms	4066×	body	80	valid
146.0ms	627×	body	640	valid
56.0ms	323×	body	320	valid
19.0ms	145×	body	160	valid