Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	93×	body	1280	valid
10.0ms	132×	body	80	valid
4.0ms	16×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	7×	body	160	valid

simplify18.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

18.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize19.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite11.0ms

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

8.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

series43.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

40.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify233.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

52.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
28.0ms	(- (+ N 1) N)
27.0ms	(+ 1 (* (+ N 1) N))
20.0ms	(- (atan (+ N 1)) (atan N))
19.0ms	(- (atan (+ N 1)) (atan N))

prune202.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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

16.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series55.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

52.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify850.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

404.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
100.0ms	(* (+ (pow N 3) (pow 1 3)) N)
76.0ms	(* (- (* N N) (* 1 1)) N)
52.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
38.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune282.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.4b	(* (cbrt N) (cbrt N))

rewrite11.0ms

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

8.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

304.0ms	(* (cbrt N) (cbrt N))
281.0ms	(cbrt N)
265.0ms	(cbrt N)
260.0ms	(cbrt N)

simplify860.0ms

Counts

63 → 89

Calls

63 calls:

Slowest

131.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
121.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
112.0ms	(* (pow (pow N 2) 1/3) (pow (cbrt -1) 2))
104.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
77.0ms	(* (* (cbrt (cbrt N)) (cbrt (cbrt N))) (* (cbrt (cbrt N)) (cbrt (cbrt N))))

prune804.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `add-log-exp`
1×	`pow3` `rem-cbrt-cube`

Counts

4 → 47

Calls

4 calls:

Slowest

35.0ms	(cbrt (* (* (cbrt N) (cbrt N)) (cbrt N)))
2.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

309.0ms	(cbrt (* (* (cbrt N) (cbrt N)) (cbrt N)))
294.0ms	(cbrt N)
285.0ms	(cbrt N)
247.0ms	(cbrt N)

simplify661.0ms

Counts

22 → 59

Calls

22 calls:

Slowest

146.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
144.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
138.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
90.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
31.0ms	(pow (/ 1 N) -1/3)

prune669.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.3b

regimes137.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.3s	2883×	body	1280	valid
245.0ms	4022×	body	80	valid
166.0ms	602×	body	640	valid
110.0ms	347×	body	320	valid
19.0ms	146×	body	160	valid