Details

sample67.0ms

Algorithm

intervals

Results

37.0ms	91×	body	1280	valid
12.0ms	141×	body	80	valid
4.0ms	11×	body	640	valid
3.0ms	12×	body	320	valid
0.0ms	1×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize35.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (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

4.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series14.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

12.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify206.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

48.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
22.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
21.0ms	(- (+ N 1) N)
20.0ms	(- (atan (+ N 1)) (atan N))
14.0ms	(+ 1 (* (+ N 1) N))

prune278.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite29.0ms

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

28.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series76.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

71.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify762.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

335.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
102.0ms	(* (+ (pow N 3) (pow 1 3)) N)
102.0ms	(* (- (* N N) (* 1 1)) N)
42.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
42.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune280.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

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))

rewrite20.0ms

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

14.0ms	(* (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

311.0ms	(* (cbrt N) (cbrt N))
296.0ms	(cbrt N)
280.0ms	(cbrt N)
243.0ms	(cbrt N)

simplify871.0ms

Counts

63 → 89

Calls

63 calls:

Slowest

144.0ms	(* (pow (pow N 2) 1/3) (pow (cbrt -1) 2))
130.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
116.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
103.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
79.0ms	(* (* (cbrt (cbrt N)) (cbrt (cbrt N))) (* (cbrt (cbrt N)) (cbrt (cbrt N))))

prune906.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (cbrt N) (cbrt N)))
0.6b	(cbrt (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

Slowest

4.0ms	(cbrt (* (cbrt N) (cbrt N)))
1.0ms	(cbrt (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.5s

Counts

4 → 12

Calls

4 calls:

Slowest

454.0ms	(cbrt (cbrt N))
390.0ms	(cbrt (* (cbrt N) (cbrt N)))
310.0ms	(cbrt N)
309.0ms	(cbrt N)

simplify1.2s

Counts

25 → 61

Calls

25 calls:

Slowest

661.0ms	(* (pow (* N -1) 1/9) (pow (cbrt -1) 1/3))
152.0ms	(* (pow (pow N 2) 1/9) (pow (pow (cbrt -1) 2) 1/3))
107.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
102.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
28.0ms	(pow (/ 1 N) -1/3)

prune673.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	2839×	body	1280	valid
280.0ms	4079×	body	80	valid
170.0ms	564×	body	640	valid
64.0ms	349×	body	320	valid
54.0ms	169×	body	160	valid