Details

sample50.0ms

Algorithm

intervals

Results

24.0ms	95×	body	1280	valid
11.0ms	132×	body	80	valid
3.0ms	15×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

15.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize10.0ms

Local error

Found 1 expressions with local error:

1.5b	(- (atan (+ N 1)) (atan N))

rewrite4.0ms

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))

series18.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

18.0ms

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

simplify202.0ms

Counts

9 → 19

Calls

9 calls:

Slowest

38.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
27.0ms	(+ 1 (* (+ N 1) N))
25.0ms	(- (atan (+ N 1)) (atan N))
23.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))
22.0ms	(- (atan (+ N 1)) (atan N))

prune153.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(+ 1 (* (+ N 1) N))
0.0b	(* (+ N 1) N)

rewrite25.0ms

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

19.0ms	(* (+ N 1) N)
5.0ms	(+ 1 (* (+ N 1) N))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series88.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

59.0ms	(* (+ N 1) N)
25.0ms	(+ 1 (* (+ N 1) N))
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.1s

Counts

21 → 51

Calls

21 calls:

Slowest

281.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
146.0ms	(* (exp 1) (exp (* (+ N 1) N)))
116.0ms	(* (- (* N N) (* 1 1)) N)
101.0ms	(* (+ (pow N 3) (pow 1 3)) N)
53.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune425.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

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))

rewrite23.0ms

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

16.0ms	(* (cbrt N) (cbrt N))
2.0ms	(cbrt N)
2.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

325.0ms	(* (cbrt N) (cbrt N))
310.0ms	(cbrt N)
282.0ms	(cbrt N)
257.0ms	(cbrt N)

simplify890.0ms

Counts

63 → 89

Calls

63 calls:

Slowest

171.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
123.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
105.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
88.0ms	(* (pow (pow N 2) 1/3) (pow (cbrt -1) 2))
73.0ms	(* (* (cbrt (cbrt N)) (cbrt (cbrt N))) (* (cbrt (cbrt N)) (cbrt (cbrt N))))

prune949.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
10×	`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 → 54

Calls

4 calls:

Slowest

1.0ms	(cbrt (cbrt N))
1.0ms	(cbrt (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

425.0ms	(cbrt (cbrt N))
352.0ms	(cbrt (cbrt N))
304.0ms	(cbrt N)
288.0ms	(cbrt N)

simplify1.8s

Counts

30 → 66

Calls

30 calls:

Slowest

703.0ms	(* (pow (* N -1) 1/9) (pow (cbrt -1) 1/3))
652.0ms	(* (pow (* N -1) 1/9) (pow (cbrt -1) 1/3))
127.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
109.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
31.0ms	(pow (/ 1 N) -1/9)

prune872.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

851.0ms	2903×	body	1280	valid
745.0ms	4040×	body	80	valid
141.0ms	613×	body	640	valid
99.0ms	306×	body	320	valid
18.0ms	138×	body	160	valid