Details

sample41.0ms

Algorithm

intervals

Results

19.0ms	86×	body	1280	valid
7.0ms	137×	body	80	valid
4.0ms	21×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify19.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize21.0ms

Local error

Found 1 expressions with local error:

1.0b	(- (atan (+ N 1)) (atan N))

rewrite5.0ms

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))

series20.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

20.0ms

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

simplify2.1s

Counts: 19 → 19

prune164.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite26.0ms

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

25.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series52.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

47.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.0s

Counts: 36 → 36

prune248.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize30.0ms

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))

rewrite22.0ms

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

17.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series943.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

255.0ms	(cbrt N)
239.0ms	(* (cbrt N) (cbrt N))
225.0ms	(cbrt N)
224.0ms	(cbrt N)

simplify1.0s

Counts: 89 → 89

prune692.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

31.7b	(cbrt (* N N))
0.6b	(cbrt N)
0.4b	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))
0.2b	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))

rewrite42.0ms

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

38.0ms	(* (* (+ 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))))

series467.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

201.0ms	(cbrt (* N N))
198.0ms	(cbrt N)
62.0ms	(* (* (+ N 1) (cbrt (* N N))) (cbrt N))
5.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (cbrt (* N N))) (cbrt N))))

simplify578.0ms

Counts: 66 → 66

prune452.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

988.0ms	2872×	body	1280	valid
236.0ms	3990×	body	80	valid
137.0ms	658×	body	640	valid
43.0ms	322×	body	320	valid
15.0ms	158×	body	160	valid