Details

sample36.0ms

Algorithm

intervals

Results

16.0ms	74×	body	1280	valid
6.0ms	137×	body	80	valid
5.0ms	28×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	3×	body	160	valid

simplify23.0ms

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize14.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (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))

series14.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

14.0ms

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

simplify2.4s

Counts: 19 → 19

prune156.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.8b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite14.0ms

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

14.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series55.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

53.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.0s

Counts: 36 → 36

prune278.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.8b	(atan2 1 (+ 1 (+ N (* N N))))
0.0b	(+ N (* N N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp`
3×	`*-un-lft-identity`
2×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`+-commutative` `sum-log` `flip3-+` `distribute-rgt-out` `distribute-rgt1-in` `flip-+`

Counts

2 → 22

Calls

2 calls:

Slowest

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

series46.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

43.0ms	(+ N (* N N))
2.0ms	(atan2 1 (+ 1 (+ N (* N N))))

simplify800.0ms

Counts: 28 → 28

prune234.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1 (+ 1 (* (* (+ N 1) (* (cbrt N) (cbrt N))) (cbrt N))))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

Slowest

2.0ms	(cbrt N)
2.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (* (cbrt N) (cbrt N))) (cbrt N))))

series728.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

248.0ms	(cbrt N)
244.0ms	(cbrt N)
225.0ms	(cbrt N)
10.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (* (cbrt N) (cbrt N))) (cbrt N))))

simplify1.8s

Counts: 56 → 56

prune433.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes82.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	2868×	body	1280	valid
213.0ms	3992×	body	80	valid
167.0ms	656×	body	640	valid
51.0ms	323×	body	320	valid
17.0ms	161×	body	160	valid