Details

sample42.0ms

Algorithm

intervals

Results

24.0ms	88×	body	1280	valid
6.0ms	128×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	6×	body	160	valid

simplify11.0ms

Calls

1 calls:

Slowest

10.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize21.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (atan (+ N 1)) (atan N))

rewrite9.0ms

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`

Calls

1 calls:

Slowest

8.0ms

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

series22.0ms

Calls

1 calls:

Slowest

21.0ms

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

simplify205.0ms

Calls

9 calls:

Slowest

59.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
34.0ms	(+ 1 (* (+ N 1) N))
31.0ms	(- (+ N 1) N)
18.0ms	(- (atan (+ N 1)) (atan N))
18.0ms	(- (atan (+ N 1)) (atan N))

prune147.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Calls

1 calls:

Slowest

0.0ms

(atan2 1 (+ 1 (* (+ N 1) N)))

series5.0ms

Calls

1 calls:

Slowest

5.0ms

(atan2 1 (+ 1 (* (+ N 1) N)))

simplify132.0ms

Calls

3 calls:

Slowest

52.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
41.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
39.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune94.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

1.0ms	(+ N (* N N))
0.0ms	(atan2 1 (+ 1 (+ N (* N N))))

series49.0ms

Calls

2 calls:

Slowest

46.0ms	(+ N (* N N))
3.0ms	(atan2 1 (+ 1 (+ N (* N N))))

simplify168.0ms

Calls

6 calls:

Slowest

49.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
48.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
28.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
16.0ms	(+ N (pow N 2))
13.0ms	(+ N (pow N 2))

prune210.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

15.3b	(cbrt (+ N (* N N)))
15.3b	(cbrt (+ N (* N N)))
15.3b	(cbrt (+ N (* N N)))
0.4b	(* (cbrt (+ N (* N N))) (cbrt (+ N (* N N))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
18×	`cbrt-div`
11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `flip3-+` `flip-+`
7×	`pow1/3` `associate-r` `associate-l`
6×	`add-exp-log`
5×	`distribute-rgt1-in`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (+ N (* N N))) (cbrt (+ N (* N N))))
1.0ms	(cbrt (+ N (* N N)))
1.0ms	(cbrt (+ N (* N N)))
1.0ms	(cbrt (+ N (* N N)))

series240.0ms

Calls

4 calls:

Slowest

65.0ms	(cbrt (+ N (* N N)))
62.0ms	(cbrt (+ N (* N N)))
62.0ms	(cbrt (+ N (* N N)))
52.0ms	(* (cbrt (+ N (* N N))) (cbrt (+ N (* N N))))

simplify5.5s

Calls

64 calls:

Slowest

358.0ms	(* (cbrt (+ (pow N 3) (pow (* N N) 3))) (cbrt (- (* N N) (* (* N N) (* N N)))))
326.0ms	(* (+ N (* N N)) (+ N (* N N)))
315.0ms	(cbrt (- (* N N) (* (* N N) (* N N))))
292.0ms	(* (cbrt (- (* N N) (* (* N N) (* N N)))) (cbrt (+ (pow N 3) (pow (* N N) 3))))
290.0ms	(* (+ N (* N N)) (+ N (* N N)))

prune775.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

974.0ms	2887×	body	1280	valid
239.0ms	4045×	body	80	valid
139.0ms	641×	body	640	valid
37.0ms	280×	body	320	valid
14.0ms	147×	body	160	valid