Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	88×	body	1280	valid
10.0ms	128×	body	80	valid
6.0ms	22×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify11.0ms

Calls

1 calls:

Slowest

11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

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))

series20.0ms

Calls

1 calls:

Slowest

20.0ms

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

simplify232.0ms

Calls

9 calls:

Slowest

48.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
44.0ms	(- (+ N 1) N)
27.0ms	(+ 1 (* (+ N 1) N))
22.0ms	(- (atan (+ N 1)) (atan N))
20.0ms	(- (atan (+ N 1)) (atan N))

prune153.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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)))

simplify143.0ms

Calls

3 calls:

Slowest

54.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
49.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
39.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune108.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

2 calls:

Slowest

31.0ms	(+ N (+ (* N N) 1))
0.0ms	(atan2 1 (+ N (+ (* N N) 1)))

series19.0ms

Calls

2 calls:

Slowest

16.0ms	(+ N (+ (* N N) 1))
3.0ms	(atan2 1 (+ N (+ (* N N) 1)))

simplify776.0ms

Calls

9 calls:

Slowest

387.0ms	(* (exp N) (* (exp (* N N)) (exp 1)))
144.0ms	(* (exp N) (exp (+ (* N N) 1)))
44.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
42.0ms	(+ N (+ (pow N 2) 1))
38.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune261.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt (+ N (+ (* N N) 1)))
15.0b	(cbrt (+ N (+ (* N N) 1)))
15.0b	(cbrt (+ N (+ (* N N) 1)))
0.2b	(* (cbrt (+ N (+ (* N N) 1))) (cbrt (+ N (+ (* N N) 1))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

128.0ms	(* (cbrt (+ N (+ (* N N) 1))) (cbrt (+ N (+ (* N N) 1))))
25.0ms	(cbrt (+ N (+ (* N N) 1)))
20.0ms	(cbrt (+ N (+ (* N N) 1)))
11.0ms	(cbrt (+ N (+ (* N N) 1)))

series259.0ms

Calls

4 calls:

Slowest

71.0ms	(cbrt (+ N (+ (* N N) 1)))
67.0ms	(cbrt (+ N (+ (* N N) 1)))
61.0ms	(cbrt (+ N (+ (* N N) 1)))
59.0ms	(* (cbrt (+ N (+ (* N N) 1))) (cbrt (+ N (+ (* N N) 1))))

simplify10.9s

Calls

94 calls:

Slowest

779.0ms	(cbrt (- (* N N) (* (+ (* N N) 1) (+ (* N N) 1))))
719.0ms	(cbrt (- (* N N) (* (+ (* N N) 1) (+ (* N N) 1))))
674.0ms	(cbrt (- (* N N) (* (+ (* N N) 1) (+ (* N N) 1))))
381.0ms	(* (cbrt (+ (pow N 3) (pow (+ (* N N) 1) 3))) (cbrt (+ (pow N 3) (pow (+ (* N N) 1) 3))))
347.0ms	(+ (* 1/3 (pow (/ 1 N) 1/3)) (+ (pow (/ 1 N) -2/3) (* 2/9 (pow (/ 1 (pow N 4)) 1/3))))

prune898.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s	2887×	body	1280	valid
187.0ms	4045×	body	80	valid
144.0ms	641×	body	640	valid
59.0ms	280×	body	320	valid
14.0ms	147×	body	160	valid