Details

sample47.0ms

Algorithm

intervals

Results

26.0ms	92×	body	1280	valid
8.0ms	136×	body	80	valid
4.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify10.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

10.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize27.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

Slowest

8.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

series24.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

21.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify207.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

44.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
29.0ms	(- (+ N 1) N)
27.0ms	(+ 1 (* (+ N 1) N))
18.0ms	(- (atan (+ N 1)) (atan N))
16.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))

prune245.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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

18.0ms	(* (+ N 1) N)
5.0ms	(+ 1 (* (+ N 1) N))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series93.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

61.0ms	(* (+ N 1) N)
29.0ms	(+ 1 (* (+ N 1) N))
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.1s

Counts

21 → 51

Calls

21 calls:

Slowest

333.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
169.0ms	(* (exp 1) (exp (* (+ N 1) N)))
131.0ms	(* (+ (pow N 3) (pow 1 3)) N)
116.0ms	(* (- (* N N) (* 1 1)) N)
50.0ms	(+ N (+ (pow N 2) 1))

prune436.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

14.8b	(cbrt (* (+ N 1) N))
14.8b	(cbrt (* (+ N 1) N))
14.8b	(cbrt (* (+ N 1) N))
0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

Slowest

35.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))

series304.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

86.0ms	(cbrt (* (+ N 1) N))
84.0ms	(cbrt (* (+ N 1) N))
69.0ms	(cbrt (* (+ N 1) N))
64.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

simplify7.2s

Counts

63 → 88

Calls

63 calls:

Slowest

522.0ms	(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
495.0ms	(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))
438.0ms	(* (cbrt (* (+ (pow N 3) (pow 1 3)) N)) (cbrt (* (- (* N N) (* 1 1)) N)))
438.0ms	(* (cbrt (* (- (* N N) (* 1 1)) N)) (cbrt (* (+ (pow N 3) (pow 1 3)) N)))
431.0ms	(- (+ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (* 1/3 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) N))) (* 1/9 (/ (* (cbrt -1) (exp (* 1/3 (- (log -1) (* 2 (log (/ -1 N))))))) (pow N 2))))

prune818.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.3b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.1b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

Slowest

8.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

23.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
3.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.2s

Counts

82 → 98

Calls

82 calls:

Slowest

129.0ms	(* (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
123.0ms	(* (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))))
56.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
44.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
44.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))

prune690.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes35.0ms

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	2921×	body	1280	valid
240.0ms	3993×	body	80	valid
159.0ms	615×	body	640	valid
52.0ms	302×	body	320	valid
19.0ms	169×	body	160	valid