Details

sample71.0ms

Algorithm

intervals

Results

39.0ms	98×	body	1280	valid
10.0ms	120×	body	80	valid
6.0ms	20×	body	640	valid
3.0ms	10×	body	320	valid
1.0ms	8×	body	160	valid

simplify34.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

34.0ms

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize22.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (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))

series23.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

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

simplify215.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

69.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
24.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
23.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))
16.0ms	(- (+ N 1) N)
15.0ms	(+ 1 (* (+ N 1) N))

prune245.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite24.0ms

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

23.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series62.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

59.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify726.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

287.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
114.0ms	(* (+ (pow N 3) (pow 1 3)) N)
83.0ms	(* (- (* N N) (* 1 1)) N)
36.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
36.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune289.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

16.9b	(cbrt (* (+ N 1) N))
16.9b	(cbrt (* (+ N 1) N))
16.9b	(cbrt (* (+ N 1) N))
0.4b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

rewrite48.0ms

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

17.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
10.0ms	(cbrt (* (+ N 1) N))
10.0ms	(cbrt (* (+ N 1) N))
6.0ms	(cbrt (* (+ N 1) N))

series287.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(cbrt (* (+ N 1) N))
77.0ms	(cbrt (* (+ N 1) N))
69.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
61.0ms	(cbrt (* (+ N 1) N))

simplify6.6s

Counts

63 → 88

Calls

63 calls:

Slowest

448.0ms	(- (+ (* (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))))
434.0ms	(- (+ (* (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))))
422.0ms	(- (+ (* (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))))
361.0ms	(* (cbrt (* (+ (pow N 3) (pow 1 3)) N)) (cbrt (* (- (* N N) (* 1 1)) N)))
294.0ms	(* (cbrt (* (- (* N N) (* 1 1)) N)) (cbrt (* (+ (pow N 3) (pow 1 3)) N)))

prune893.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize25.0ms

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))

rewrite11.0ms

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

8.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

280.0ms	(* (cbrt N) (cbrt N))
266.0ms	(cbrt N)
243.0ms	(cbrt N)
239.0ms	(cbrt N)

simplify782.0ms

Counts

63 → 89

Calls

63 calls:

Slowest

121.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
114.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
106.0ms	(* (pow (* N -1) 1/3) (cbrt -1))
93.0ms	(* (pow (pow N 2) 1/3) (pow (cbrt -1) 2))
65.0ms	(* (* (cbrt (cbrt N)) (cbrt (cbrt N))) (* (cbrt (cbrt N)) (cbrt (cbrt N))))

prune771.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes42.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	2844×	body	1280	valid
268.0ms	4019×	body	80	valid
188.0ms	655×	body	640	valid
59.0ms	168×	body	160	valid
54.0ms	314×	body	320	valid