Details

sample52.0ms

Algorithm

intervals

Results

27.0ms	98×	body	1280	valid
7.0ms	117×	body	80	valid
5.0ms	21×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	10×	body	160	valid

simplify21.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize30.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite6.0ms

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

4.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series21.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

18.0ms	(- (atan (+ N 1)) (atan N))
3.0ms	(atan (+ N 1))

simplify2.0s

Counts: 30 → 30

prune271.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite15.0ms

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)))

series59.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

52.0ms	(* (+ N 1) N)
6.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.2s

Counts: 36 → 36

prune273.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

15.1b	(cbrt (* (+ N 1) N))
15.1b	(cbrt (* (+ N 1) N))
15.1b	(cbrt (* (+ N 1) N))
0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))

rewrite53.0ms

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

22.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
10.0ms	(cbrt (* (+ N 1) N))
10.0ms	(cbrt (* (+ N 1) N))
9.0ms	(cbrt (* (+ N 1) N))

series283.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
65.0ms	(cbrt (* (+ N 1) N))
62.0ms	(cbrt (* (+ N 1) N))
58.0ms	(cbrt (* (+ N 1) N))

simplify1.2s

Counts: 88 → 88

prune759.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

14.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite16.0ms

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

13.0ms	(* (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)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

21.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.0ms	(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)))

simplify2.3s

Counts: 98 → 98

prune765.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes87.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

956.0ms	2951×	body	1280	valid
296.0ms	3960×	body	80	valid
138.0ms	616×	body	640	valid
57.0ms	312×	body	320	valid
20.0ms	161×	body	160	valid