Details

sample50.0ms

Algorithm

intervals

Results

27.0ms	97×	body	1280	valid
8.0ms	133×	body	80	valid
5.0ms	21×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize39.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
0.7b	(- (atan (+ N 1)) (atan N))

rewrite13.0ms

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:

2.0ms	(atan (+ N 1))
10.0ms	(- (atan (+ N 1)) (atan N))

series24.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
22.0ms	(- (atan (+ N 1)) (atan N))

simplify2.5s

Counts

30 → 30

Iterations

Iter	Nodes
6	5474
5	1652
4	618
3	287
2	149
1	75
0	41

prune283.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

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:

17.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series63.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.1s

Counts

36 → 36

Iterations

Iter	Nodes
4	3175
3	832
2	305
1	119
0	55

prune274.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
17.5b	(cbrt (* (+ N 1) N))
17.5b	(cbrt (* (+ N 1) N))
17.5b	(cbrt (* (+ N 1) N))

rewrite34.0ms

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:

17.0ms	(* (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))

series261.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
63.0ms	(cbrt (* (+ N 1) N))
57.0ms	(cbrt (* (+ N 1) N))
65.0ms	(cbrt (* (+ N 1) N))

simplify991.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2145
2	916
1	325
0	138

prune796.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
16.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite15.0ms

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:

0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
9.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
4.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
3.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
19.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify2.0s

Counts

98 → 98

Iterations

Iter	Nodes
5	3261
4	872
3	416
2	237
1	123
0	65

prune693.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	9
1	9
0	6

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.3s	2859×	body	1280	valid
265.0ms	4124×	body	80	valid
129.0ms	584×	body	640	valid
48.0ms	295×	body	320	valid
16.0ms	138×	body	160	valid