Details

sample36.0ms

Algorithm

intervals

Results

19.0ms	97×	body	1280	valid
6.0ms	134×	body	80	valid
3.0ms	15×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
0.9b	(- (atan (+ N 1)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

1.0ms	(atan (+ N 1))
5.0ms	(- (atan (+ N 1)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
13.0ms	(- (atan (+ N 1)) (atan N))

simplify1.3s

Counts

46 → 46

Iterations

Iter	Nodes
4	2081
3	752
2	286
1	138
0	67

prune359.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef`

Counts

2 → 21

Calls

2 calls:

0.0ms	(fma N (+ 1 N) 1)
0.0ms	(atan2 1 (fma N (+ 1 N) 1))

series30.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(fma N (+ 1 N) 1)
2.0ms	(atan2 1 (fma N (+ 1 N) 1))

simplify5.6s

Counts

27 → 27

Iterations

Iter	Nodes
5	5729
4	886
3	225
2	83
1	51
0	33

prune202.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma N (+ 1 N) 1)) (cbrt (fma N (+ 1 N) 1)))
16.6b	(cbrt (fma N (+ 1 N) 1))
16.6b	(cbrt (fma N (+ 1 N) 1))
16.6b	(cbrt (fma N (+ 1 N) 1))

rewrite12.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `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 → 85

Calls

4 calls:

9.0ms	(* (cbrt (fma N (+ 1 N) 1)) (cbrt (fma N (+ 1 N) 1)))
1.0ms	(cbrt (fma N (+ 1 N) 1))
1.0ms	(cbrt (fma N (+ 1 N) 1))
1.0ms	(cbrt (fma N (+ 1 N) 1))

series215.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cbrt (fma N (+ 1 N) 1)) (cbrt (fma N (+ 1 N) 1)))
49.0ms	(cbrt (fma N (+ 1 N) 1))
48.0ms	(cbrt (fma N (+ 1 N) 1))
67.0ms	(cbrt (fma N (+ 1 N) 1))

simplify990.0ms

Counts

97 → 97

Iterations

Iter	Nodes
4	2416
3	1040
2	489
1	208
0	93

prune903.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

16.2b	(sqrt (fma N (+ 1 N) 1))
16.2b	(sqrt (fma N (+ 1 N) 1))
16.6b	(cbrt (fma N (+ 1 N) 1))
16.6b	(cbrt (fma N (+ 1 N) 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (fma N (+ 1 N) 1))
1.0ms	(sqrt (fma N (+ 1 N) 1))
1.0ms	(cbrt (fma N (+ 1 N) 1))
1.0ms	(cbrt (fma N (+ 1 N) 1))

series199.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(sqrt (fma N (+ 1 N) 1))
42.0ms	(sqrt (fma N (+ 1 N) 1))
52.0ms	(cbrt (fma N (+ 1 N) 1))
68.0ms	(cbrt (fma N (+ 1 N) 1))

simplify1.5s

Counts

72 → 72

Iterations

Iter	Nodes
5	2306
4	1157
3	602
2	281
1	133
0	66

prune828.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	6
1	6
0	5

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	2905×	body	1280	valid
310.0ms	4085×	body	80	valid
202.0ms	577×	body	640	valid
55.0ms	298×	body	320	valid
16.0ms	135×	body	160	valid