Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	94×	body	1280	valid
4.0ms	133×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize6.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

3.0ms

(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(- (atan (+ N 1.0)) (atan N))

simplify895.0ms

Counts

32 → 32

Iterations

Useful iterations: 3 (177.0ms)

Iter	Nodes	Cost
0	62	552
1	133	439
2	354	352
3	1306	291
done	5001	291

prune55.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b	(atan2 (- 1.0 0) (fma N (+ N 1.0) 1))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

0.0ms

(atan2 (- 1.0 0) (fma N (+ N 1.0) 1))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(atan2 (- 1.0 0) (fma N (+ N 1.0) 1))

simplify10.2s

Counts

12 → 12

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	18	156
1	25	132
2	56	116
3	117	116
4	287	116
5	1147	116
done	5001	116

prune26.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
13.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
7.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: 3 (296.0ms)

Iter	Nodes	Cost
0	63	1755
1	100	1206
2	334	1086
3	1662	1041
done	5000	1041

prune151.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))
13.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify3.1s

Counts

60 → 60

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	29	686
1	38	638
2	63	592
3	96	592
4	144	592
5	326	592
6	889	592
7	3393	592
done	5000	592

prune150.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 2 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	10	10
2	12	8
done	12	8

end0.0ms

sample716.0ms

Algorithm

intervals

Results

385.0ms	2850×	body	1280	valid
122.0ms	4080×	body	80	valid
70.0ms	618×	body	640	valid
28.0ms	317×	body	320	valid
9.0ms	135×	body	160	valid