Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	94×	body	1280	valid
4.0ms	133×	body	80	valid
4.0ms	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))

series11.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify881.0ms

Counts

32 → 32

Iterations

Useful iterations: 3 (145.0ms)

Iter	Nodes	Cost
0	62	552
1	124	439
2	298	352
3	1132	291
done	5000	291

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 1 expressions with local error:

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify1.2s

Counts

12 → 12

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	18	156
1	24	132
2	44	116
3	82	116
4	165	116
5	524	116
done	5000	116

prune27.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize8.0ms

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))
6.0ms	(* (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)))

series29.0ms

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)))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: 3 (260.0ms)

Iter	Nodes	Cost
0	63	1755
1	97	1200
2	278	1086
3	1555	1059
done	5000	1059

prune158.0ms

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)))

series25.0ms

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

simplify2.6s

Counts

60 → 60

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	29	686
1	38	638
2	60	592
3	90	592
4	136	592
5	284	592
6	782	592
7	3168	592
done	5000	592

prune158.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes27.0ms

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: done (1.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
done	11	8

end0.0ms

sample730.0ms

Algorithm

intervals

Results

392.0ms	2850×	body	1280	valid
127.0ms	4080×	body	80	valid
71.0ms	618×	body	640	valid
28.0ms	317×	body	320	valid
8.0ms	135×	body	160	valid