Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	89×	body	1280	valid
4.0ms	121×	body	80	valid
3.0ms	26×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	6×	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: 15.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

0.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.8s

Counts

44 → 44

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	66	624
1	127	503
2	301	416
3	1115	355
4	4770	346
done	5000	346

prune78.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.2b	(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))

simplify2.1s

Counts

12 → 12

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	18	156
1	24	132
2	35	116
3	52	116
4	64	116
5	74	116
6	97	116
7	159	116
8	360	116
9	1280	116
done	5000	116

prune32.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))
16.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.0b	(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)))

series28.0ms

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)))

simplify3.4s

Counts

102 → 102

Iterations

Useful iterations: 5 (1.8s)

Iter	Nodes	Cost
0	63	1755
1	97	1200
2	214	1086
3	511	1041
4	1003	1009
5	4642	982
done	5001	982

prune173.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))))
16.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-r` `*-commutative`

Counts

4 → 93

Calls

4 calls:

25.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (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)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))))
13.0ms	(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)))

simplify2.7s

Counts

105 → 105

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	83	1994
1	181	1012
2	270	982
3	409	925
4	890	925
5	2733	925
done	5000	925

prune172.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample746.0ms

Algorithm

intervals

Results

400.0ms	2833×	body	1280	valid
125.0ms	4034×	body	80	valid
72.0ms	624×	body	640	valid
33.0ms	347×	body	320	valid
11.0ms	162×	body	160	valid