Details

sample60.0ms

Algorithm

intervals

Results

27.0ms	87×	body	1280	valid
9.0ms	129×	body	80	valid
6.0ms	22×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	3×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.9b	(- (atan (+ N 1.0)) (atan N))

rewrite18.0ms

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:

2.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

series41.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
37.0ms	(- (atan (+ N 1.0)) (atan N))

simplify9.4s

Counts

44 → 44

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	66	624
1	139	506
2	506	416
3	4476	355
done	5000	355

prune80.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 1 expressions with local error:

0.6b	(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

rewrite1.0ms

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))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify1.0s

Counts

12 → 12

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	18	156
1	24	132
2	36	116
3	60	116
4	84	116
5	118	116
6	187	116
7	362	116
8	1140	116
done	5000	116

prune30.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(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))))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite18.0ms

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))
13.0ms	(* (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)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
3.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify746.0ms

Counts

102 → 102

Iterations

Useful iterations: done (743.0ms)

Iter	Nodes	Cost
0	63	1755
1	122	1211
2	598	1086
done	5000	1053

prune169.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize15.0ms

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))))))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.3b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite60.0ms

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:

52.0ms	(* (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)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (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))))))
19.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.5s

Counts

105 → 105

Iterations

Useful iterations: 3 (478.0ms)

Iter	Nodes	Cost
0	83	1994
1	197	1012
2	539	943
3	2008	925
done	5000	925

prune264.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	11	8
2	12	8
done	12	8

end0.0ms

sample1.6s

Algorithm

intervals

Results

650.0ms	2816×	body	1280	valid
520.0ms	4082×	body	80	valid
167.0ms	605×	body	640	valid
83.0ms	330×	body	320	valid
16.0ms	167×	body	160	valid