Details

sample37.0ms

Algorithm

intervals

Results

17.0ms	90×	body	1280	valid
7.0ms	137×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	6×	body	160	valid

simplify5.0ms

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: 15.4b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.6b	(- (atan (+ N 1.0)) (atan N))

rewrite20.0ms

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))
15.0ms	(- (atan (+ N 1.0)) (atan N))

series27.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
24.0ms	(- (atan (+ N 1.0)) (atan N))

simplify10.2s

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

prune99.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ N 1.0) 1)
0.5b	(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`fma-udef`

Counts

2 → 19

Calls

2 calls:

0.0ms	(fma N (+ N 1.0) 1)
0.0ms	(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

series30.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(fma N (+ N 1.0) 1)
4.0ms	(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

simplify495.0ms

Counts

25 → 25

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	33	272
1	54	245
2	134	211
3	683	210
done	5002	210

prune61.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(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))))
13.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite22.0ms

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)))
5.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series33.0ms

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

simplify759.0ms

Counts

102 → 102

Iterations

Useful iterations: done (757.0ms)

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

prune174.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

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))))))
13.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0b	(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)))

series43.0ms

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))))))
13.0ms	(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)))

simplify1.5s

Counts

105 → 105

Iterations

Useful iterations: 3 (497.0ms)

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

prune193.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes24.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b 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

sample1.1s

Algorithm

intervals

Results

638.0ms	2904×	body	1280	valid
189.0ms	3996×	body	80	valid
87.0ms	610×	body	640	valid
36.0ms	319×	body	320	valid
14.0ms	171×	body	160	valid