Details

sample52.0ms

Algorithm

intervals

Results

27.0ms	97×	body	1280	valid
8.0ms	131×	body	80	valid
3.0ms	14×	body	640	valid
2.0ms	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	292
1	9	292
2	10	292
done	10	292

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.2b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
6.0ms	(- (atan (+ N 1.0)) (atan N))

series22.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
19.0ms	(- (atan (+ N 1.0)) (atan N))

simplify3.5s

Counts

44 → 44

Iterations

Useful iterations: 4 (1.1s)

Iter	Nodes	Cost
0	66	17920
1	139	16712
2	286	14965
3	738	14790
4	2193	12955
done	5004	12955

prune168.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 9

Calls

1 calls:

0.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify8.7s

Counts

12 → 12

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	3516
1	21	3516
2	32	3516
3	56	3516
4	77	3516
5	89	3516
6	111	3516
7	153	3516
8	335	3516
9	827	3516
10	3329	3516
done	5092	3516

prune82.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(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))))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
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` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
22.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
4.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
22.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
30.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify5.5s

Counts

102 → 102

Iterations

Useful iterations: 3 (366.0ms)

Iter	Nodes	Cost
0	63	34379
1	117	30569
2	240	30529
3	661	30489
4	3828	30489
done	5000	30489

prune275.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
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-l` `*-commutative`

Counts

4 → 99

Calls

4 calls:

52.0ms	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
3.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify5.2s

Counts

111 → 111

Iterations

Useful iterations: 2 (132.0ms)

Iter	Nodes	Cost
0	84	35537
1	184	27676
2	345	27596
3	689	27596
4	942	27596
5	1368	27596
6	3526	27596
done	5000	27596

prune279.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes51.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	238
1	9	238
done	9	238

end0.0ms

sample1.2s

Algorithm

intervals

Results

723.0ms	2881×	body	1280	valid
178.0ms	4022×	body	80	valid
103.0ms	639×	body	640	valid
70.0ms	299×	body	320	valid
15.0ms	159×	body	160	valid