Details

sample28.0ms

Algorithm

intervals

Results

14.0ms	102×	body	1280	valid
4.0ms	122×	body	80	valid
3.0ms	25×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	2×	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: 15.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.5b	(- (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))

simplify889.0ms

Counts

44 → 44

Iterations

Useful iterations: 3 (156.0ms)

Iter	Nodes	Cost
0	66	624
1	127	503
2	301	416
3	1137	355
done	5002	355

prune69.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

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))

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: 0.2b

localize10.0ms

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))))
15.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.8b	(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)))

series26.0ms

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

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: 3 (265.0ms)

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

prune161.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.3b	(pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)
15.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.8b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `unpow-prod-down` `cube-prod`
6×	`sqrt-pow1`
5×	`add-exp-log` `pow-pow` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
3.0ms	(pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
144.0ms	(pow (sqrt (sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))) 3)
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify2.2s

Counts

93 → 93

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	80	1383
1	176	1137
2	490	1112
3	2873	1093
done	5000	1090

prune190.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes28.0ms

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

sample740.0ms

Algorithm

intervals

Results

403.0ms	2906×	body	1280	valid
126.0ms	4030×	body	80	valid
67.0ms	598×	body	640	valid
28.0ms	317×	body	320	valid
10.0ms	149×	body	160	valid