Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	94×	body	1280	valid
4.0ms	133×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms

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: 15.2b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 15

Calls

1 calls:

3.0ms

(- (atan (+ N 1.0)) (atan N))

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

(- (atan (+ N 1.0)) (atan N))

simplify2.4s

Counts

18 → 18

Iterations

Useful iterations: 4 (75.0ms)

Iter	Nodes	Cost
0	36	209
1	73	205
2	141	191
3	235	187
4	458	185
5	1161	185
6	4325	185
done	5001	185

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

14.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.2s

Counts

34 → 34

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	347	264
3	1178	264
4	3505	264
done	5001	264

prune64.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
14.6b	(cbrt (* (+ N 1.0) N))
14.6b	(cbrt (* (+ N 1.0) N))
14.6b	(cbrt (* (+ N 1.0) N))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`associate-*r/` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

12.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
3.0ms	(cbrt (* (+ N 1.0) N))
3.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))

series416.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
97.0ms	(cbrt (* (+ N 1.0) N))
98.0ms	(cbrt (* (+ N 1.0) N))
97.0ms	(cbrt (* (+ N 1.0) N))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: 3 (439.0ms)

Iter	Nodes	Cost
0	152	1527
1	354	1427
2	1066	1328
3	3708	1135
done	5000	1135

prune240.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
13.8b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.8b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

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×	`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 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
18.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify3.4s

Counts

94 → 94

Iterations

Useful iterations: 5 (1.1s)

Iter	Nodes	Cost
0	64	1843
1	107	1267
2	225	1115
3	520	1064
4	1030	1052
5	4691	1022
done	5001	1022

prune115.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.3b

regimes25.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	12	9
done	12	9

end0.0ms

sample698.0ms

Algorithm

intervals

Results

372.0ms	2850×	body	1280	valid
122.0ms	4080×	body	80	valid
68.0ms	618×	body	640	valid
27.0ms	317×	body	320	valid
8.0ms	135×	body	160	valid