Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	90×	body	1280	valid
5.0ms	132×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.2s

Counts

28 → 28

Iterations

Useful iterations: 4 (116.0ms)

Iter	Nodes	Cost
0	40	271
1	76	259
2	145	245
3	270	241
4	534	239
5	1497	239
done	5000	239

prune50.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite23.0ms

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:

22.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify2.9s

Counts

34 → 34

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	55	317
1	120	312
2	356	264
3	1001	264
4	4336	264
done	5002	264

prune57.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
15.8b	(cbrt (* (+ N 1.0) N))
15.8b	(cbrt (* (+ N 1.0) N))
15.8b	(cbrt (* (+ N 1.0) N))

rewrite43.0ms

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:

22.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
6.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))

series404.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
97.0ms	(cbrt (* (+ N 1.0) N))
93.0ms	(cbrt (* (+ N 1.0) N))
95.0ms	(cbrt (* (+ N 1.0) N))

simplify1.2s

Counts

84 → 84

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	152	1527
1	354	1427
2	973	1328
3	2854	1135
done	5001	1091

prune241.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt N) (cbrt (* (+ N 1.0) N)))
0.6b	(cbrt N)
15.8b	(cbrt (* (+ N 1.0) N))
15.8b	(cbrt (* (+ N 1.0) N))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

14.0ms	(* (cbrt N) (cbrt (* (+ N 1.0) N)))
1.0ms	(cbrt N)
6.0ms	(cbrt (* (+ N 1.0) N))
6.0ms	(cbrt (* (+ N 1.0) N))

series456.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(* (cbrt N) (cbrt (* (+ N 1.0) N)))
174.0ms	(cbrt N)
92.0ms	(cbrt (* (+ N 1.0) N))
90.0ms	(cbrt (* (+ N 1.0) N))

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	149	999
1	362	984
2	995	919
3	2991	799
done	5000	767

prune225.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

regimes15.0ms

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

sample762.0ms

Algorithm

intervals

Results

388.0ms	2797×	body	1280	valid
127.0ms	4123×	body	80	valid
69.0ms	602×	body	640	valid
29.0ms	331×	body	320	valid
9.0ms	147×	body	160	valid