Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	99×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	20×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize6.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

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:

5.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify77.0ms

Counts

18 → 18

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	72	123
1	142	114
2	286	112
3	678	111
4	2488	111
5	5001	111
done	5001	111

prune38.0ms

Pruning

1 alts after pruning (1 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)))

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)))

series54.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify57.0ms

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127
done	5002	127

prune67.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
40.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ N 1.0))
91.0ms	(cbrt (+ N 1.0))
108.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
4.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify156.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (149.0ms)

Iter	Nodes	Cost
0	330	806
1	1079	745
2	4794	696
3	5001	692
done	5001	692

prune269.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
9.4b	(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
18.0b	(cbrt (- (* N N) (* 1.0 1.0)))
18.0b	(cbrt (- (* N N) (* 1.0 1.0)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-div`
16×	`add-exp-log`
14×	`flip3--` `flip--`
8×	`cbrt-prod` `frac-times` `associate-/r/` `add-cbrt-cube` `associate-/l/`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`pow1/3` `difference-of-squares`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 72

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
46.0ms	(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
6.0ms	(cbrt (- (* N N) (* 1.0 1.0)))
6.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

series586.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 1.0 (+ 1 (* (/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0)))) (* (cbrt (+ N 1.0)) N))))
179.0ms	(/ (* (cbrt (- (* N N) (* 1.0 1.0))) (cbrt (- (* N N) (* 1.0 1.0)))) (* (cbrt (- N 1.0)) (cbrt (- N 1.0))))
194.0ms	(cbrt (- (* N N) (* 1.0 1.0)))
200.0ms	(cbrt (- (* N N) (* 1.0 1.0)))

simplify61.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	565	1288
1	2133	1070
2	5001	1030
done	5001	1030

prune352.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes223.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4
done	12	4

end0.0ms

sample775.0ms

Algorithm

intervals

Results

395.0ms	2937×	body	1280	valid
133.0ms	4020×	body	80	valid
73.0ms	615×	body	640	valid
24.0ms	275×	body	320	valid
10.0ms	153×	body	160	valid