Details

sample58.0ms

Algorithm

intervals

Results

28.0ms	100×	body	1280	valid
9.0ms	124×	body	80	valid
4.0ms	17×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
8.0ms	(- (atan (+ N 1.0)) (atan N))

series43.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
40.0ms	(- (atan (+ N 1.0)) (atan N))

simplify2.1s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
5	3795
4	981
3	326
2	151
1	76
0	40

prune130.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ 1.0 N) N)
0.1b	(atan2 1.0 (+ (* (+ 1.0 N) N) 1))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
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:

18.0ms	(* (+ 1.0 N) N)
0.0ms	(atan2 1.0 (+ (* (+ 1.0 N) N) 1))

series50.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* (+ 1.0 N) N)
3.0ms	(atan2 1.0 (+ (* (+ 1.0 N) N) 1))

simplify420.0ms

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
2	698
1	127
0	55

prune217.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

18.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.6s

Counts

4 → 12

Calls

4 calls:

297.0ms	(* (cbrt N) (cbrt N))
244.0ms	(cbrt N)
732.0ms	(cbrt N)
285.0ms	(cbrt N)

simplify1.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	727
1	138
0	61

prune366.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 1.0 (+ (* (* (* (pow (cbrt -1) 2) (cbrt (pow N 2))) (+ N 1.0)) (cbrt N)) 1))
0.2b	(* (* (* (pow (cbrt -1) 2) (cbrt (pow N 2))) (+ N 1.0)) (cbrt N))
0.6b	(cbrt N)
29.3b	(cbrt (pow N 2))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
14×	`cbrt-prod`
12×	`prod-exp`
9×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`associate-r` `cbrt-unprod`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-prod-down`
2×	`pow1/3` `associate-l/` `associate-r/`
1×	`pow-to-exp` `flip3-+` `associate-l` `pow-exp` `*-commutative` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 61

Calls

4 calls:

0.0ms	(atan2 1.0 (+ (* (* (* (pow (cbrt -1) 2) (cbrt (pow N 2))) (+ N 1.0)) (cbrt N)) 1))
162.0ms	(* (* (* (pow (cbrt -1) 2) (cbrt (pow N 2))) (+ N 1.0)) (cbrt N))
1.0ms	(cbrt N)
3.0ms	(cbrt (pow N 2))

series722.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(atan2 1.0 (+ (* (* (* (pow (cbrt -1) 2) (cbrt (pow N 2))) (+ N 1.0)) (cbrt N)) 1))
191.0ms	(* (* (* (pow (cbrt -1) 2) (cbrt (pow N 2))) (+ N 1.0)) (cbrt N))
253.0ms	(cbrt N)
247.0ms	(cbrt (pow N 2))

simplify1.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	2383
1	353
0	135

prune295.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes89.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.2s

Algorithm

intervals

Results

617.0ms	2854×	body	1280	valid
229.0ms	4046×	body	80	valid
94.0ms	617×	body	640	valid
69.0ms	326×	body	320	valid
13.0ms	157×	body	160	valid