Details

sample23.0ms

Algorithm

intervals

Results

4.0ms	194×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	25×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify71.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	34	6
2	52	6
3	73	6
4	123	6
5	172	6
6	224	6
7	261	6
8	323	6
9	411	6
10	532	6
11	612	6
12	654	6
13	697	6
14	922	6
15	980	6
16	1007	6
17	1027	6
18	1035	6
19	1035	6
done	1035	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
153.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series112.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify38.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	320	535
1	1022	510
2	5001	502
done	5001	502

prune143.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite645.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

396.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
34.0ms	(/ alpha (+ (+ alpha beta) 2.0))
34.0ms	(/ beta (+ (+ alpha beta) 2.0))
175.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series243.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
52.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify44.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	450	903
1	1596	871
2	5002	859
done	5002	859

prune272.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
1.6b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`cbrt-prod`
12×	`add-sqr-sqrt`
9×	`distribute-lft-out`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

17.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
16.0ms	(cbrt (+ (+ alpha beta) 2.0))
176.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series377.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(cbrt (+ (+ alpha beta) 2.0))
99.0ms	(cbrt (+ (+ alpha beta) 2.0))
100.0ms	(cbrt (+ (+ alpha beta) 2.0))
78.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify66.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	278	567
1	708	537
2	2658	521
3	5001	512
done	5001	512

prune268.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.1b	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
4.1b	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

90×	`*-un-lft-identity`
47×	`times-frac`
41×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
33×	`distribute-lft-out`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/r*`
7×	`pow1`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `flip3--` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `inv-pow`

Counts

4 → 134

Calls

4 calls:

35.0ms	(/ 1 (+ (+ alpha beta) 2.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
77.0ms	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
31.0ms	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

series217.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1 (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
51.0ms	(* alpha (/ 1 (+ (+ alpha beta) 2.0)))
79.0ms	(- (* alpha (/ 1 (+ (+ alpha beta) 2.0))) 1.0)

simplify50.0ms

Counts

146 → 146

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	436	818
1	1801	737
2	5002	682
done	5002	682

prune249.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.7b

regimes107.0ms

Accuracy

77.2% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.7b

bsearch65.0ms

Steps

Iters	Range		Point
9	388973939020430.44	2.0000525779394545e+23	6665734284871154.0

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	48
1	59	48
done	59	48

end0.0ms

sample615.0ms

Algorithm

intervals

Results

139.0ms	5835×	body	80	valid
104.0ms	868×	body	1280	valid
84.0ms	8000×	pre	80	true
63.0ms	721×	body	640	valid
27.0ms	374×	body	320	valid
9.0ms	202×	body	160	valid