Details

sample25.0ms

Algorithm

intervals

Results

4.0ms	180×	body	80	valid
3.0ms	31×	body	1280	valid
3.0ms	256×	pre	80	true
2.0ms	26×	body	640	valid
1.0ms	17×	body	320	valid
0.0ms	2×	body	160	valid

simplify72.0ms

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: 17.7b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite195.0ms

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:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
149.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series115.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify34.0ms

Counts

71 → 71

Iterations

Useful iterations: 2 (28.0ms)

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

prune145.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.6b

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

rewrite626.0ms

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:

384.0ms	(- (/ 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))
171.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series249.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify46.0ms

Counts

123 → 123

Iterations

Useful iterations: 2 (36.0ms)

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

prune300.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.0b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite881.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`exp-prod` `distribute-lft-out`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

319.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
33.0ms	(/ beta (+ (+ alpha beta) 2.0))
353.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
173.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series282.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
80.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify134.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	347	660
1	1103	606
2	4865	589
3	5002	589
done	5002	589

prune283.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
6.7b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

168.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
20.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
17.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
144.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
150.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
145.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify120.0ms

Counts

117 → 117

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	333	1077
1	892	1029
2	4058	992
3	5001	980
done	5001	980

prune421.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

regimes78.0ms

Accuracy

76.6% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.1b

bsearch58.0ms

Steps

Iters	Range		Point
10	7.61445106428951e+17	2.9705373761200776e+32	6.566215071237633e+18

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	27
1	40	27
done	40	27

end0.0ms

sample638.0ms

Algorithm

intervals

Results

140.0ms	5785×	body	80	valid
105.0ms	879×	body	1280	valid
91.0ms	8000×	pre	80	true
70.0ms	741×	body	640	valid
27.0ms	406×	body	320	valid
9.0ms	189×	body	160	valid