Details

sample85.0ms

Algorithm

intervals

Results

22.0ms	186×	body	80	valid
15.0ms	25×	body	1280	valid
12.0ms	256×	pre	80	true
11.0ms	24×	body	640	valid
4.0ms	13×	body	320	valid
2.0ms	8×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
32	4930
31	4722
30	4510
29	4301
28	4120
27	3916
26	3715
25	3502
24	3325
23	3117
22	2909
21	2698
20	2516
19	2291
18	2012
17	1763
16	1558
15	1364
14	1138
13	931
12	742
11	607
10	526
9	431
8	318
7	267
6	197
5	124
4	69
3	50
2	33
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.3b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite141.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `insert-posit16` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 67

Calls

2 calls:

29.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
110.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series146.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
87.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5007
2	1126
1	328
0	126

prune306.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite993.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `insert-posit16` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `div-inv` `flip--`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 141

Calls

4 calls:

754.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
29.0ms	(/ alpha (+ (+ alpha beta) 2.0))
43.0ms	(/ beta (+ (+ alpha beta) 2.0))
164.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series295.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
85.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	1885
1	567
0	242

prune675.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize61.0ms

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))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite196.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`difference-of-squares`
1×	`sub-neg` `times-frac` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

13.0ms	(cbrt (+ (+ alpha beta) 2.0))
9.0ms	(cbrt (+ (+ alpha beta) 2.0))
10.0ms	(cbrt (+ (+ alpha beta) 2.0))
163.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series526.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (+ (+ alpha beta) 2.0))
157.0ms	(cbrt (+ (+ alpha beta) 2.0))
127.0ms	(cbrt (+ (+ alpha beta) 2.0))
117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5005
3	2443
2	751
1	284
0	122

prune564.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.8b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.3b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.8b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite750.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
64×	`times-frac`
50×	`log-prod`
37×	`add-cube-cbrt`
25×	`exp-sum`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod` `insert-posit16`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `associate-/r/` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `exp-diff` `diff-log` `flip-+` `flip--` `rem-exp-log`

Counts

4 → 130

Calls

4 calls:

23.0ms	(/ beta (+ (+ alpha beta) 2.0))
284.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
170.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
271.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series488.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ beta (+ (+ alpha beta) 2.0))
107.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
134.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
183.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.5s

Counts

142 → 142

Iterations

Iter	Nodes
done	5007
2	1466
1	568
0	273

prune722.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

regimes176.0ms

Accuracy

77.4% (2.9b remaining)

Error of 5.9b against oracle of 3.0b and baseline of 15.9b

bsearch98.0ms

Steps

Iters	Range		Point
10	0.06193883622199307	464811167.6258734	460518623.3564523

simplify7.0ms

Iterations

Iter	Nodes
done	36
1	36
0	31

end0.0ms

sample2.4s

Algorithm

intervals

Results

877.0ms	851×	body	1280	valid
560.0ms	5820×	body	80	valid
322.0ms	8000×	pre	80	true
263.0ms	713×	body	640	valid
138.0ms	418×	body	320	valid
34.0ms	198×	body	160	valid