Details

sample86.0ms

Algorithm

intervals

Results

22.0ms	189×	body	80	valid
17.0ms	29×	body	1280	valid
12.0ms	256×	pre	80	true
11.0ms	24×	body	640	valid
4.0ms	11×	body	320	valid
1.0ms	3×	body	160	valid

simplify3.9s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.5b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite219.0ms

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:

47.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
171.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series122.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
72.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

73 → 73

Iterations

Iter	Nodes
done	5007
2	1126
1	328
0	126

prune287.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ beta (+ (+ alpha beta) 2.0))
166.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series257.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(/ alpha (+ (+ alpha beta) 2.0))
63.0ms	(/ beta (+ (+ alpha beta) 2.0))
131.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5004
3	4504
2	1024
1	344
0	156

prune454.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
1.5b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite476.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
24×	`distribute-lft-out`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`log-pow`
6×	`exp-prod` `associate-/l*` `add-log-exp`
5×	`pow1` `log-prod`
4×	`associate-/r/` `insert-posit16` `difference-of-squares`
2×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `exp-sum` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 114

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
27.0ms	(/ beta (+ (+ alpha beta) 2.0))
261.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
151.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series380.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ alpha (+ (+ alpha beta) 2.0))
87.0ms	(/ beta (+ (+ alpha beta) 2.0))
110.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
93.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	4984
2	1145
1	400
0	186

prune795.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize39.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
7.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.2b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite215.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16`
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 → 109

Calls

4 calls:

165.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
19.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
12.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
16.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series709.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
211.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
187.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
194.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify2.6s

Counts

121 → 121

Iterations

Iter	Nodes
done	5015
3	2997
2	906
1	340
0	163

prune589.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

regimes408.0ms

Accuracy

99% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 15.8b

bsearch2.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample2.0s

Algorithm

intervals

Results

659.0ms	5827×	body	80	valid
379.0ms	8000×	pre	80	true
377.0ms	873×	body	1280	valid
243.0ms	702×	body	640	valid
111.0ms	362×	body	320	valid
75.0ms	236×	body	160	valid