Details

sample80.0ms

Algorithm

intervals

Results

21.0ms	182×	body	80	valid
14.0ms	26×	body	1280	valid
11.0ms	26×	body	640	valid
11.0ms	256×	pre	80	true
5.0ms	14×	body	320	valid
2.0ms	8×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite136.0ms

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:

43.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
91.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series142.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
84.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5007
2	1126
1	328
0	126

prune253.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.7b

localize29.0ms

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

rewrite562.0ms

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-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `insert-posit16` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 115

Calls

4 calls:

279.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
42.0ms	(/ alpha (+ (+ alpha beta) 2.0))
43.0ms	(/ beta (+ (+ alpha beta) 2.0))
196.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series318.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms	(/ alpha (+ (+ alpha beta) 2.0))
64.0ms	(/ beta (+ (+ alpha beta) 2.0))
104.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5019
2	1580
1	467
0	197

prune534.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
48×	`times-frac`
46×	`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` `insert-posit16`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `cbrt-unprod` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 141

Calls

4 calls:

41.0ms	(/ alpha (+ (+ alpha beta) 2.0))
22.0ms	(/ 1 (+ (+ alpha beta) 2.0))
44.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
203.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series629.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ alpha (+ (+ alpha beta) 2.0))
47.0ms	(/ 1 (+ (+ alpha beta) 2.0))
411.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
106.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

153 → 153

Iterations

Iter	Nodes
done	5002
2	1476
1	470
0	197

prune668.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite547.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
43×	`add-sqr-sqrt`
34×	`times-frac`
26×	`add-cube-cbrt`
21×	`associate-r` `distribute-lft-out`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `add-log-exp`
5×	`log-prod` `associate-/r*`
4×	`div-exp` `prod-exp` `associate-/r/` `insert-posit16` `difference-of-squares`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `flip3-+` `1-exp` `exp-sum` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--`
1×	`log-div` `clear-num` `frac-2neg` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `flip--` `inv-pow`

Counts

4 → 125

Calls

4 calls:

28.0ms	(/ 1 (+ (+ alpha beta) 2.0))
56.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
133.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
326.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series337.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ 1 (+ (+ alpha beta) 2.0))
61.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
98.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify2.5s

Counts

137 → 137

Iterations

Iter	Nodes
done	5003
3	4936
2	1268
1	458
0	192

prune573.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

regimes229.0ms

Accuracy

75.9% (3.0b remaining)

Error of 6.0b against oracle of 3.0b and baseline of 15.4b

bsearch64.0ms

Steps

Iters	Range		Point
8	28342861701.492744	542402004696104.94	11629067263522.379

simplify6.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample1.9s

Algorithm

intervals

Results

592.0ms	5886×	body	80	valid
392.0ms	817×	body	1280	valid
295.0ms	732×	body	640	valid
288.0ms	8000×	pre	80	true
137.0ms	373×	body	320	valid
33.0ms	192×	body	160	valid