Details

sample56.0ms

Algorithm

intervals

Results

13.0ms	198×	body	80	valid
9.0ms	27×	body	1280	valid
7.0ms	256×	pre	80	true
3.0ms	16×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify10.3s

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize119.0ms

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)

rewrite678.0ms

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:

138.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
530.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series172.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
105.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5005
2	1125
1	328
0	126

prune788.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.0b

localize126.0ms

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

rewrite3.4s

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:

2.8s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
89.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(/ alpha (+ (+ alpha beta) 2.0))
470.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series441.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
88.0ms	(/ beta (+ (+ alpha beta) 2.0))
71.0ms	(/ alpha (+ (+ alpha beta) 2.0))
147.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.3s

Counts

153 → 153

Iterations

Iter	Nodes
done	5007
2	1882
1	567
0	242

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize187.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `times-frac` `flip3--` `add-cbrt-cube` `add-exp-log` `insert-posit16` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

179.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
465.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
540.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
512.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series709.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
133.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
129.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.7s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
3	1720
2	629
1	264
0	122

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.9b

localize211.0ms

Local error

Found 4 expressions with local error:

0.6b	(log (exp (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
10×	`log-pow` `add-log-exp`
9×	`exp-prod`
8×	`difference-of-squares`
7×	`add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`times-frac` `add-cbrt-cube` `add-exp-log` `insert-posit16` `distribute-lft-out--`
3×	`log-prod` `sub-neg` `flip3--` `diff-log` `flip--`
1×	`rem-log-exp`

Counts

4 → 70

Calls

4 calls:

951.0ms	(log (exp (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
583.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
595.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
475.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series814.0ms

Counts

4 → 12

Calls

4 calls:

383.0ms	(log (exp (cbrt (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
149.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
134.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
147.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.8s

Counts

82 → 82

Iterations

Iter	Nodes
done	5002
3	1768
2	672
1	290
0	145

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.9b

regimes946.0ms

Accuracy

97.9% (0.3b remaining)

Error of 3.1b against oracle of 2.9b and baseline of 15.5b

bsearch5.0ms

simplify26.0ms

Iterations

Iter	Nodes
done	33
1	33
0	30

end0.0ms

sample1.8s

Algorithm

intervals

Results

512.0ms	5874×	body	80	valid
338.0ms	830×	body	1280	valid
302.0ms	8000×	pre	80	true
229.0ms	692×	body	640	valid
110.0ms	390×	body	320	valid
30.0ms	214×	body	160	valid