Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	256×	pre	80	true
8.0ms	185×	body	80	valid
7.0ms	31×	body	1280	valid
4.0ms	25×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify3.6s

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: 16.7b

localize19.0ms

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)

rewrite349.0ms

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:

88.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
256.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series138.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
75.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5007
2	1126
1	328
0	126

prune272.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.9b

localize23.0ms

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

rewrite1.5s

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:

1.2s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
33.0ms	(/ alpha (+ (+ alpha beta) 2.0))
37.0ms	(/ beta (+ (+ alpha beta) 2.0))
214.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series355.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
66.0ms	(/ alpha (+ (+ alpha beta) 2.0))
72.0ms	(/ beta (+ (+ alpha beta) 2.0))
116.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts

153 → 153

Iterations

Iter	Nodes
done	5001
2	1885
1	567
0	242

prune742.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.9s

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
19×	`add-sqr-sqrt`
14×	`associate-*l/`
10×	`*-un-lft-identity` `add-log-exp`
8×	`associate-*r/`
6×	`difference-of-squares`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out--`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 85

Calls

4 calls:

1.1s	(cbrt (* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
248.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
263.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
235.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series471.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (* (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
105.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
112.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1262
1	359
0	166

prune573.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
0.4b	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
0.6b	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite582.0ms

Algorithm

rewrite-expression-head

Rules

146×	`*-un-lft-identity`
119×	`add-sqr-sqrt` `times-frac`
81×	`sqrt-prod`
68×	`add-cube-cbrt`
42×	`distribute-lft-out`
32×	`add-exp-log`
30×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`unswap-sqr`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`flip3-+` `cbrt-unprod` `flip-+` `insert-posit16` `div-inv`
3×	`rec-exp` `1-exp` `pow-flip`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`frac-times` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 222

Calls

4 calls:

194.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
67.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
56.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
257.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series445.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ 1 (sqrt (+ (+ alpha beta) 2.0))) (/ beta (sqrt (+ (+ alpha beta) 2.0))))
149.0ms	(/ beta (sqrt (+ (+ alpha beta) 2.0)))
104.0ms	(/ 1 (sqrt (+ (+ alpha beta) 2.0)))
105.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts

234 → 234

Iterations

Iter	Nodes
done	5000
2	2209
1	791
0	292

prune898.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.5b

regimes199.0ms

Accuracy

71.8% (3.5b remaining)

Error of 6.5b against oracle of 3.0b and baseline of 15.4b

bsearch108.0ms

Steps

Iters	Range		Point
8	2.5944574887415813e+32	4.736445516336521e+35	6.404044802162421e+32

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	28

end0.0ms

sample1.9s

Algorithm

intervals

Results

863.0ms	5895×	body	80	valid
288.0ms	817×	body	1280	valid
280.0ms	8000×	pre	80	true
164.0ms	707×	body	640	valid
94.0ms	385×	body	320	valid
22.0ms	196×	body	160	valid