Details

sample51.0ms

Algorithm

intervals

Results

11.0ms	182×	body	80	valid
8.0ms	26×	body	1280	valid
7.0ms	256×	pre	80	true
6.0ms	26×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	4445
19	4445
18	4437
17	4417
16	4272
15	3180
14	2343
13	1971
12	1789
11	1369
10	694
9	463
8	341
7	297
6	226
5	136
4	73
3	52
2	34
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize26.0ms

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)

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 102

Calls

2 calls:

48.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
146.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series150.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
86.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	1199
1	342
0	130

prune433.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.7b

localize35.0ms

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)

rewrite727.0ms

Algorithm

rewrite-expression-head

Rules

512×	`*-un-lft-identity`
328×	`add-sqr-sqrt`
263×	`times-frac`
252×	`prod-diff`
213×	`add-cube-cbrt`
150×	`distribute-lft-out`
65×	`associate--r+`
46×	`difference-of-squares`
42×	`fma-neg`
32×	`associate-/r/`
25×	`distribute-lft-out--`
16×	`flip3-+` `flip-+` `div-inv`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub`
1×	`associate--r-`

Counts

4 → 417

Calls

4 calls:

482.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
45.0ms	(/ alpha (+ (+ alpha beta) 2.0))
30.0ms	(/ beta (+ (+ alpha beta) 2.0))
157.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series302.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
61.0ms	(/ alpha (+ (+ alpha beta) 2.0))
52.0ms	(/ beta (+ (+ alpha beta) 2.0))
105.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

429 → 429

Iterations

Iter	Nodes
done	5000
2	2770
1	995
0	406

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize37.0ms

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)

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

209×	`*-un-lft-identity`
108×	`times-frac`
103×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
69×	`distribute-lft-out`
63×	`prod-diff`
21×	`fma-neg` `associate-r`
19×	`add-exp-log`
14×	`associate-/r/`
13×	`add-cbrt-cube`
10×	`associate-/r*`
7×	`pow1` `flip3-+` `flip-+` `div-inv`
6×	`associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-l` `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 → 233

Calls

4 calls:

35.0ms	(/ alpha (+ (+ alpha beta) 2.0))
27.0ms	(/ 1 (+ (+ alpha beta) 2.0))
82.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
164.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series279.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ alpha (+ (+ alpha beta) 2.0))
58.0ms	(/ 1 (+ (+ alpha beta) 2.0))
63.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
104.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

245 → 245

Iterations

Iter	Nodes
done	5003
2	2015
1	642
0	267

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.1b

localize45.0ms

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)))

rewrite704.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
139×	`times-frac`
131×	`add-cube-cbrt`
126×	`prod-diff`
84×	`distribute-lft-out`
68×	`log-prod`
65×	`exp-sum`
21×	`fma-neg` `associate-r`
18×	`associate-/r/`
17×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`flip3-+` `flip-+` `div-inv`
8×	`pow1`
7×	`log-pow`
6×	`exp-prod` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `sub-neg` `1-exp` `cbrt-unprod` `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 → 280

Calls

4 calls:

48.0ms	(/ 1 (+ (+ alpha beta) 2.0))
97.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
204.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
342.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1 (+ (+ alpha beta) 2.0))
76.0ms	(* beta (/ 1 (+ (+ alpha beta) 2.0)))
120.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
108.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.6s

Counts

292 → 292

Iterations

Iter	Nodes
done	5001
2	2044
1	748
0	376

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

regimes203.0ms

Accuracy

75.9% (3.0b remaining)

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

bsearch107.0ms

Steps

Iters	Range		Point
8	28342861701.492744	542402004696104.94	11629067263522.379

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	30

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.1s	5886×	body	80	valid
386.0ms	817×	body	1280	valid
300.0ms	8000×	pre	80	true
279.0ms	732×	body	640	valid
92.0ms	373×	body	320	valid
33.0ms	192×	body	160	valid