Details

sample92.0ms

Algorithm

intervals

Results

34.0ms	198×	body	80	valid
16.0ms	27×	body	1280	valid
12.0ms	256×	pre	80	true
7.0ms	16×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	6×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4691
8	1531
7	665
6	318
5	164
4	74
3	53
2	34
1	20
0	10

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize21.0ms

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)

rewrite204.0ms

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:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
138.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series149.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	1442
1	342
0	130

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.0b

localize19.0ms

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)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

215×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
116×	`times-frac`
93×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
12×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 233

Calls

4 calls:

1.0s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
47.0ms	(/ alpha (+ (+ alpha beta) 2.0))
228.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series389.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
82.0ms	(/ beta (+ (+ alpha beta) 2.0))
70.0ms	(/ alpha (+ (+ alpha beta) 2.0))
122.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.9s

Counts

245 → 245

Iterations

Iter	Nodes
done	5000
2	2987
1	745
0	312

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.5b	(exp (log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)))
1.5b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
8.2b	(log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0))

rewrite625.0ms

Algorithm

rewrite-expression-head

Rules

206×	`*-un-lft-identity`
129×	`add-sqr-sqrt`
124×	`times-frac`
94×	`add-cube-cbrt`
63×	`prod-diff`
50×	`log-prod`
48×	`distribute-lft-out`
25×	`exp-sum`
21×	`fma-neg`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log`
7×	`div-inv`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `exp-prod` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3--` `exp-diff` `diff-log` `flip--` `rem-exp-log`

Counts

4 → 222

Calls

4 calls:

39.0ms	(/ alpha (+ beta (+ alpha 2.0)))
207.0ms	(exp (log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)))
150.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
220.0ms	(log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0))

series458.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ alpha (+ beta (+ alpha 2.0)))
102.0ms	(exp (log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)))
106.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
178.0ms	(log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0))

simplify1.8s

Counts

234 → 234

Iterations

Iter	Nodes
done	5003
2	2382
1	731
0	340

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.9b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.5b	(pow E (log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)))
1.5b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
8.2b	(log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0))

rewrite665.0ms

Algorithm

rewrite-expression-head

Rules

207×	`*-un-lft-identity`
130×	`add-sqr-sqrt`
124×	`times-frac`
95×	`add-cube-cbrt`
63×	`prod-diff`
50×	`log-prod`
48×	`distribute-lft-out`
25×	`unpow-prod-up`
21×	`fma-neg`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
10×	`add-exp-log` `associate-/r/`
7×	`pow1` `div-inv`
6×	`add-cbrt-cube` `add-log-exp`
5×	`associate-/r*` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `pow-unpow` `insert-posit16` `log1p-expm1-u`
3×	`unpow-prod-down` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `pow-exp` `log-pow`
1×	`pow-to-exp` `cbrt-undiv` `e-exp-1` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `flip3--` `diff-log` `flip--` `pow-sub` `sqr-pow`

Counts

4 → 229

Calls

4 calls:

30.0ms	(/ alpha (+ beta (+ alpha 2.0)))
247.0ms	(pow E (log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)))
147.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
235.0ms	(log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0))

series660.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ alpha (+ beta (+ alpha 2.0)))
257.0ms	(pow E (log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)))
144.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)
194.0ms	(log (/ (- (/ beta (+ beta (+ alpha 2.0))) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0))

simplify2.4s

Counts

241 → 241

Iterations

Iter	Nodes
done	5001
2	3304
1	940
0	354

prune965.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.9b

regimes180.0ms

Accuracy

73.7% (3.3b remaining)

Error of 6.2b against oracle of 2.8b and baseline of 15.5b

bsearch89.0ms

Steps

Iters	Range		Point
8	1.5961117227142164e+26	1.6835726942401143e+29	5.669431488829545e+27

simplify13.0ms

Iterations

Iter	Nodes
done	43
2	43
1	42
0	33

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	5874×	body	80	valid
525.0ms	830×	body	1280	valid
355.0ms	8000×	pre	80	true
262.0ms	692×	body	640	valid
105.0ms	390×	body	320	valid
40.0ms	214×	body	160	valid