Details

sample36.0ms

Algorithm

intervals

Results

6.0ms	177×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	256×	pre	80	true
4.0ms	27×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	53	13
4	74	13
5	163	13
6	314	13
7	647	13
8	1463	13
9	4388	13
done	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.4b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.8b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite386.0ms

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-exp-log` `associate-/r/` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--`

Counts

2 → 100

Calls

2 calls:

77.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
303.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series156.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

106 → 106

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	128	1178
1	341	1110
2	1440	1056
done	5000	1056

prune399.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 17.7b

localize12.0ms

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))
2.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.3s

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-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `frac-sub`
1×	`associate--r-`

Counts

4 → 413

Calls

4 calls:

761.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
67.0ms	(/ alpha (+ (+ alpha beta) 2.0))
67.0ms	(/ beta (+ (+ alpha beta) 2.0))
361.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series331.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
59.0ms	(/ alpha (+ (+ alpha beta) 2.0))
61.0ms	(/ beta (+ (+ alpha beta) 2.0))
144.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.4s

Counts

425 → 425

Iterations

Useful iterations: 2 (977.0ms)

Iter	Nodes	Cost
0	402	16706
1	993	13424
2	3868	11385
done	5000	11385

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize37.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.0b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

314.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
35.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
40.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
37.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
180.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
190.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
206.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.2s

Counts

209 → 209

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	241	4333
1	523	3621
2	1584	3227
done	5001	3056

prune903.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.7b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
2.8b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
12.1b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

166×	`*-un-lft-identity`
89×	`add-sqr-sqrt`
78×	`times-frac`
74×	`add-cube-cbrt`
63×	`prod-diff`
48×	`distribute-lft-out`
21×	`fma-neg`
14×	`log-prod`
10×	`associate-/r/`
8×	`log-div`
7×	`add-exp-log` `exp-sum` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`flip3--` `flip3-+` `associate-/r*` `flip--` `flip-+` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `exp-diff` `frac-sub` `log1p-expm1-u`
3×	`associate-/l*`
2×	`log-pow`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `rem-exp-log`

Counts

4 → 187

Calls

4 calls:

65.0ms	(/ beta (+ (+ alpha beta) 2.0))
487.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
430.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
700.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ beta (+ (+ alpha beta) 2.0))
83.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
128.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
192.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify2.4s

Counts

199 → 199

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	299	4746
1	687	3959
2	2551	3535
done	5000	3378

prune725.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.4b

regimes160.0ms

Accuracy

77.3% (3.0b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 16.3b

bsearch88.0ms

Steps

Iters	Range		Point
9	0.5849616174094538	51624944.521682866	49032803.70070513

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	98
1	39	98
done	39	98

end0.0ms

sample1.4s

Algorithm

intervals

Results

371.0ms	883×	body	1280	valid
326.0ms	5789×	body	80	valid
202.0ms	8000×	pre	80	true
137.0ms	750×	body	640	valid
50.0ms	371×	body	320	valid
19.0ms	207×	body	160	valid