Details

sample56.0ms

Algorithm

intervals

Results

10.0ms	169×	body	80	valid
10.0ms	33×	body	1280	valid
8.0ms	33×	body	640	valid
6.0ms	256×	pre	80	true
2.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	244
1	20	244
2	34	244
3	53	244
4	74	244
5	164	244
6	318	244
7	665	244
8	1531	244
9	4691	244
done	5001	244

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize16.0ms

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)

rewrite243.0ms

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` `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 → 100

Calls

2 calls:

56.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
182.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series155.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
100.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

106 → 106

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	128	23780
1	340	21196
2	1431	20789
done	5002	20764

prune467.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.2b

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

rewrite1.5s

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` `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 → 229

Calls

4 calls:

1.2s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
34.0ms	(/ alpha (+ (+ alpha beta) 2.0))
27.0ms	(/ beta (+ (+ alpha beta) 2.0))
236.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series318.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
81.0ms	(/ beta (+ (+ alpha beta) 2.0))
96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts

241 → 241

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	308	92607
1	741	80213
2	2982	69034
done	5000	68289

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize69.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.1b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite291.0ms

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×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `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:

197.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
30.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
27.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
27.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series746.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
215.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
205.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
224.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.5s

Counts

209 → 209

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	241	93408
1	522	78983
2	1591	67771
done	5001	66082

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.8b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
2.0b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.8b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.0s

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` `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 → 218

Calls

4 calls:

36.0ms	(/ beta (+ (+ alpha beta) 2.0))
382.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
234.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
373.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series519.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(/ beta (+ (+ alpha beta) 2.0))
101.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
222.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify2.1s

Counts

230 → 230

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	357	112903
1	768	92048
2	2440	80892
done	5000	79633

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

regimes286.0ms

Accuracy

75.5% (3.1b remaining)

Error of 6.0b against oracle of 2.8b and baseline of 15.7b

bsearch72.0ms

Steps

Iters	Range		Point
7	46374.558514477714	3809480.5813382245	417035.8774050207

simplify10.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	26	793
1	31	793
done	31	793

end0.0ms

sample1.7s

Algorithm

intervals

Results

686.0ms	864×	body	1280	valid
397.0ms	5858×	body	80	valid
220.0ms	8000×	pre	80	true
129.0ms	666×	body	640	valid
56.0ms	392×	body	320	valid
20.0ms	220×	body	160	valid