Details

sample31.0ms

Algorithm

intervals

Results

7.0ms	44×	body	1280	valid
6.0ms	182×	body	80	valid
4.0ms	256×	pre	80	true
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify642.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	34	13
3	52	13
4	73	13
5	118	13
6	161	13
7	199	13
8	230	13
9	268	13
10	296	13
11	307	13
12	319	13
13	323	13
done	323	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite390.0ms

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:

72.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
309.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series195.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
106.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify2.3s

Counts

106 → 106

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	128	1178
1	335	1110
2	950	1056
3	3094	1048
done	5001	1043

prune370.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.8b

localize16.0ms

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))
0.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.4s

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-exp-log` `add-cbrt-cube` `difference-of-squares`
7×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--`
2×	`frac-sub`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 229

Calls

4 calls:

2.0s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
58.0ms	(/ beta (+ (+ alpha beta) 2.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
338.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series384.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
82.0ms	(/ beta (+ (+ alpha beta) 2.0))
66.0ms	(/ alpha (+ (+ alpha beta) 2.0))
121.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts

241 → 241

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	308	5116
1	713	4369
2	1884	3978
done	5000	3802

prune795.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(cbrt (+ (+ alpha beta) 2.0))
0.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite508.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
63×	`prod-diff`
61×	`times-frac`
45×	`distribute-lft-out`
21×	`fma-neg`
15×	`cbrt-prod`
8×	`associate-/r/`
7×	`flip3-+` `flip-+`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 152

Calls

4 calls:

34.0ms	(cbrt (+ (+ alpha beta) 2.0))
34.0ms	(cbrt (+ (+ alpha beta) 2.0))
35.0ms	(cbrt (+ (+ alpha beta) 2.0))
395.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series563.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(cbrt (+ (+ alpha beta) 2.0))
139.0ms	(cbrt (+ (+ alpha beta) 2.0))
132.0ms	(cbrt (+ (+ alpha beta) 2.0))
132.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.9s

Counts

164 → 164

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	204	3412
1	464	2733
2	1064	2423
3	3119	1966
done	5000	1876

prune588.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.4b	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.3b	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

rewrite1.4s

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×	`flip3-+` `associate-/r*` `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` `sub-neg` `flip3--` `frac-2neg` `exp-diff` `diff-log` `clear-num` `flip--` `rem-exp-log`

Counts

4 → 218

Calls

4 calls:

56.0ms	(/ alpha (+ (+ alpha beta) 2.0))
499.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
325.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
456.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series539.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ alpha (+ (+ alpha beta) 2.0))
130.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
114.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
209.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify2.8s

Counts

230 → 230

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	336	5840
1	703	4976
2	1554	4554
3	4568	4066
done	5000	4066

prune786.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.3b

regimes114.0ms

Accuracy

72.8% (3.7b remaining)

Error of 6.8b against oracle of 3.1b and baseline of 16.7b

bsearch109.0ms

Steps

Iters	Range		Point
10	925325.9807075356	3.4641089617611155e+20	5062494549189153.0

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	78
1	44	78
done	44	78

end0.0ms

sample1.9s

Algorithm

intervals

Results

867.0ms	5818×	body	80	valid
302.0ms	869×	body	1280	valid
193.0ms	8000×	pre	80	true
142.0ms	731×	body	640	valid
95.0ms	378×	body	320	valid
22.0ms	204×	body	160	valid