Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	200×	body	80	valid
5.0ms	22×	body	1280	valid
5.0ms	256×	pre	80	true
4.0ms	22×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4613
8	1507
7	644
6	306
5	164
4	74
3	53
2	34
1	20
0	10

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite298.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `div-inv` `flip--`

Counts

2 → 65

Calls

2 calls:

70.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
225.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series159.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
90.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1359
1	326
0	124

prune355.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.5b

localize26.0ms

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))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite812.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
32×	`times-frac`
24×	`add-cube-cbrt` `distribute-lft-out`
11×	`add-log-exp`
10×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*`
4×	`pow1` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `flip3--` `flip--`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `frac-sub` `flip-+` `div-inv` `associate--r+`
1×	`associate--r-`

Counts

4 → 111

Calls

4 calls:

497.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
49.0ms	(/ alpha (+ (+ alpha beta) 2.0))
35.0ms	(/ beta (+ (+ alpha beta) 2.0))
223.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series340.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
65.0ms	(/ alpha (+ (+ alpha beta) 2.0))
56.0ms	(/ beta (+ (+ alpha beta) 2.0))
113.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.4s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	1916
1	463
0	193

prune808.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ beta (+ (+ alpha beta) 2.0))
0.6b	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.3b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite988.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
14×	`log-prod`
12×	`distribute-lft-out`
8×	`log-div`
7×	`exp-sum` `add-exp-log` `distribute-lft-out--`
6×	`pow1` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
5×	`associate-/r*` `flip3--` `flip--`
4×	`exp-prod` `exp-diff` `frac-sub`
3×	`associate-/l*`
2×	`associate-/r/` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `rem-log-exp` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 95

Calls

4 calls:

56.0ms	(/ beta (+ (+ alpha beta) 2.0))
399.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
199.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
327.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ beta (+ (+ alpha beta) 2.0))
93.0ms	(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
94.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
175.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.7s

Counts

107 → 107

Iterations

Iter	Nodes
done	5001
2	1873
1	476
0	211

prune754.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.6b

localize78.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
10.3b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
10.3b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
10.3b	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
21×	`log-prod`
12×	`log-div`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`pow1` `flip3--` `add-exp-log` `add-cube-cbrt` `flip--`
6×	`frac-sub` `add-log-exp`
4×	`times-frac` `add-cbrt-cube`
3×	`rem-log-exp` `log-pow`
1×	`sub-neg` `diff-log`

Counts

4 → 75

Calls

4 calls:

209.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
385.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
385.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
385.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
162.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
175.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
173.0ms	(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1096
1	295
0	125

prune709.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.6b

regimes228.0ms

Accuracy

73.4% (3.3b remaining)

Error of 6.2b against oracle of 2.9b and baseline of 15.3b

bsearch86.0ms

Steps

Iters	Range		Point
9	7.141495025384564e+25	1.1524881963593713e+31	1.6348256570929846e+27

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

294.0ms	715×	body	640	valid
267.0ms	5915×	body	80	valid
226.0ms	810×	body	1280	valid
210.0ms	8000×	pre	80	true
49.0ms	364×	body	320	valid
17.0ms	196×	body	160	valid