Details

sample47.0ms

Algorithm

intervals

Results

8.0ms	33×	body	1280	valid
8.0ms	169×	body	80	valid
6.0ms	33×	body	640	valid
5.0ms	256×	pre	80	true
2.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	244
1	20	244
2	34	244
3	53	244
4	74	244
5	164	244
6	306	244
7	644	244
8	1507	244
9	4613	244
done	5001	244

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize13.0ms

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)

rewrite218.0ms

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:

49.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
167.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series168.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
79.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.3s

Counts

71 → 71

Iterations

Useful iterations: 2 (374.0ms)

Iter	Nodes	Cost
0	124	22726
1	326	20277
2	1359	19795
done	5001	19795

prune328.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.3b

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

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

Counts

4 → 137

Calls

4 calls:

1.3s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
48.0ms	(/ alpha (+ (+ alpha beta) 2.0))
37.0ms	(/ beta (+ (+ alpha beta) 2.0))
183.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series362.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
72.0ms	(/ alpha (+ (+ alpha beta) 2.0))
60.0ms	(/ beta (+ (+ alpha beta) 2.0))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.1s

Counts

149 → 149

Iterations

Useful iterations: 2 (855.0ms)

Iter	Nodes	Cost
0	238	49822
1	563	45597
2	2417	44833
done	5002	44833

prune724.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize71.0ms

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)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
63×	`cbrt-prod`
46×	`times-frac`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
27×	`distribute-lft-out`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 105

Calls

4 calls:

187.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
29.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
21.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
15.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
198.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
240.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
226.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.1s

Counts

117 → 117

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	161	50465
1	338	44379
2	1047	43537
done	5000	42897

prune834.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize34.0ms

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))

rewrite895.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
64×	`times-frac`
50×	`log-prod`
37×	`add-cube-cbrt`
25×	`exp-sum`
19×	`distribute-lft-out--`
14×	`difference-of-squares`
12×	`distribute-lft-out`
9×	`add-exp-log`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`associate-/r*`
4×	`exp-prod`
3×	`div-inv` `associate-/l*`
2×	`log-div` `div-exp` `rem-log-exp` `associate-/r/` `log-pow`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `flip3--` `exp-diff` `diff-log` `flip-+` `flip--` `rem-exp-log`

Counts

4 → 126

Calls

4 calls:

49.0ms	(/ beta (+ (+ alpha beta) 2.0))
276.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
215.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
349.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ beta (+ (+ alpha beta) 2.0))
93.0ms	(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
99.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
200.0ms	(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.6s

Counts

138 → 138

Iterations

Useful iterations: 2 (666.0ms)

Iter	Nodes	Cost
0	269	69376
1	563	56920
2	1836	56154
done	5001	56154

prune867.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

regimes354.0ms

Accuracy

75.5% (3.1b remaining)

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

bsearch65.0ms

Steps

Iters	Range		Point
7	46374.558514477714	3809480.5813382245	417035.8774050207

simplify6.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	27	917
1	30	917
done	30	917

end0.0ms

sample1.7s

Algorithm

intervals

Results

649.0ms	864×	body	1280	valid
397.0ms	5858×	body	80	valid
155.0ms	8000×	pre	80	true
132.0ms	666×	body	640	valid
95.0ms	392×	body	320	valid
64.0ms	220×	body	160	valid