Details

sample39.0ms

Algorithm

intervals

Results

8.0ms	193×	body	80	valid
7.0ms	37×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify2.1s

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
1.6b	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

rewrite270.0ms

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:

53.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
212.0ms	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

series157.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(/ (- beta alpha) (+ (+ alpha 2.0) beta))
97.0ms	(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

simplify576.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5002
2	1315
1	326
0	123

prune312.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
0.0b	(/ beta (+ (+ alpha 2.0) beta))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
1.6b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite699.0ms

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:

444.0ms	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
46.0ms	(/ beta (+ (+ alpha 2.0) beta))
24.0ms	(/ alpha (+ beta (+ alpha 2.0)))
181.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series333.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0))
63.0ms	(/ beta (+ (+ alpha 2.0) beta))
77.0ms	(/ alpha (+ beta (+ alpha 2.0)))
102.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify1.0s

Counts

123 → 123

Iterations

Iter	Nodes
done	5002
2	2206
1	501
0	205

prune543.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ beta alpha) 2.0))
0.0b	(/ alpha (+ beta (+ alpha 2.0)))
0.1b	(* beta (/ 1 (+ (+ beta alpha) 2.0)))
1.6b	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite329.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
48×	`times-frac`
46×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
33×	`distribute-lft-out`
21×	`associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/r*`
7×	`pow1`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`prod-exp`
3×	`cbrt-undiv` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `cbrt-unprod` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `flip--` `distribute-lft-out--` `inv-pow`

Counts

4 → 137

Calls

4 calls:

39.0ms	(/ 1 (+ (+ beta alpha) 2.0))
35.0ms	(/ alpha (+ beta (+ alpha 2.0)))
89.0ms	(* beta (/ 1 (+ (+ beta alpha) 2.0)))
157.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series306.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1 (+ (+ beta alpha) 2.0))
72.0ms	(/ alpha (+ beta (+ alpha 2.0)))
74.0ms	(* beta (/ 1 (+ (+ beta alpha) 2.0)))
112.0ms	(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify1.0s

Counts

149 → 149

Iterations

Iter	Nodes
done	5001
2	2512
1	534
0	210

prune663.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ alpha (+ alpha (+ 2.0 beta))) 3)
0.1b	(* beta (/ 1 (+ (+ beta alpha) 2.0)))
1.6b	(- (cbrt (pow (/ alpha (+ alpha (+ 2.0 beta))) 3)) 1.0)
26.9b	(cbrt (pow (/ alpha (+ alpha (+ 2.0 beta))) 3))

rewrite577.0ms

Algorithm

rewrite-expression-head

Rules

130×	`*-un-lft-identity`
79×	`times-frac`
74×	`add-sqr-sqrt`
54×	`cbrt-prod`
52×	`add-cube-cbrt`
45×	`distribute-lft-out`
44×	`unpow-prod-down` `cube-prod`
21×	`associate-r`
16×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`associate-/r/`
7×	`pow1` `difference-of-squares`
6×	`add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`prod-exp`
3×	`pow-unpow` `div-exp` `associate-l` `unswap-sqr` `sqr-pow`
2×	`cube-div` `cube-mult` `cbrt-undiv` `unpow3` `pow-exp` `cbrt-unprod` `rem-cube-cbrt`
1×	`pow-to-exp` `rec-exp` `cbrt-div` `sub-neg` `pow-pow` `flip3--` `pow1/3` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `rem-cbrt-cube` `flip--` `distribute-lft-out--`

Counts

4 → 184

Calls

4 calls:

37.0ms	(pow (/ alpha (+ alpha (+ 2.0 beta))) 3)
87.0ms	(* beta (/ 1 (+ (+ beta alpha) 2.0)))
407.0ms	(- (cbrt (pow (/ alpha (+ alpha (+ 2.0 beta))) 3)) 1.0)
27.0ms	(cbrt (pow (/ alpha (+ alpha (+ 2.0 beta))) 3))

series384.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(pow (/ alpha (+ alpha (+ 2.0 beta))) 3)
63.0ms	(* beta (/ 1 (+ (+ beta alpha) 2.0)))
120.0ms	(- (cbrt (pow (/ alpha (+ alpha (+ 2.0 beta))) 3)) 1.0)
114.0ms	(cbrt (pow (/ alpha (+ alpha (+ 2.0 beta))) 3))

simplify2.1s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
2	4477
1	931
0	291

prune824.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.4b

regimes176.0ms

Accuracy

76.4% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 16.0b

bsearch84.0ms

Steps

Iters	Range		Point
10	11.185988325186578	7.337575201769413e+19	1.982135388898922e+16

simplify4.0ms

Iterations

Iter	Nodes
done	42
1	42
0	34

end0.0ms

sample1.9s

Algorithm

intervals

Results

639.0ms	728×	body	640	valid
363.0ms	5804×	body	80	valid
307.0ms	846×	body	1280	valid
154.0ms	8000×	pre	80	true
59.0ms	399×	body	320	valid
20.0ms	223×	body	160	valid