Details

sample24.0ms

Algorithm

intervals

Results

5.0ms	195×	body	80	valid
3.0ms	256×	pre	80	true
3.0ms	28×	body	1280	valid
2.0ms	22×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	1×	body	160	valid

simplify293.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	33	13
3	51	13
4	70	13
5	119	13
6	144	13
7	180	13
8	213	13
9	264	13
10	304	13
11	316	13
12	328	13
13	340	13
done	340	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
0.4b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite116.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

25.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
88.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series110.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
64.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

71 → 71

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	124	1134
1	319	1074
2	811	1014
3	2431	1006
done	5001	1005

prune163.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.2b

localize9.0ms

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))
0.4b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite736.0ms

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

Counts

4 → 137

Calls

4 calls:

584.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
19.0ms	(/ alpha (+ (+ alpha beta) 2.0))
21.0ms	(/ beta (+ (+ alpha beta) 2.0))
106.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series257.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
56.0ms	(/ alpha (+ (+ alpha beta) 2.0))
46.0ms	(/ beta (+ (+ alpha beta) 2.0))
81.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.0s

Counts

149 → 149

Iterations

Useful iterations: 3 (968.0ms)

Iter	Nodes	Cost
0	238	2750
1	542	2646
2	1446	2490
3	4731	2474
done	5000	2474

prune335.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (/ beta (+ (+ alpha beta) 2.0))) (cbrt (/ beta (+ (+ alpha beta) 2.0))))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

260×	`*-un-lft-identity`
195×	`cbrt-prod`
147×	`times-frac`
107×	`add-sqr-sqrt`
99×	`distribute-lft-out`
83×	`add-cube-cbrt`
42×	`swap-sqr`
24×	`associate-r` `associate-l`
14×	`associate-/r/`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `flip3-+` `flip-+` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 210

Calls

4 calls:

98.0ms	(* (cbrt (/ beta (+ (+ alpha beta) 2.0))) (cbrt (/ beta (+ (+ alpha beta) 2.0))))
12.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (/ beta (+ (+ alpha beta) 2.0))) (cbrt (/ beta (+ (+ alpha beta) 2.0))))
156.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
149.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
152.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.5s

Counts

222 → 222

Iterations

Useful iterations: 3 (938.0ms)

Iter	Nodes	Cost
0	215	4784
1	421	4411
2	1147	4231
3	3434	3980
done	5000	3980

prune597.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6)
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
7.9b	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
27.2b	(pow (pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6) 1/3)

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
84×	`cbrt-prod`
76×	`unpow-prod-down`
60×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`distribute-lft-out`
8×	`associate-/r/`
7×	`add-exp-log`
6×	`pow-unpow`
5×	`pow1` `pow-exp`
4×	`flip3-+` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow1/3` `sqr-pow`
2×	`cbrt-div`
1×	`unpow1/3`

Counts

4 → 144

Calls

4 calls:

23.0ms	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6)
11.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
10.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
52.0ms	(pow (pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6) 1/3)

series51.4s

Counts

4 → 12

Calls

4 calls:

50.8s	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6)
158.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
154.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
276.0ms	(pow (pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6) 1/3)

simplify1.7s

Counts

156 → 156

Iterations

Useful iterations: 3 (783.0ms)

Iter	Nodes	Cost
0	243	3000
1	607	2722
2	1427	2458
3	4735	2322
done	5000	2322

prune470.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

regimes88.0ms

Accuracy

72.9% (3.6b remaining)

Error of 6.4b against oracle of 2.8b and baseline of 16.1b

bsearch56.0ms

Steps

Iters	Range		Point
9	7.490363752984876e+34	4.809804475959991e+41	1.3056787770045593e+40

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	63
1	36	63
done	36	63

end0.0ms

sample599.0ms

Algorithm

intervals

Results

145.0ms	5858×	body	80	valid
105.0ms	865×	body	1280	valid
102.0ms	8000×	pre	80	true
63.0ms	693×	body	640	valid
28.0ms	409×	body	320	valid
8.0ms	175×	body	160	valid