Details

sample23.0ms

Algorithm

intervals

Results

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

simplify314.0ms

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	155	13
7	201	13
8	234	13
9	285	13
10	325	13
11	335	13
12	347	13
13	359	13
done	359	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)

rewrite126.0ms

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:

24.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
98.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series108.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
62.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	128	1178
1	334	1110
2	875	1056
3	2687	1048
done	5000	1047

prune222.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize10.0ms

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)

rewrite836.0ms

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:

670.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
18.0ms	(/ alpha (+ (+ alpha beta) 2.0))
18.0ms	(/ beta (+ (+ alpha beta) 2.0))
119.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series244.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
51.0ms	(/ alpha (+ (+ alpha beta) 2.0))
45.0ms	(/ beta (+ (+ alpha beta) 2.0))
79.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify929.0ms

Counts

241 → 241

Iterations

Useful iterations: done (921.0ms)

Iter	Nodes	Cost
0	308	5116
1	694	4369
2	1854	3978
done	5000	3894

prune447.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize14.0ms

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)))

rewrite136.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 218

Calls

4 calls:

92.0ms	(* (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)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (cbrt (/ beta (+ (+ alpha beta) 2.0))) (cbrt (/ beta (+ (+ alpha beta) 2.0))))
144.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
140.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
144.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify1.5s

Counts

230 → 230

Iterations

Useful iterations: 3 (951.0ms)

Iter	Nodes	Cost
0	219	4874
1	435	4484
2	1206	4309
3	3656	4049
done	5000	4049

prune569.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.7b

localize21.0ms

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)

rewrite96.0ms

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×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow1/3` `sqr-pow`
2×	`cbrt-div`
1×	`unpow1/3`

Counts

4 → 152

Calls

4 calls:

22.0ms	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6)
12.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
46.0ms	(pow (pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6) 1/3)

series51.7s

Counts

4 → 12

Calls

4 calls:

51.1s	(pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6)
160.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
142.0ms	(cbrt (/ beta (+ (+ alpha beta) 2.0)))
260.0ms	(pow (pow (cbrt (/ beta (+ (+ alpha beta) 2.0))) 6) 1/3)

simplify1.7s

Counts

164 → 164

Iterations

Useful iterations: 3 (804.0ms)

Iter	Nodes	Cost
0	249	3084
1	624	2792
2	1496	2534
3	4933	2398
done	5000	2398

prune514.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

regimes86.0ms

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

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample614.0ms

Algorithm

intervals

Results

148.0ms	5858×	body	80	valid
111.0ms	865×	body	1280	valid
103.0ms	8000×	pre	80	true
66.0ms	693×	body	640	valid
29.0ms	409×	body	320	valid
9.0ms	175×	body	160	valid