Details

sample23.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify79.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17
done	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

3.1b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

321.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

468.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

272.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series370.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

150.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

79.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify121.0ms

Counts

459 → 459

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1439	12925
1	5002	12452
done	5002	12452

prune900.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
11.8b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

7742×	`times-frac`
4062×	`*-un-lft-identity`
3062×	`add-sqr-sqrt`
3060×	`add-cube-cbrt`
2004×	`sqrt-prod`
501×	`distribute-lft-out`
193×	`div-inv`
185×	`associate-/r/`
89×	`associate-/r*`
82×	`flip3-+` `flip-+`
36×	`add-exp-log`
32×	`associate-/l*`
27×	`add-cbrt-cube`
25×	`div-exp`
16×	`cbrt-undiv`
6×	`pow1` `sqrt-div`
4×	`add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 2367

Calls

4 calls:

198.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
109.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
110.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
406.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
149.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify893.0ms

Counts

2379 → 2379

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5001	98865
done	5001	98865

prune5.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
57×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt`
37×	`add-cube-cbrt`
10×	`sqrt-div` `distribute-lft-out`
7×	`pow1` `associate-/l*`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 120

Calls

4 calls:

203.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
111.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
109.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
111.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series255.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify90.0ms

Counts

132 → 132

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	325	1790
1	1021	1680
2	4270	1636
3	5001	1636
done	5001	1636

prune399.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.9b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

248×	`times-frac`
202×	`*-un-lft-identity`
152×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
66×	`associate-r`
54×	`add-exp-log`
38×	`distribute-lft-out`
34×	`add-cbrt-cube`
28×	`associate-/r/`
26×	`div-exp`
22×	`associate-/l*`
18×	`associate-l`
15×	`flip3-+` `flip-+`
14×	`cbrt-undiv` `div-inv`
10×	`prod-exp` `associate-/r*`
8×	`unswap-sqr`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 286

Calls

4 calls:

33.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
164.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
678.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
272.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series347.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
72.0ms	(/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
159.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify65.0ms

Counts

298 → 298

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1120	5100
1	5001	4699
done	5001	4699

prune594.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.9b

regimes59.0ms

Accuracy

50.5% (1.2b remaining)

Error of 2.5b against oracle of 1.3b and baseline of 3.8b

bsearch60.0ms

Steps

Iters	Range		Point
8	9.744633061993862e+157	3.306991807817575e+162	6.279416890340405e+161

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	38
1	40	38
done	40	38

end0.0ms

sample539.0ms

Algorithm

intervals

Results

281.0ms	8000×	body	80	valid
84.0ms	8000×	pre	80	true