Details

sample34.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5255
4	2870
3	497
2	106
1	33
0	14

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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))
2.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

135.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
397.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
572.0ms	(/ (/ (/ (+ (+ (+ 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))
305.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
211.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
228.0ms	(/ (/ (/ (+ (+ (+ 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))
105.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.3s

Counts

477 → 477

Iterations

Iter	Nodes
done	5013
2	4622
1	1447
0	602

prune2.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

3614×	`times-frac`
2164×	`*-un-lft-identity`
1424×	`add-sqr-sqrt` `add-cube-cbrt`
370×	`distribute-lft-out`
192×	`associate-/l*`
152×	`associate-/r/`
89×	`div-inv`
84×	`associate-/r*`
65×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`clear-num` `frac-2neg` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1332

Calls

4 calls:

283.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
255.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
534.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
371.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
186.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
241.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
138.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify5.2s

Counts

1344 → 1344

Iterations

Iter	Nodes
done	5003
1	4263
0	1588

prune8.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.3b	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
2.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

1494×	`times-frac`
1264×	`sqrt-prod`
987×	`*-un-lft-identity`
975×	`add-sqr-sqrt`
617×	`add-cube-cbrt`
238×	`swap-sqr`
161×	`distribute-lft-out`
132×	`associate-r` `associate-l`
84×	`associate-/r/`
49×	`unswap-sqr`
44×	`flip3-+` `flip-+`
42×	`div-inv`
29×	`associate-/l*`
22×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`pow1` `sqrt-div`
7×	`cbrt-undiv` `div-exp`
5×	`sqrt-undiv` `associate-/l/`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 816

Calls

4 calls:

365.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
1.3s	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
342.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
269.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
197.0ms	(* (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))
109.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.0s

Counts

828 → 828

Iterations

Iter	Nodes
done	5000
1	2365
0	665

prune4.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.7b	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.9b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
2.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

3718×	`times-frac`
2278×	`*-un-lft-identity`
1580×	`add-sqr-sqrt` `add-cube-cbrt`
1263×	`sqrt-prod`
349×	`distribute-lft-out`
206×	`associate-/l*`
128×	`associate-/r/`
110×	`sqrt-div`
72×	`div-inv`
65×	`flip3-+` `flip-+`
44×	`add-exp-log`
31×	`div-exp`
29×	`add-cbrt-cube`
23×	`associate-/r*`
16×	`cbrt-undiv`
6×	`1-exp`
5×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
2×	`rec-exp`

Counts

4 → 1624

Calls

4 calls:

592.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
245.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
410.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
354.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

401.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
178.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
286.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
149.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify5.1s

Counts

1636 → 1636

Iterations

Iter	Nodes
done	5001
1	4080
0	1676

prune10.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

71.1% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 3.7b

bsearch116.0ms

Steps

Iters	Range		Point
9	9.443501199947021e+151	3.458076511006716e+160	2.5282382379867205e+158

simplify7.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample1.5s

Algorithm

intervals

Results

727.0ms	8000×	body	80	valid
569.0ms	8000×	pre	80	true