Details

sample81.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
24.0ms	256×	pre	80	true

simplify863.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	557	35
done	5001	35

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize49.0ms

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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.6s

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-exp-log` `add-cbrt-cube`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

227.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
689.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
1.0s	(/ (/ (/ (+ (+ (+ 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))
595.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
262.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
295.0ms	(/ (/ (/ (+ (+ (+ 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))
162.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.3s

Counts

477 → 477

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	603	25954
1	1608	25182
done	5000	24265

prune3.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize47.0ms

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 (+ 3.0 beta)))

3.4b

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

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
827×	`*-un-lft-identity`
382×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
32×	`flip3-+` `flip-+`
31×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 511

Calls

3 calls:

725.0ms

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

856.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))

629.0ms

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

series727.0ms

Counts

3 → 9

Calls

3 calls:

286.0ms

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

299.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))

141.0ms

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

simplify1.3s

Counts

520 → 520

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	584	27351
1	1571	26487
done	5001	25464

prune3.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize56.0ms

Local error

Found 4 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 (+ 3.0 beta)) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ (/ 1 1) (/ (+ alpha (+ 3.0 beta)) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

18173×	`times-frac`
12294×	`*-un-lft-identity`
6389×	`add-sqr-sqrt` `add-cube-cbrt`
3403×	`distribute-lft-out`
636×	`associate-/r/`
632×	`div-inv`
371×	`associate-/r*`
312×	`flip3-+` `flip-+`
114×	`add-exp-log`
96×	`div-exp`
52×	`add-cbrt-cube`
40×	`associate-/l*`
34×	`cbrt-undiv`
20×	`1-exp`
8×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4842

Calls

4 calls:

704.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
524.0ms	(/ (+ alpha (+ 3.0 beta)) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
727.0ms	(/ (/ 1 1) (/ (+ alpha (+ 3.0 beta)) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
640.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
438.0ms	(/ (+ alpha (+ 3.0 beta)) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
313.0ms	(/ (/ 1 1) (/ (+ alpha (+ 3.0 beta)) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
146.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify5.5s

Counts

4854 → 4854

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	4159	343361
done	5000	316001

prune18.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize81.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
76×	`sqrt-prod`
63×	`times-frac`
54×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
14×	`associate-/l*`
13×	`distribute-lft-out`
10×	`sqrt-div`
9×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 151

Calls

4 calls:

445.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
410.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
226.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
252.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series767.0ms

Counts

4 → 12

Calls

4 calls:

361.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
210.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
108.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
87.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.6s

Counts

163 → 163

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	221	4616
1	488	4253
2	1956	4105
done	5001	4101

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

regimes230.0ms

Accuracy

53.9% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.8b

bsearch169.0ms

Steps

Iters	Range		Point
10	5.186387406567574e+149	1.776725756984014e+163	2.364521894300773e+162

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	36
1	28	36
done	28	36

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
264.0ms	8000×	pre	80	true