Details

sample40.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify634.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize15.0ms

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))
3.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

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:

125.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
491.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
730.0ms	(/ (/ (/ (+ (+ (+ 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))
403.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
177.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
262.0ms	(/ (/ (/ (+ (+ (+ 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))
92.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify696.0ms

Counts

477 → 477

Iterations

Useful iterations: done (667.0ms)

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

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.4b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (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))))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite931.0ms

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:

338.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
271.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
155.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
156.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series476.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
128.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
63.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
73.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify825.0ms

Counts

163 → 163

Iterations

Useful iterations: done (811.0ms)

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

prune658.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.5b	(/ (sqrt 1) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.8b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite926.0ms

Algorithm

rewrite-expression-head

Rules

603×	`times-frac`
486×	`sqrt-prod`
405×	`*-un-lft-identity`
311×	`add-sqr-sqrt`
309×	`add-cube-cbrt`
51×	`associate-/r*`
48×	`distribute-lft-out`
20×	`sqrt-div`
17×	`associate-/r/`
13×	`associate-/l*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

284.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
268.0ms	(/ (sqrt 1) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
156.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
171.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
126.0ms	(/ (sqrt 1) (/ (sqrt (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
76.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
60.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify821.0ms

Counts

449 → 449

Iterations

Useful iterations: done (782.0ms)

Iter	Nodes	Cost
0	476	18142
1	1223	15001
done	5001	14780

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
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)))
0.9b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
3.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

2490×	`times-frac`
1662×	`*-un-lft-identity`
1068×	`add-sqr-sqrt` `add-cube-cbrt`
911×	`sqrt-prod`
297×	`distribute-lft-out`
154×	`associate-/l*`
96×	`associate-/r/`
78×	`sqrt-div`
49×	`flip3-+` `flip-+`
48×	`div-inv`
29×	`add-exp-log`
25×	`add-cbrt-cube`
23×	`associate-/r*`
16×	`div-exp`
13×	`cbrt-undiv`
5×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
1×	`rec-exp` `1-exp`

Counts

4 → 1202

Calls

4 calls:

307.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
766.0ms	(/ (/ (/ (+ (+ (+ 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)))
461.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
439.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series1.0s

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
414.0ms	(/ (/ (/ (+ (+ (+ 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)))
331.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify2.4s

Counts

1214 → 1214

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	1194	74963
1	3179	68872
done	5000	68327

prune4.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

regimes115.0ms

Accuracy

55.4% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch31.0ms

Steps

Iters	Range		Point
2	8.248631289177518e+174	1.0146313625995505e+175	8.960262165484263e+174

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	32	93
1	42	92
done	42	92

end0.0ms

sample1.4s

Algorithm

intervals

Results

787.0ms	8000×	body	80	valid
262.0ms	8000×	pre	80	true