Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	550	35
4	4087	35
done	5000	35

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 463

Calls

4 calls:

35.0ms	(+ (+ alpha beta) (* beta alpha))
519.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
813.0ms	(/ (/ (/ (+ (+ (+ 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))
401.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ alpha beta) (* beta alpha))
187.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
219.0ms	(/ (/ (/ (+ (+ (+ 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))
111.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.9s

Counts

475 → 475

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	604	25900
1	1467	25129
2	4953	24192
done	5000	23452

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* beta alpha))
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (* 1 (/ (/ (+ (+ (+ 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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
102×	`*-un-lft-identity`
66×	`add-sqr-sqrt` `add-cube-cbrt`
34×	`add-exp-log`
25×	`add-cbrt-cube`
23×	`associate-/l*`
18×	`distribute-lft-out`
17×	`div-exp`
14×	`associate-/r/`
11×	`cbrt-undiv`
10×	`associate-/r*`
9×	`flip3-+` `flip-+` `add-log-exp`
7×	`div-inv`
6×	`prod-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `1-exp` `clear-num` `sum-log` `cbrt-unprod`
1×	`+-commutative` `associate-+l+` `associate-*r/`

Counts

4 → 173

Calls

4 calls:

60.0ms	(+ (+ alpha beta) (* beta alpha))
572.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
443.0ms	(/ (* 1 (/ (/ (+ (+ (+ 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))
474.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (+ alpha beta) (* beta alpha))
168.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
209.0ms	(/ (* 1 (/ (/ (+ (+ (+ 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))
127.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.0s

Counts

185 → 185

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	301	6907
1	792	6612
2	2984	5949
done	5001	5789

prune818.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.3b	(/ (/ (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)))))

rewrite1.9s

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:

349.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
175.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
181.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
629.0ms	(/ (/ (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)))))

series647.0ms

Counts

4 → 12

Calls

4 calls:

295.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
69.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
212.0ms	(/ (/ (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)))))

simplify2.5s

Counts

2379 → 2379

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	2510	189842
done	5000	175863

prune9.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.9b

localize65.0ms

Local error

Found 4 expressions with local error:

2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.2b	(cbrt (* (* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
8.3b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (* (* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

1391×	`times-frac`
698×	`*-un-lft-identity`
552×	`add-sqr-sqrt`
550×	`add-cube-cbrt`
296×	`sqrt-prod`
189×	`cbrt-div`
183×	`associate-/r/`
135×	`frac-times` `associate-*l/`
81×	`associate-*r/`
79×	`cbrt-prod`
74×	`distribute-lft-out`
51×	`div-inv`
25×	`associate-/l*`
23×	`associate-/r*`
21×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`div-exp`
8×	`cbrt-undiv`
6×	`pow1`
4×	`sqrt-div` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `1-exp` `flip-+`
1×	`frac-2neg` `pow1/3` `pow3` `clear-num` `rem-cbrt-cube` `associate-/l/`

Counts

4 → 694

Calls

4 calls:

161.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
159.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
964.0ms	(cbrt (* (* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
364.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (* (* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
64.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
285.0ms	(cbrt (* (* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))
197.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (* (* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))))

simplify2.6s

Counts

706 → 706

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	956	82933
1	2312	66206
2	4243	47056
done	5000	43831

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.9b

regimes106.0ms

Accuracy

58.8% (1.1b remaining)

Error of 2.4b against oracle of 1.3b and baseline of 3.9b

bsearch72.0ms

Steps

Iters	Range		Point
6	2.050539660644998e+192	8.989128788768659e+192	3.0975586046167533e+192

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	42
1	29	40
done	29	40

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
246.0ms	8000×	pre	80	true