Details

sample68.0ms

Algorithm

intervals

Results

38.0ms	256×	body	80	valid
10.0ms	256×	pre	80	true

simplify748.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2244
3	434
2	100
1	33
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 2 (+ beta alpha)) 1.0)
0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite899.0ms

Algorithm

rewrite-expression-head

Rules

4332×	`*-un-lft-identity`
2696×	`times-frac`
2173×	`distribute-lft-out`
778×	`add-sqr-sqrt` `add-cube-cbrt`
166×	`associate-/l*`
102×	`associate-/r/`
53×	`flip3-+` `flip-+`
51×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 1221

Calls

4 calls:

67.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
158.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
383.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
195.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
207.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
196.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
124.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.5s

Counts

1233 → 1233

Iterations

Iter	Nodes
2	4172
1	1424
0	605

prune4.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
0.2b	(* (/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) (/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

13678×	`*-un-lft-identity`
10347×	`times-frac`
6472×	`distribute-lft-out`
5865×	`sqrt-prod`
3744×	`add-sqr-sqrt`
3095×	`add-cube-cbrt`
1434×	`associate-r`
718×	`associate-l`
296×	`associate-/r/`
246×	`associate-/l*`
150×	`flip3-+` `flip-+`
149×	`div-inv`
120×	`unswap-sqr`
70×	`add-exp-log`
49×	`add-cbrt-cube`
38×	`div-exp`
32×	`sqrt-div`
23×	`cbrt-undiv`
16×	`associate-/r*`
15×	`prod-exp`
9×	`cbrt-unprod`
6×	`pow1` `1-exp`
5×	`associate-/l/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 4091

Calls

4 calls:

379.0ms	(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
1.8s	(* (/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) (/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
175.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
202.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series683.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0))
225.0ms	(* (/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) 1) (/ (/ (sqrt (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha)))) (+ (+ 2 (+ beta alpha)) 1.0)))
144.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))
126.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify25.3s

Counts

4103 → 4103

Iterations

Iter	Nodes
1	5579
0	1609

prune18.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
0.1b	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
0.6b	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

19157×	`*-un-lft-identity`
13943×	`times-frac`
9343×	`distribute-lft-out`
3996×	`add-sqr-sqrt` `add-cube-cbrt`
967×	`associate-/r*`
394×	`associate-/r/`
200×	`div-inv`
196×	`flip3-+` `flip-+`
54×	`add-exp-log`
39×	`associate-/l*`
36×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `insert-posit16` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 4520

Calls

4 calls:

227.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
357.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
215.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
188.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
295.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
203.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
97.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify39.1s

Counts

4532 → 4532

Iterations

Iter	Nodes
1	4385
0	1531

prune12.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
0.1b	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
0.1b	(/ (/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ 2 (+ beta alpha)))
2.4b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

15692×	`*-un-lft-identity`
12209×	`times-frac`
7445×	`distribute-lft-out`
3649×	`add-sqr-sqrt` `add-cube-cbrt`
501×	`associate-/l*`
312×	`associate-/r/`
197×	`associate-/r*`
171×	`div-inv`
143×	`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` `insert-posit16` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 3886

Calls

4 calls:

187.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
356.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
325.0ms	(/ (/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ 2 (+ beta alpha)))
168.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))))
146.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))
222.0ms	(/ (/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))))) (+ 2 (+ beta alpha)))
131.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify51.0s

Counts

3898 → 3898

Iterations

Iter	Nodes
1	4508
0	1593

prune12.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes108.0ms

Accuracy

74.8% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 3.5b

bsearch133.0ms

Steps

Iters	Range		Point
9	5.720656236215882e+160	1.474456540048641e+169	5.874077370608373e+160

simplify8.0ms

Iterations

Iter	Nodes
2	32
1	32
0	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
287.0ms	8000×	pre	80	true