Details

sample52.0ms

Algorithm

intervals

Results

33.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify630.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize27.0ms

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))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite988.0ms

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:

64.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
226.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
420.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
202.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ 2 (+ beta alpha)) 1.0)
184.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
246.0ms	(/ (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))) (+ (+ 2 (+ beta alpha)) 1.0))
104.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify2.2s

Counts

1233 → 1233

Iterations

Iter	Nodes
2	4172
1	1424
0	605

prune14.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.9b

localize52.0ms

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))))
0.3b	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
3.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

rewrite1.5s

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:

205.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
359.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
324.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
214.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

series891.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))
339.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha))))
236.0ms	(/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha))) (+ 2 (+ beta alpha)))))
116.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (+ 2 (+ beta alpha)))

simplify39.0s

Counts

4532 → 4532

Iterations

Iter	Nodes
1	4385
0	1531

prune58.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (+ alpha beta))
0.0b	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))))
0.1b	(* (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (- 4 (* (+ alpha beta) (+ alpha beta)))) (/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))))))
15.7b	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (- 4 (* (+ alpha beta) (+ alpha beta))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

3415×	`*-un-lft-identity`
2340×	`times-frac`
1460×	`distribute-lft-out`
1011×	`add-sqr-sqrt`
697×	`add-cube-cbrt`
672×	`associate-r`
250×	`distribute-lft-out--`
134×	`difference-of-squares`
87×	`add-exp-log`
59×	`associate-/r/`
45×	`add-cbrt-cube`
44×	`div-exp`
40×	`associate-/r*`
33×	`flip3-+` `flip-+`
32×	`div-inv`
26×	`associate-l`
21×	`prod-exp`
20×	`cbrt-undiv`
15×	`unswap-sqr`
13×	`pow1`
10×	`associate-/l*`
9×	`cbrt-unprod`
6×	`rec-exp` `1-exp` `swap-sqr`
5×	`frac-times`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`associate-l/` `associate-r/`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `un-div-inv` `pow-prod-up`

Counts

4 → 1104

Calls

4 calls:

44.0ms	(* (+ alpha beta) (+ alpha beta))
242.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))))
651.0ms	(* (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (- 4 (* (+ alpha beta) (+ alpha beta)))) (/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))))))
274.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (- 4 (* (+ alpha beta) (+ alpha beta))))

series935.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (+ alpha beta) (+ alpha beta))
85.0ms	(/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))))
662.0ms	(* (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (- 4 (* (+ alpha beta) (+ alpha beta)))) (/ 1 (/ (+ (+ 2 (+ beta alpha)) 1.0) (/ (- 2 (+ beta alpha)) (+ 2 (+ beta alpha))))))
162.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (- 4 (* (+ alpha beta) (+ alpha beta))))

simplify5.0s

Counts

1116 → 1116

Iterations

Iter	Nodes
1	3044
0	825

prune16.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
0.5b	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
3.6b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
3.6b	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

rewrite567.0ms

Algorithm

rewrite-expression-head

Rules

194×	`*-un-lft-identity`
160×	`sqrt-prod`
112×	`times-frac`
76×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
68×	`distribute-lft-out`
16×	`associate-/r*`
14×	`associate-/l*`
12×	`sqrt-div`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `insert-posit16` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 212

Calls

4 calls:

174.0ms	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
190.0ms	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
106.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
91.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

series417.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
126.0ms	(/ (sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha)))) (sqrt (+ 2 (+ beta alpha))))
78.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))
80.0ms	(sqrt (+ 1.0 (+ (* alpha beta) (+ beta alpha))))

simplify1.1s

Counts

224 → 224

Iterations

Iter	Nodes
3	2666
2	815
1	328
0	161

prune3.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

regimes153.0ms

Accuracy

48.9% (1.7b remaining)

Error of 2.9b against oracle of 1.2b and baseline of 4.5b

bsearch85.0ms

Steps

Iters	Range		Point
8	1.3778561594943785e+141	9.602781638389914e+144	9.447545610483609e+144

simplify7.0ms

Iterations

Iter	Nodes
2	44
1	44
0	35

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
289.0ms	8000×	pre	80	true