Details

sample24.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify912.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	110	35
3	480	35
4	2398	35
done	5001	35

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.8b

localize12.0ms

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite642.0ms

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:

13.0ms	(+ (+ alpha beta) (* beta alpha))
180.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
266.0ms	(/ (/ (/ (+ (+ (+ 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))
151.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series410.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (+ alpha beta) (* beta alpha))
150.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
161.0ms	(/ (/ (/ (+ (+ (+ 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))
84.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify572.0ms

Counts

475 → 475

Iterations

Useful iterations: done (545.0ms)

Iter	Nodes	Cost
0	604	25900
1	1509	25129
done	5001	24972

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize18.0ms

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

5500×	`times-frac`
3739×	`*-un-lft-identity`
2185×	`add-sqr-sqrt` `add-cube-cbrt`
1821×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
777×	`distribute-lft-out`
450×	`associate-/l*`
302×	`neg-mul-1`
260×	`associate-/r/`
132×	`flip3-+` `flip-+`
130×	`div-inv`
17×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube` `distribute-neg-frac`
9×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `sum-log`
2×	`neg-sub0`
1×	`+-commutative` `associate-+l+`

Counts

4 → 2568

Calls

4 calls:

13.0ms	(+ (+ alpha beta) (* beta alpha))
291.0ms	(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
462.0ms	(/ (/ (- (/ (+ (+ (+ 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))
148.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ alpha beta) (* beta alpha))
228.0ms	(/ (- (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0))))
231.0ms	(/ (/ (- (/ (+ (+ (+ 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))
76.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify920.0ms

Counts

2580 → 2580

Iterations

Useful iterations: 0 (303.0ms)

Iter	Nodes	Cost
0	2642	161931
done	5000	161931

prune6.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize21.0ms

Local error

Found 4 expressions with local error:

3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.9b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
5.0b	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (- (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))))

rewrite3.1s

Algorithm

rewrite-expression-head

Rules

42016×	`times-frac`
17214×	`*-un-lft-identity`
14088×	`add-sqr-sqrt` `add-cube-cbrt`
10140×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8478×	`sqrt-prod`
6252×	`cbrt-prod`
2546×	`associate-/r/`
2532×	`sqrt-div`
1563×	`distribute-lft-out`
1430×	`neg-mul-1`
1280×	`div-inv`
1269×	`flip3-+` `flip-+`
1005×	`associate-/r*`
25×	`add-exp-log`
21×	`add-cbrt-cube`
13×	`cbrt-undiv` `div-exp` `distribute-neg-frac`
12×	`associate-/l*`
6×	`cbrt-div`
4×	`pow1` `add-log-exp`
3×	`pow1/3`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 13143

Calls

4 calls:

31.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
31.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
37.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
716.0ms	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (- (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
63.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
160.0ms	(/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (- (+ (+ alpha beta) (* 2.0 1.0))) (- (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))))))

simplify6.6s

Counts

13155 → 13155

Iterations

Useful iterations: 0 (2.3s)

Iter	Nodes	Cost
0	12954	1382012
done	12954	1382012

prune49.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (- (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
1.9b	(* (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (- (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite27.4s

Algorithm

rewrite-expression-head

Rules

25151×	`times-frac`
14487×	`*-un-lft-identity`
10533×	`add-sqr-sqrt`
9963×	`add-cube-cbrt`
9009×	`sqrt-prod`
6660×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4108×	`associate-r`
2217×	`distribute-lft-out`
1020×	`neg-mul-1`
636×	`associate-/r/`
586×	`associate-/l*`
559×	`associate-l`
346×	`div-inv`
320×	`flip3-+` `flip-+`
117×	`add-exp-log`
115×	`unswap-sqr`
78×	`div-exp`
63×	`add-cbrt-cube`
33×	`cbrt-undiv`
30×	`distribute-neg-frac`
24×	`prod-exp`
15×	`1-exp`
12×	`cbrt-unprod`
10×	`sqrt-div`
8×	`pow1`
7×	`associate-/r*`
4×	`distribute-frac-neg` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-sub`
1×	`neg-sub0` `frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `distribute-rgt-neg-out` `associate-/l/`

Counts

4 → 9577

Calls

4 calls:

560.0ms	(/ (/ (- (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
25.4s	(* (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (- (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
62.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
63.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series680.0ms

Counts

4 → 12

Calls

4 calls:

407.0ms	(/ (/ (- (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
166.0ms	(* (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (- (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))) (- (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
47.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
58.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify3.2s

Counts

9589 → 9589

Iterations

Useful iterations: 0 (1.2s)

Iter	Nodes	Cost
0	7036	688112
done	7036	688112

prune29.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.8b

regimes67.0ms

Accuracy

56.2% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.7b

bsearch55.0ms

Steps

Iters	Range		Point
8	4.8266542845792594e+173	1.0069133071674746e+178	8.48564295701033e+177

simplify8.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	34	42
2	50	42
3	53	42
4	57	42
done	57	42

end0.0ms

sample550.0ms

Algorithm

intervals

Results

302.0ms	8000×	body	80	valid
98.0ms	8000×	pre	80	true