Details

sample42.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify2.7s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.2s

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:

170.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
485.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
791.0ms	(/ (/ (/ (+ (+ (+ 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))
712.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
181.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
175.0ms	(/ (/ (/ (+ (+ (+ 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))
122.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.4s

Counts

477 → 477

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	603	25954
1	1443	25182
2	4754	24241
done	5001	23501

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize17.0ms

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 (+ 3.0 beta)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
828×	`*-un-lft-identity`
383×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
62×	`associate-/r/`
33×	`flip3-+` `flip-+`
31×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 524

Calls

4 calls:

47.0ms	(+ (+ alpha beta) (* beta alpha))
499.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
564.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))
465.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (+ alpha beta) (* beta alpha))
223.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
239.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ alpha (+ 3.0 beta)))
125.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.9s

Counts

536 → 536

Iterations

Useful iterations: 2 (1.4s)

Iter	Nodes	Cost
0	608	27532
1	1482	26661
2	4991	25612
done	5001	25612

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta))))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.3s

Algorithm

rewrite-expression-head

Rules

1777×	`times-frac`
1545×	`*-un-lft-identity`
761×	`add-sqr-sqrt`
747×	`sqrt-prod`
678×	`add-cube-cbrt`
497×	`distribute-lft-out`
321×	`associate-r`
104×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
54×	`flip3-+` `flip-+`
52×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r*`
6×	`pow1`
5×	`associate-/l/`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`frac-2neg` `sqrt-div` `clear-num`
2×	`prod-exp` `cbrt-unprod`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 888

Calls

4 calls:

1.8s	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta))))
477.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta)))
454.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
459.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series672.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta))))
159.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ alpha (+ 3.0 beta)))
122.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
125.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Counts

900 → 900

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	911	52975
1	1822	50323
done	5001	47683

prune3.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (+ alpha beta))
0.0b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ alpha (+ 3.0 beta)) (- (+ alpha beta) (* 2.0 1.0))))
1.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

5607×	`times-frac`
3674×	`*-un-lft-identity`
1911×	`add-sqr-sqrt`
1909×	`add-cube-cbrt`
1000×	`distribute-lft-out`
415×	`difference-of-squares`
393×	`associate-/r/`
197×	`div-inv`
102×	`flip3--` `flip--`
101×	`flip3-+` `flip-+`
100×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r*`
19×	`cbrt-undiv` `div-exp`
11×	`pow1`
6×	`swap-sqr`
4×	`frac-times` `associate-r` `associate-l` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-r/` `associate-l/`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 1947

Calls

4 calls:

60.0ms	(* (+ alpha beta) (+ alpha beta))
719.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ alpha (+ 3.0 beta)) (- (+ alpha beta) (* 2.0 1.0))))
503.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
509.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series713.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ alpha beta) (+ alpha beta))
313.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ alpha (+ 3.0 beta)) (- (+ alpha beta) (* 2.0 1.0))))
241.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
135.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.7s

Counts

1959 → 1959

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	2281	169890
done	5000	164256

prune9.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.3b

regimes107.0ms

Accuracy

59.1% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.8b

bsearch101.0ms

Steps

Iters	Range		Point
8	1.7519304510016456e+160	7.027642810475786e+162	6.375269332570683e+160

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	74
1	44	74
done	44	74

end0.0ms

sample1.3s

Algorithm

intervals

Results

789.0ms	8000×	body	80	valid
240.0ms	8000×	pre	80	true