Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

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))
4.3b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.9s

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:

173.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
577.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
688.0ms	(/ (/ (/ (+ (+ (+ 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))
427.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series596.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
215.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
216.0ms	(/ (/ (/ (+ (+ (+ 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))
140.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.7s

Counts

477 → 477

Iterations

Useful iterations: done (2.7s)

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

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

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)))
4.3b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

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*`
66×	`associate-/r/`
37×	`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` `frac-add` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 528

Calls

4 calls:

46.0ms	(+ (+ alpha beta) (* beta alpha))
507.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
767.0ms	(/ (/ (/ (+ (+ (+ 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)))
443.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series579.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (+ alpha beta) (* beta alpha))
218.0ms	(/ (/ (+ (+ (+ 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)))
120.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify992.0ms

Counts

540 → 540

Iterations

Useful iterations: done (947.0ms)

Iter	Nodes	Cost
0	637	30076
1	1587	29197
done	5001	28112

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* beta alpha) (+ alpha beta))
0.0b	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
4.3b	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.1s

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*`
66×	`associate-/r/`
37×	`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` `frac-add` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+r+`

Counts

4 → 528

Calls

4 calls:

29.0ms	(+ (* beta alpha) (+ alpha beta))
529.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
1.0s	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
449.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (* beta alpha) (+ alpha beta))
177.0ms	(/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
217.0ms	(/ (/ (/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)))
99.0ms	(/ (+ (+ (* beta alpha) (+ alpha beta)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.2s

Counts

540 → 540

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	637	30076
1	1592	29197
done	5000	28110

prune1.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b	(/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
4.3b	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))
4.3b	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
522×	`sqrt-prod`
425×	`*-un-lft-identity`
325×	`add-sqr-sqrt`
323×	`add-cube-cbrt`
55×	`associate-/l*`
51×	`distribute-lft-out`
24×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-undiv` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 464

Calls

4 calls:

393.0ms	(/ (/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
295.0ms	(/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
218.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))
149.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))

series554.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(/ (/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
141.0ms	(/ (sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
74.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))
68.0ms	(sqrt (+ (+ (* beta alpha) (+ alpha beta)) 1.0))

simplify1.6s

Counts

476 → 476

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	455	23023
1	1031	20455
2	2170	19368
done	5000	18678

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

regimes93.0ms

Accuracy

55.8% (1.2b remaining)

Error of 2.3b against oracle of 1.1b and baseline of 3.9b

bsearch27.0ms

Steps

Iters	Range		Point
3	2.964554085996149e+160	3.844672684397608e+160	3.789665271997516e+160

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	27	40
done	27	40

end0.0ms

sample1.2s

Algorithm

intervals

Results

669.0ms	8000×	body	80	valid
217.0ms	8000×	pre	80	true