Details

sample43.0ms

Algorithm

intervals

Results

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

simplify622.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	554
2	111
1	33
0	14

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize45.0ms

Local error

Found 3 expressions with local error:

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))

2.2b

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

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

377.0ms

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

657.0ms

(/ (/ (/ (+ (+ (+ 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))

294.0ms

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

series550.0ms

Counts

3 → 9

Calls

3 calls:

204.0ms

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

228.0ms

(/ (/ (/ (+ (+ (+ 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))

118.0ms

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

simplify808.0ms

Counts

459 → 459

Iterations

Iter	Nodes
done	5001
1	1558
0	579

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))
0.0b	(/ (/ 1 1) (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))))
0.1b	(/ (/ (/ 1 1) (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.2b	(/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

23821×	`times-frac`
15184×	`*-un-lft-identity`
8354×	`add-sqr-sqrt` `add-cube-cbrt`
3415×	`distribute-lft-out`
1026×	`associate-/l*`
872×	`div-inv`
732×	`associate-/r/`
325×	`flip3-+` `flip-+`
154×	`add-exp-log`
134×	`div-exp`
103×	`associate-/r*`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
30×	`1-exp`
12×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`

Counts

4 → 6352

Calls

4 calls:

192.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))
175.0ms	(/ (/ 1 1) (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))))
789.0ms	(/ (/ (/ 1 1) (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
306.0ms	(/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))

series766.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))
203.0ms	(/ (/ 1 1) (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))))
242.0ms	(/ (/ (/ 1 1) (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
119.0ms	(/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))

simplify3.1s

Counts

6364 → 6364

Iterations

Iter	Nodes
done	5279
0	5279

prune31.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 1) (/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0))))))
0.1b	(/ (/ (/ 1 1) (/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.2b	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
2.2b	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))

rewrite9.4s

Algorithm

rewrite-expression-head

Rules

121081×	`times-frac`
67127×	`*-un-lft-identity`
41261×	`add-sqr-sqrt` `add-cube-cbrt`
12933×	`distribute-lft-out`
5854×	`associate-/r/`
4945×	`div-inv`
4317×	`associate-/l*`
2885×	`flip3-+` `flip-+`
523×	`add-exp-log`
503×	`div-exp`
354×	`associate-/r*`
120×	`1-exp`
112×	`add-cbrt-cube`
82×	`cbrt-undiv`
66×	`rec-exp`
5×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`

Counts

4 → 26625

Calls

4 calls:

389.0ms	(/ (/ 1 1) (/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0))))))
2.2s	(/ (/ (/ 1 1) (/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
292.0ms	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
145.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (/ 1 1) (/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0))))))
239.0ms	(/ (/ (/ 1 1) (/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
188.0ms	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
147.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))

simplify13.3s

Counts

26637 → 26637

Iterations

Iter	Nodes
done	21305
0	21305

prune1.7m

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
0.2b	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
2.2b	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))
2.2b	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))

rewrite592.0ms

Algorithm

rewrite-expression-head

Rules

1584×	`times-frac`
1102×	`*-un-lft-identity`
630×	`add-sqr-sqrt` `add-cube-cbrt`
236×	`distribute-lft-out`
158×	`associate-/r/`
80×	`flip3-+` `flip-+` `div-inv`
52×	`add-exp-log`
44×	`associate-/l*`
42×	`associate-/r*`
34×	`div-exp`
32×	`add-cbrt-cube`
18×	`cbrt-undiv`
6×	`associate-/l/`
4×	`pow1` `rec-exp` `clear-num` `frac-2neg` `1-exp` `add-log-exp`

Counts

4 → 838

Calls

4 calls:

167.0ms	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
167.0ms	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
103.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))
104.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
143.0ms	(/ (/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
93.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))
98.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (+ (* alpha beta) (+ (+ beta alpha) 1.0)))

simplify792.0ms

Counts

850 → 850

Iterations

Iter	Nodes
done	5000
1	2021
0	570

prune2.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes121.0ms

Accuracy

70.7% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 4.3b

bsearch78.0ms

Steps

Iters	Range		Point
9	1.1416104037604334e+156	8.001771365916775e+161	1.8040289506123877e+158

simplify6.0ms

Iterations

Iter	Nodes
done	48
2	48
1	47
0	34

end0.0ms

sample1.1s

Algorithm

intervals

Results

430.0ms	8000×	body	80	valid
426.0ms	8000×	pre	80	true