Details

sample56.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify927.0ms

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

localize25.0ms

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)))

rewrite1.5s

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:

390.0ms

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

635.0ms

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

402.0ms

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

series489.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms

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

211.0ms

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

100.0ms

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

simplify751.0ms

Counts

459 → 459

Iterations

Iter	Nodes
done	5001
1	1558
0	579

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.1b

localize55.0ms

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

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

4754×	`times-frac`
3436×	`*-un-lft-identity`
1746×	`add-sqr-sqrt` `add-cube-cbrt`
845×	`distribute-lft-out`
246×	`associate-/l*`
192×	`associate-/r/`
109×	`div-inv`
103×	`associate-/r*`
85×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1` `associate-/l/`
4×	`clear-num` `frac-2neg` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1693

Calls

4 calls:

187.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))
186.0ms	(/ 1 (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))))
503.0ms	(/ (/ 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))
312.0ms	(/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

227.0ms	(/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0)))))
196.0ms	(/ 1 (/ (+ alpha (+ beta (* 2.0 1.0))) (/ (+ (* alpha beta) (+ (+ beta alpha) 1.0)) (+ alpha (+ beta (* 2.0 1.0))))))
256.0ms	(/ (/ 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))))

simplify4.7s

Counts

1705 → 1705

Iterations

Iter	Nodes
done	5002
1	4629
0	1594

prune4.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.2s

Algorithm

rewrite-expression-head

Rules

25046×	`times-frac`
15107×	`*-un-lft-identity`
8781×	`add-sqr-sqrt` `add-cube-cbrt`
3163×	`distribute-lft-out`
1474×	`associate-/r/`
1017×	`associate-/l*`
750×	`div-inv`
725×	`flip3-+` `flip-+`
354×	`associate-/r*`
213×	`add-exp-log`
177×	`div-exp`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
32×	`rec-exp` `1-exp`
5×	`pow1`
4×	`clear-num` `frac-2neg` `add-log-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 6794

Calls

4 calls:

228.0ms	(/ 1 (/ (/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0)))) (/ 1 (+ alpha (+ beta (* 2.0 1.0))))))
769.0ms	(/ (/ 1 (/ (/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0)))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
261.0ms	(/ (/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0)))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
159.0ms	(/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ 1 (/ (/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0)))) (/ 1 (+ alpha (+ beta (* 2.0 1.0))))))
190.0ms	(/ (/ 1 (/ (/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0)))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
188.0ms	(/ (/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0)))) (/ 1 (+ alpha (+ beta (* 2.0 1.0)))))
110.0ms	(/ (+ alpha (+ (* 1.0 2.0) beta)) (+ (* alpha beta) (+ beta (+ alpha 1.0))))

simplify3.3s

Counts

6806 → 6806

Iterations

Iter	Nodes
done	6054
0	6054

prune42.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
65×	`times-frac`
49×	`add-sqr-sqrt`
44×	`add-cube-cbrt`
35×	`distribute-lft-out`
26×	`associate-r`
15×	`add-cbrt-cube` `add-exp-log`
13×	`associate-/r*`
12×	`sqrt-prod`
10×	`associate-/l*`
9×	`sqrt-div`
8×	`associate-/r/`
7×	`associate-/l/`
6×	`frac-times` `pow1` `flip3-+` `associate-*l/` `flip-+`
4×	`cbrt-undiv` `div-exp` `associate-l` `associate-*r/` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 168

Calls

4 calls:

219.0ms	(/ (sqrt (* (/ 1 (+ alpha (+ (* 1.0 2.0) beta))) (/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta))))) (+ (+ alpha (+ (* 1.0 2.0) beta)) 1.0))
979.0ms	(* (sqrt (* (/ 1 (+ alpha (+ (* 1.0 2.0) beta))) (/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta))))) (/ (sqrt (* (/ 1 (+ alpha (+ (* 1.0 2.0) beta))) (/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta))))) (+ (+ alpha (+ (* 1.0 2.0) beta)) 1.0)))
193.0ms	(/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta)))
185.0ms	(/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta)))

series668.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(/ (sqrt (* (/ 1 (+ alpha (+ (* 1.0 2.0) beta))) (/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta))))) (+ (+ alpha (+ (* 1.0 2.0) beta)) 1.0))
225.0ms	(* (sqrt (* (/ 1 (+ alpha (+ (* 1.0 2.0) beta))) (/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta))))) (/ (sqrt (* (/ 1 (+ alpha (+ (* 1.0 2.0) beta))) (/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta))))) (+ (+ alpha (+ (* 1.0 2.0) beta)) 1.0)))
123.0ms	(/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta)))
100.0ms	(/ (+ (* alpha beta) (+ beta (+ alpha 1.0))) (+ alpha (+ (* 1.0 2.0) beta)))

simplify2.1s

Counts

180 → 180

Iterations

Iter	Nodes
done	5002
2	4011
1	614
0	224

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes224.0ms

Accuracy

70.8% (1.2b remaining)

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

bsearch159.0ms

Steps

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

simplify10.0ms

Iterations

Iter	Nodes
done	67
3	67
2	63
1	59
0	39

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
207.0ms	8000×	pre	80	true