Details

sample46.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5255
4	2870
3	497
2	106
1	33
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize43.0ms

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

rewrite1.3s

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-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 465

Calls

4 calls:

122.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
374.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
504.0ms	(/ (/ (/ (+ (+ (+ 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))
310.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
182.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
207.0ms	(/ (/ (/ (+ (+ (+ 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))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify3.0s

Counts

477 → 477

Iterations

Iter	Nodes
done	5013
2	4622
1	1447
0	602

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize27.0ms

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

3614×	`times-frac`
2164×	`*-un-lft-identity`
1424×	`add-sqr-sqrt` `add-cube-cbrt`
370×	`distribute-lft-out`
192×	`associate-/l*`
152×	`associate-/r/`
89×	`div-inv`
84×	`associate-/r*`
65×	`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 → 1332

Calls

4 calls:

258.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
233.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
580.0ms	(/ (/ 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))
289.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series723.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
231.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
221.0ms	(/ (/ 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))
92.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify5.3s

Counts

1344 → 1344

Iterations

Iter	Nodes
done	5003
1	4263
0	1588

prune8.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.2b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.4s

Algorithm

rewrite-expression-head

Rules

13728×	`times-frac`
8082×	`*-un-lft-identity`
5318×	`add-sqr-sqrt` `add-cube-cbrt`
4110×	`sqrt-prod`
1382×	`distribute-lft-out`
826×	`associate-/l*`
550×	`associate-/r/`
276×	`flip3-+` `flip-+`
275×	`div-inv`
88×	`sqrt-div`
34×	`add-cbrt-cube` `add-exp-log`
20×	`cbrt-undiv` `div-exp`
19×	`associate-/r*`
5×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `add-log-exp`

Counts

4 → 4482

Calls

4 calls:

949.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
502.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
451.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
358.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series840.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
212.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
256.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
113.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify8.0s

Counts

4494 → 4494

Iterations

Iter	Nodes
done	5001
0	3264

prune23.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize170.0ms

Local error

Found 4 expressions with local error:

1.1b	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite527.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
17×	`*-un-lft-identity`
12×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`flip3-+` `flip-+`
9×	`add-exp-log`
8×	`associate-/l/`
7×	`add-cbrt-cube`
6×	`associate-/r*` `times-frac` `sqrt-prod`
4×	`frac-times` `pow1` `add-log-exp`
3×	`pow1/3` `distribute-lft-out`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-l/` `associate-r/` `associate-/r/`
1×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

271.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
95.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
96.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
61.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series616.0ms

Counts

4 → 12

Calls

4 calls:

346.0ms	(/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
92.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
91.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
87.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.8s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1565
1	539
0	200

prune966.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

72.4% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 3.5b

bsearch136.0ms

Steps

Iters	Range		Point
8	3.5374683156153913e+155	1.4141214901686598e+159	6.983660355824238e+156

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

814.0ms	8000×	body	80	valid
154.0ms	8000×	pre	80	true