Details

sample35.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify746.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	110	35
3	489	35
4	2430	35
done	5001	35

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 2.4b

Counts

2 → 1

localize13.0ms

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

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
584×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
9×	`add-log-exp`
4×	`pow1` `associate-/l/`
3×	`frac-2neg` `clear-num` `sum-log`
1×	`+-commutative` `associate-+l+`

Counts

4 → 463

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* beta alpha))
21.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms	(/ (/ (/ (+ (+ (+ 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))
22.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (+ alpha beta) (* beta alpha))
27.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
26.0ms	(/ (/ (/ (+ (+ (+ 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))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify444.0ms

Counts

475 → 475

Iterations

Useful iterations: done (415.0ms)

Iter	Nodes	Cost
0	605	25900
1	1530	25140
done	5001	25071

prune1.5s

Filtered

296 candidates to 475 candidates (-60.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	466	9	475
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	467	9	476

Merged error: 0.5b

Counts

476 → 9

localize17.0ms

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

rewrite427.0ms

Algorithm

rewrite-expression-head

Rules

1471×	`times-frac`
1040×	`*-un-lft-identity`
673×	`add-sqr-sqrt`
627×	`sqrt-prod`
590×	`add-cube-cbrt`
258×	`associate-r`
225×	`distribute-lft-out`
88×	`associate-/r/`
71×	`associate-/l*`
63×	`associate-l`
46×	`flip3-+` `flip-+`
44×	`div-inv`
20×	`unswap-sqr`
15×	`add-exp-log` `add-cbrt-cube`
10×	`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 → 761

Calls

4 calls:

41.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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))
263.0ms	(* (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 beta) (* 2.0 1.0)) 1.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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))
27.0ms	(* (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 beta) (* 2.0 1.0)) 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
14.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify610.0ms

Counts

773 → 773

Iterations

Useful iterations: done (545.0ms)

Iter	Nodes	Cost
0	907	48746
1	1957	46624
done	5001	46560

prune5.2s

Filtered

503 candidates to 773 candidates (-53.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	773	0	773
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	773	9	782

Merged error: 0.5b

Counts

782 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.4b	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
2.2b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

3939×	`times-frac`
2530×	`*-un-lft-identity`
1518×	`add-sqr-sqrt` `add-cube-cbrt`
506×	`distribute-lft-out`
311×	`associate-/r*`
186×	`associate-/r/`
96×	`div-inv`
92×	`flip3-+` `flip-+`
54×	`add-exp-log`
36×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/l*`
20×	`cbrt-undiv`
5×	`pow1` `associate-/l/`
4×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1462

Calls

4 calls:

22.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
39.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
77.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
16.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
50.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
26.0ms	(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
13.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.0s

Counts

1474 → 1474

Iterations

Useful iterations: done (924.0ms)

Iter	Nodes	Cost
0	1529	94784
1	3726	89916
done	5000	89620

prune7.5s

Filtered

848 candidates to 1474 candidates (-73.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1473	1	1474
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	1474	9	1483

Merged error: 0.5b

Counts

1483 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(* (+ alpha beta) (+ alpha beta))
0.1b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
18.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac`
216×	`*-un-lft-identity`
145×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
70×	`associate-r`
46×	`distribute-lft-out`
34×	`add-exp-log` `add-cbrt-cube`
26×	`associate-l` `associate-/r/`
19×	`associate-/l*`
18×	`flip3-+` `flip-+`
13×	`pow1` `cbrt-undiv` `div-exp` `div-inv`
9×	`difference-of-squares`
8×	`associate-/r*`
7×	`prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`swap-sqr`
5×	`frac-times`
4×	`add-log-exp`
3×	`associate-r/` `associate-l/` `associate-/l/`
2×	`flip3--` `frac-2neg` `div-sub` `pow-prod-down` `clear-num` `*-commutative` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 295

Calls

4 calls:

27.0ms	(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
9.0ms	(* (+ alpha beta) (+ alpha beta))
66.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
20.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
8.0ms	(* (+ alpha beta) (+ alpha beta))
40.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
19.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify381.0ms

Counts

307 → 307

Iterations

Useful iterations: done (365.0ms)

Iter	Nodes	Cost
0	434	13594
1	1385	13228
done	5000	13188

prune1.1s

Filtered

222 candidates to 307 candidates (-38.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	307	9	316

Merged error: 0.5b

Counts

316 → 9

regimes144.0ms

Accuracy

49.1% (1.3b remaining)

Error of 2.3b against oracle of 1.0b and baseline of 3.6b

bsearch21.0ms

Steps

Iters	Range		Point
7	7.177480459497802e+164	8.235032861842214e+166	1.8185956649680582e+165

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	100
1	43	100
done	43	100

end0.0ms

sample975.0ms

Algorithm

intervals

Results

571.0ms	8000×	body	80	valid
140.0ms	8000×	pre	80	true

Details

sample35.0ms

simplify746.0ms

prune3.0ms

localize13.0ms

rewrite131.0ms

series71.0ms

simplify444.0ms

prune1.5s

localize17.0ms

rewrite427.0ms

series79.0ms

simplify610.0ms

prune5.2s

localize15.0ms

rewrite335.0ms

series112.0ms

simplify1.0s

prune7.5s

localize20.0ms

rewrite140.0ms

series81.0ms

simplify381.0ms

prune1.1s

regimes144.0ms

bsearch21.0ms

simplify3.0ms

end0.0ms

sample975.0ms

Profiling