Details

sample30.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify77.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17
done	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize15.0ms

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))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

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:

27.0ms	(+ (+ alpha beta) (* beta alpha))
327.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
470.0ms	(/ (/ (/ (+ (+ (+ 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))
275.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ alpha beta) (* beta alpha))
149.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
163.0ms	(/ (/ (/ (+ (+ (+ 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))
77.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify125.0ms

Counts

475 → 475

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1512	13008
1	5001	12540
done	5001	12540

prune952.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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)))
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))
3.2b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

3618×	`times-frac`
2167×	`*-un-lft-identity`
1425×	`add-sqr-sqrt` `add-cube-cbrt`
371×	`distribute-lft-out`
248×	`associate-/l*`
158×	`associate-/r/`
89×	`div-inv`
70×	`flip3-+` `flip-+`
64×	`add-exp-log`
44×	`div-exp`
34×	`add-cbrt-cube`
29×	`associate-/r*`
20×	`cbrt-undiv`
6×	`rec-exp` `1-exp`
5×	`pow1`
4×	`frac-2neg` `clear-num` `associate-/l/` `add-log-exp`
1×	`pow-flip` `inv-pow`

Counts

4 → 1337

Calls

4 calls:

266.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
153.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
438.0ms	(/ (/ (/ 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))
181.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series482.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
76.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
159.0ms	(/ (/ (/ 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))
96.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify376.0ms

Counts

1349 → 1349

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3844	42670
1	5001	41449
done	5001	41449

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite813.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
80×	`sqrt-prod`
70×	`times-frac`
56×	`add-sqr-sqrt`
54×	`add-cube-cbrt`
22×	`distribute-lft-out`
13×	`associate-/r*`
11×	`associate-/l*`
10×	`sqrt-div`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`
1×	`sqrt-undiv`

Counts

4 → 159

Calls

4 calls:

369.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
207.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
113.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
116.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series411.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
106.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
51.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
48.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify65.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	507	2617
1	1942	2448
2	5003	2394
done	5003	2394

prune420.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))
0.1b	(/ (+ (+ (+ 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))))
0.2b	(/ 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)))))
3.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

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:

331.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
444.0ms	(/ (+ (+ (+ 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))))
347.0ms	(/ 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)))))
281.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series606.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
228.0ms	(/ (+ (+ (+ 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))))
153.0ms	(/ 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)))))
81.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify425.0ms

Counts

1474 → 1474

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3703	48039
1	5001	46602
done	5001	46602

prune2.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

58.7% (1.4b remaining)

Error of 1.4b against oracle of 0.0b and baseline of 3.4b

bsearch75.0ms

Steps

Iters	Range		Point
10	1.0155293812022926e+156	5.027089316835925e+165	2.733428746494648e+158

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	35
1	41	35
done	41	35

end0.0ms

sample565.0ms

Algorithm

intervals

Results

293.0ms	8000×	body	80	valid
85.0ms	8000×	pre	80	true