Details

sample41.0ms

Algorithm

intervals

Results

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

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	550	35
4	4087	35
done	5000	35

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize22.0ms

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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

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:

29.0ms	(+ (+ alpha beta) (* beta alpha))
463.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
736.0ms	(/ (/ (/ (+ (+ (+ 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))
393.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (+ alpha beta) (* beta alpha))
166.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
225.0ms	(/ (/ (/ (+ (+ (+ 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))
101.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.5s

Counts

475 → 475

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	604	25900
1	1467	25129
2	4953	24192
done	5000	23452

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize42.0ms

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))))
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))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

819×	`times-frac`
601×	`*-un-lft-identity`
360×	`sqrt-prod`
355×	`add-sqr-sqrt`
349×	`add-cube-cbrt`
126×	`distribute-lft-out`
71×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `associate-/l/`
4×	`add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
2×	`sqrt-div`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 477

Calls

4 calls:

305.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
545.0ms	(/ (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))
426.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
355.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series674.0ms

Counts

4 → 12

Calls

4 calls:

297.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
167.0ms	(/ (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))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
106.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.8s

Counts

489 → 489

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	686	27614
1	1164	26690
2	2741	25484
done	5000	24659

prune2.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.4b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.6b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

624×	`times-frac`
522×	`sqrt-prod`
425×	`*-un-lft-identity`
325×	`add-sqr-sqrt`
323×	`add-cube-cbrt`
55×	`associate-/l*`
51×	`distribute-lft-out`
24×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`sqrt-undiv` `associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 464

Calls

4 calls:

429.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
343.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
192.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
235.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series620.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
168.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
81.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
52.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.7s

Counts

476 → 476

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	455	23023
1	1032	20455
2	2184	19368
done	5000	18678

prune1.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
3.0b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.0b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite689.0ms

Algorithm

rewrite-expression-head

Rules

357×	`times-frac`
285×	`*-un-lft-identity`
220×	`cbrt-prod`
175×	`add-sqr-sqrt` `add-cube-cbrt`
55×	`distribute-lft-out`
27×	`associate-/r*`
24×	`cbrt-div`
17×	`associate-/r/`
12×	`flip3-+` `flip-+`
9×	`add-exp-log` `div-inv`
7×	`associate-/l*`
6×	`add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `pow1/3` `div-exp`
2×	`associate-/l/`
1×	`frac-2neg` `clear-num`

Counts

4 → 282

Calls

4 calls:

444.0ms	(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
68.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
78.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
79.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series585.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))))
70.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
82.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
92.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.2s

Counts

294 → 294

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	409	14622
1	914	14135
2	3186	13793
done	5001	13487

prune1.1s

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.9b

regimes155.0ms

Accuracy

88.2% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 3.6b

bsearch2.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	102
1	36	102
done	36	102

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.0s	8000×	body	80	valid
170.0ms	8000×	pre	80	true