Details

sample56.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.9b

localize16.0ms

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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

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:

57.0ms	(+ (+ alpha beta) (* beta alpha))
559.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
765.0ms	(/ (/ (/ (+ (+ (+ 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))
424.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series623.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ alpha beta) (* beta alpha))
191.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
264.0ms	(/ (/ (/ (+ (+ (+ 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))
150.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.9s

Counts

475 → 475

Iterations

Useful iterations: done (2.9s)

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

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
0.0b	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.7b	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
65×	`*-un-lft-identity`
54×	`add-exp-log`
49×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
34×	`add-cbrt-cube`
24×	`div-exp`
18×	`associate-/r/`
15×	`associate-r`
14×	`cbrt-undiv`
13×	`flip3-+` `flip-+` `associate-/l*`
12×	`prod-exp`
11×	`distribute-lft-out`
10×	`associate-/r*`
9×	`div-inv`
7×	`pow1` `associate-/l/`
6×	`cbrt-unprod`
4×	`frac-times` `rec-exp` `1-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`associate-*r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 181

Calls

4 calls:

38.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
304.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
515.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
596.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ 1 (+ (+ alpha beta) (* 2.0 1.0)))
249.0ms	(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0)))
260.0ms	(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
111.0ms	(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))

simplify2.1s

Counts

193 → 193

Iterations

Useful iterations: 2 (705.0ms)

Iter	Nodes	Cost
0	281	6833
1	767	6239
2	3334	5641
done	5001	5641

prune697.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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)) 1.0))
0.3b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
3.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

10323×	`times-frac`
6511×	`*-un-lft-identity`
3883×	`add-sqr-sqrt`
3881×	`add-cube-cbrt`
2904×	`sqrt-prod`
1315×	`distribute-lft-out`
591×	`associate-/l*`
239×	`associate-/r/`
216×	`sqrt-div`
127×	`div-inv`
115×	`flip3-+` `flip-+`
20×	`add-exp-log` `add-cbrt-cube`
11×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 3044

Calls

4 calls:

1.1s	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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)) 1.0))
357.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
205.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
207.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series800.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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)) 1.0))
381.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
74.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
89.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify3.0s

Counts

3056 → 3056

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	2802	265860
done	5000	252463

prune11.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

localize47.0ms

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))))
3.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.5b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.2s

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:

422.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
370.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
192.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
177.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series630.0ms

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
140.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
85.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
97.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.6s

Counts

476 → 476

Iterations

Useful iterations: done (1.6s)

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

prune1.4s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.1b

regimes113.0ms

Accuracy

57.6% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.7b

bsearch89.0ms

Steps

Iters	Range		Point
8	3.734405037488181e+157	1.4098134330683202e+162	1.3830890874159494e+162

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	42
1	29	42
done	29	42

end0.0ms

sample1.4s

Algorithm

intervals

Results

873.0ms	8000×	body	80	valid
213.0ms	8000×	pre	80	true