Details

sample70.0ms

Algorithm

intervals

Results

40.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5015
3	808
2	131
1	36
0	15

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize54.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

3.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
4×	`associate-/l/`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

3 → 459

Calls

3 calls:

360.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

485.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

314.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series513.0ms

Counts

3 → 9

Calls

3 calls:

192.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

210.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))

112.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.9s

Counts

468 → 468

Iterations

Iter	Nodes
done	5000
1	1399
0	588

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `div-exp`
2×	`sqrt-div`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 489

Calls

4 calls:

176.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
396.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
297.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
296.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series638.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
163.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
101.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
107.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.6s

Counts

501 → 501

Iterations

Iter	Nodes
done	5012
2	3200
1	1229
0	697

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
0.5b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

12132×	`times-frac`
7340×	`*-un-lft-identity`
4744×	`add-sqr-sqrt` `add-cube-cbrt`
3270×	`sqrt-prod`
1298×	`distribute-lft-out`
784×	`associate-/l*`
298×	`associate-/r/`
284×	`sqrt-div`
150×	`flip3-+` `flip-+`
149×	`div-inv`
34×	`add-cbrt-cube` `add-exp-log`
20×	`cbrt-undiv` `div-exp`
19×	`associate-/r*`
5×	`associate-/l/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 3906

Calls

4 calls:

378.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
440.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
302.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
267.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

series618.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
210.0ms	(/ (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
108.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
137.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

simplify5.4s

Counts

3918 → 3918

Iterations

Iter	Nodes
done	5000
0	2923

prune16.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.7b

localize99.0ms

Local error

Found 4 expressions with local error:

3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-prod` `times-frac`
7×	`distribute-lft-out`
6×	`cbrt-div` `add-cbrt-cube` `add-exp-log`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-/r*` `pow1/3`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 89

Calls

4 calls:

281.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
38.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
49.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series410.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
95.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
80.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
96.0ms	(cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.6s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	1394
1	398
0	147

prune1.1s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.7b

regimes108.0ms

Accuracy

0% (2.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	32
3	32
2	30
1	28
0	18

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
301.0ms	8000×	pre	80	true