Details

sample49.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5255
4	2870
3	497
2	106
1	33
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
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)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 465

Calls

4 calls:

111.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
315.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
530.0ms	(/ (/ (/ (+ (+ (+ 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))
296.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
146.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
174.0ms	(/ (/ (/ (+ (+ (+ 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))
111.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.7s

Counts

477 → 477

Iterations

Iter	Nodes
done	5013
2	4622
1	1447
0	602

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.5b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite730.0ms

Algorithm

rewrite-expression-head

Rules

112×	`sqrt-prod`
98×	`*-un-lft-identity`
84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
16×	`distribute-lft-out`
14×	`associate-/l*`
12×	`associate-/r*` `sqrt-div`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `flip3-+` `flip-+`
4×	`associate-/r/` `add-log-exp` `associate-/l/`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 176

Calls

4 calls:

178.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
259.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
126.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
156.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series412.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 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))))
82.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
72.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.9s

Counts

188 → 188

Iterations

Iter	Nodes
done	5008
3	3452
2	899
1	330
0	160

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.5b

localize106.0ms

Local error

Found 4 expressions with local error:

2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity` `sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `sqrt-div` `add-cube-cbrt`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

150.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
120.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
162.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
117.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series235.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
53.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
65.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
66.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify1.4s

Counts

76 → 76

Iterations

Iter	Nodes
done	5004
3	2094
2	420
1	125
0	55

prune644.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
8.3b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

7742×	`times-frac`
4062×	`*-un-lft-identity`
3062×	`add-sqr-sqrt`
3060×	`add-cube-cbrt`
2004×	`sqrt-prod`
501×	`distribute-lft-out`
193×	`div-inv`
185×	`associate-/r/`
89×	`associate-/r*`
82×	`flip3-+` `flip-+`
36×	`add-exp-log`
32×	`associate-/l*`
27×	`add-cbrt-cube`
25×	`div-exp`
16×	`cbrt-undiv`
6×	`pow1` `sqrt-div`
4×	`add-log-exp`
3×	`1-exp` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 2367

Calls

4 calls:

206.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
121.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
134.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
818.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
68.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
70.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
181.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))))

simplify4.2s

Counts

2379 → 2379

Iterations

Iter	Nodes
done	5001
0	2509

prune13.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

regimes176.0ms

Accuracy

61.3% (1.0b remaining)

Error of 2.3b against oracle of 1.3b and baseline of 3.8b

bsearch142.0ms

Steps

Iters	Range		Point
9	7.624367775541029e+182	5.1966063590768564e+188	7.725152532273347e+182

simplify15.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.1s	8000×	body	80	valid
211.0ms	8000×	pre	80	true