Details

sample477.0ms

Algorithm

intervals

Results

36.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify919.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	641
2	119
1	36
0	15

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
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))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

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` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 469

Calls

4 calls:

124.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
364.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
491.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
317.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series604.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
197.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
242.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
141.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.9s

Counts

481 → 481

Iterations

Iter	Nodes
done	2005
2	2005
1	1435
0	606

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1)))
0.0b	(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.1b	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
3.6b	(/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.3s

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×	`clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 1341

Calls

4 calls:

285.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1)))
186.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
466.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
237.0ms	(/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series698.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1)))
108.0ms	(/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
251.0ms	(/ (/ (/ 1 (/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
129.0ms	(/ (+ (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.8s

Counts

1353 → 1353

Iterations

Iter	Nodes
done	2001
1	2001
0	1603

prune7.6s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
0.1b	(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

15533×	`times-frac`
8586×	`*-un-lft-identity`
5508×	`add-sqr-sqrt` `add-cube-cbrt`
1539×	`distribute-lft-out`
932×	`associate-/r/`
570×	`div-inv`
443×	`flip3-+` `flip-+`
110×	`add-exp-log`
98×	`associate-/r*`
94×	`div-exp`
57×	`associate-/l*`
47×	`add-cbrt-cube`
31×	`cbrt-undiv`
18×	`1-exp`
13×	`add-log-exp`
6×	`rec-exp` `sum-log`
5×	`associate-/l/`
4×	`pow1` `insert-posit16`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 4112

Calls

4 calls:

129.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
468.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
333.0ms	(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
300.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
191.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))))
201.0ms	(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))))
135.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify7.4s

Counts

4124 → 4124

Iterations

Iter	Nodes
done	4722
0	4722

prune25.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.1b	(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
0.1b	(/ (/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1)))
3.6b	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

20583×	`times-frac`
11381×	`*-un-lft-identity`
7423×	`add-sqr-sqrt` `add-cube-cbrt`
1979×	`distribute-lft-out`
1167×	`associate-/r/`
1136×	`associate-/l*`
697×	`div-inv`
583×	`flip3-+` `flip-+`
140×	`add-exp-log`
122×	`div-exp`
56×	`add-cbrt-cube`
38×	`cbrt-undiv`
29×	`associate-/r*`
24×	`1-exp`
13×	`add-log-exp`
8×	`rec-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 5618

Calls

4 calls:

79.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
377.0ms	(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
485.0ms	(/ (/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1)))
373.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series618.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
200.0ms	(/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0)))
252.0ms	(/ (/ (/ (/ 1 (+ (+ alpha beta) (* 2 1))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (+ (+ alpha beta) (* 2 1)))
142.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify9.7s

Counts

5630 → 5630

Iterations

Iter	Nodes
done	6082
0	6082

prune34.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes128.0ms

Accuracy

70.2% (1.2b remaining)

Error of 1.2b against oracle of 0.0b and baseline of 4.1b

bsearch148.0ms

Steps

Iters	Range		Point
8	2.9257751932980255e+155	1.754451746414951e+158	3.5888856498529296e+157

simplify10.0ms

Iterations

Iter	Nodes
done	38
1	38
0	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	8000×	body	80	valid
386.0ms	8000×	pre	80	true