Details

sample59.0ms

Algorithm

intervals

Results

33.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify745.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize47.0ms

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

rewrite1.4s

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:

74.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
657.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
402.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
247.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
159.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
225.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
121.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts

481 → 481

Iterations

Iter	Nodes
done	2005
2	2005
1	1435
0	606

prune5.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.1b

localize40.0ms

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

rewrite981.0ms

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-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
9×	`add-log-exp`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `sum-log` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 467

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* beta alpha))
309.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
379.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
263.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (+ alpha beta) (* beta alpha))
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
167.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ 1.0 (+ (+ alpha beta) (* 2 1))))
113.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.3s

Counts

479 → 479

Iterations

Iter	Nodes
done	2002
2	2002
1	1457
0	608

prune5.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.1b

localize53.0ms

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

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

1930×	`times-frac`
1248×	`*-un-lft-identity`
945×	`add-sqr-sqrt`
777×	`sqrt-prod`
742×	`add-cube-cbrt`
258×	`associate-r`
243×	`distribute-lft-out`
193×	`associate-l`
104×	`associate-/r/`
71×	`associate-/l*`
54×	`flip3-+` `flip-+`
53×	`div-inv`
45×	`unswap-sqr`
27×	`add-exp-log`
22×	`add-cbrt-cube`
10×	`associate-/r*` `div-exp`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
5×	`associate-/l/`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`1-exp`
1×	`frac-times` `sqrt-div` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 926

Calls

4 calls:

1.2s	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
372.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
218.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
274.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

265.0ms	(* (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
182.0ms	(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
94.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
100.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.5s

Counts

938 → 938

Iterations

Iter	Nodes
done	2000
1	2000
0	1183

prune16.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.1b

localize91.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

543×	`times-frac`
363×	`sqrt-prod`
330×	`*-un-lft-identity`
252×	`add-sqr-sqrt` `add-cube-cbrt`
214×	`associate-l`
92×	`add-exp-log`
51×	`add-cbrt-cube`
39×	`prod-exp` `distribute-lft-out`
38×	`div-exp`
24×	`associate-/r/`
18×	`cbrt-unprod`
16×	`cbrt-undiv` `div-inv`
15×	`flip3-+` `flip-+`
13×	`1-exp`
12×	`associate-/l*`
9×	`pow1` `associate-/r*`
6×	`associate-/l/`
5×	`frac-times` `associate-*r/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/`
1×	`associate-r` `*-commutative`

Counts

4 → 372

Calls

4 calls:

1.0s	(* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1)) 1) (* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
276.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
258.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
273.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) 1)) 1) (* (/ (sqrt (/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))) 1) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
98.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
110.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
122.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts

384 → 384

Iterations

Iter	Nodes
done	2004
2	2004
1	1704
0	615

prune8.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.1b

regimes132.0ms

Accuracy

38.7% (1.5b remaining)

Error of 2.7b against oracle of 1.2b and baseline of 3.6b

bsearch60.0ms

Steps

Iters	Range		Point
5	1.3154968375234933e+114	3.987194372781887e+114	3.9275252152036123e+114

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	27

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.7s	8000×	body	80	valid
274.0ms	8000×	pre	80	true