Details

sample55.0ms

Algorithm

intervals

Results

29.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5193
4	4059
3	641
2	119
1	36
0	15

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize25.0ms

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))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.2s

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:

102.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
339.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
479.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
269.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
140.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
219.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
113.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.6s

Counts

481 → 481

Iterations

Iter	Nodes
done	5003
2	4498
1	1435
0	606

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
0.0b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1))))
1.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

4788×	`times-frac`
2658×	`*-un-lft-identity`
1682×	`add-sqr-sqrt` `add-cube-cbrt`
488×	`distribute-lft-out`
365×	`associate-/r/`
361×	`difference-of-squares`
183×	`div-inv`
104×	`associate-/l*`
100×	`flip3--` `flip--`
84×	`flip3-+` `flip-+`
34×	`add-cbrt-cube` `add-exp-log`
28×	`associate-/r*`
20×	`cbrt-undiv` `div-exp`
6×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`

Counts

4 → 1709

Calls

4 calls:

223.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
420.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1))))
318.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
205.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
262.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1))))
199.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
118.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.8s

Counts

1721 → 1721

Iterations

Iter	Nodes
done	5000
0	2257

prune10.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (- (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.0b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (/ 1 (/ (- (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
1.8b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
4.1b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

19158×	`times-frac`
9504×	`*-un-lft-identity`
6580×	`add-sqr-sqrt` `add-cube-cbrt`
1462×	`distribute-lft-out`
1177×	`associate-/r/`
1099×	`difference-of-squares`
629×	`div-inv`
488×	`flip3-+` `flip-+`
103×	`associate-/l*`
100×	`add-exp-log`
84×	`associate-/r*`
74×	`div-exp`
61×	`flip3--` `flip--`
52×	`add-cbrt-cube`
34×	`cbrt-undiv`
8×	`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 → 5027

Calls

4 calls:

160.0ms	(/ 1 (/ (- (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
540.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (/ 1 (/ (- (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
335.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
317.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 1 (/ (- (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
284.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) (/ 1 (/ (- (+ alpha beta) (* 2 1)) (+ (+ (+ alpha beta) (* 2 1)) 1.0))))
267.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
139.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify9.9s

Counts

5039 → 5039

Iterations

Iter	Nodes
done	6430
0	6430

prune34.9s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))
0.0b	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))))
16.5b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

19020×	`times-frac`
10253×	`*-un-lft-identity`
6497×	`add-sqr-sqrt` `add-cube-cbrt`
1878×	`distribute-lft-out`
1051×	`associate-/r/`
797×	`difference-of-squares`
628×	`div-inv`
292×	`flip3-+` `flip-+`
200×	`flip3--` `flip--`
87×	`associate-/r*`
81×	`associate-/l*`
70×	`add-exp-log`
53×	`div-exp`
49×	`add-cbrt-cube`
32×	`cbrt-undiv`
7×	`associate-/l/`
6×	`1-exp`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
1×	`div-sub`

Counts

4 → 4893

Calls

4 calls:

79.0ms	(/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))
287.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))))
557.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))))
290.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))
82.0ms	(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))))
273.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1)))) 1) (/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))))
143.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))

simplify9.1s

Counts

4905 → 4905

Iterations

Iter	Nodes
done	5911
0	5911

prune30.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.7b

regimes105.0ms

Accuracy

51.4% (1.5b remaining)

Error of 2.8b against oracle of 1.3b and baseline of 4.3b

bsearch144.0ms

Steps

Iters	Range		Point
10	1.972616410681917e+143	1.347314599677347e+159	1.3353325288374214e+154

simplify7.0ms

Iterations

Iter	Nodes
done	47
1	47
0	32

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
268.0ms	8000×	pre	80	true