Details

sample90.0ms

Algorithm

intervals

Results

55.0ms	256×	body	80	valid
12.0ms	256×	pre	80	true

simplify3.2s

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.6b

localize50.0ms

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))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite5.9s

Algorithm

rewrite-expression-head

Rules

58384×	`*-un-lft-identity`
38843×	`distribute-lft-out`
23496×	`times-frac`
7082×	`associate-l`
5078×	`*-commutative`
3665×	`add-sqr-sqrt` `add-cube-cbrt`
888×	`associate-/l*`
248×	`associate-/r/`
162×	`associate-/l/`
128×	`flip3-+` `flip-+`
124×	`div-inv`
55×	`associate-/r*`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
6×	`associate-+l+` `clear-num` `sum-log` `frac-2neg`
4×	`pow1` `insert-posit16`
3×	`+-commutative`

Counts

4 → 8888

Calls

4 calls:

258.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
931.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
1.8s	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
599.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series582.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
218.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
224.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
118.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify6.7s

Counts

8900 → 8900

Iterations

Iter	Nodes
done	5000
1	2109
0	862

prune3.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.8b

localize61.0ms

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)))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite5.5s

Algorithm

rewrite-expression-head

Rules

64001×	`*-un-lft-identity`
42504×	`distribute-lft-out`
25554×	`times-frac`
7544×	`associate-l`
5378×	`*-commutative`
3906×	`add-sqr-sqrt` `add-cube-cbrt`
888×	`associate-/l*`
272×	`associate-/r/`
162×	`associate-/l/`
146×	`flip3-+` `flip-+`
134×	`div-inv`
56×	`associate-/r*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`add-log-exp`
10×	`cbrt-undiv` `div-exp`
8×	`sum-log` `frac-add`
6×	`clear-num` `frac-2neg`
4×	`pow1` `insert-posit16`
3×	`+-commutative`
2×	`associate-+l+` `associate-+r+`

Counts

4 → 9607

Calls

4 calls:

87.0ms	(+ (+ alpha beta) (+ (* 2 1) 1.0))
972.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
1.8s	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
624.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (+ alpha beta) (+ (* 2 1) 1.0))
213.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
231.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
122.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify7.0s

Counts

9619 → 9619

Iterations

Iter	Nodes
done	5000
1	2244
0	898

prune4.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.8b

localize49.0ms

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	(/ (+ (+ alpha beta) (+ (* 2 1) 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
4.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite6.4s

Algorithm

rewrite-expression-head

Rules

64361×	`*-un-lft-identity`
42731×	`distribute-lft-out`
25662×	`times-frac`
9204×	`sqrt-prod`
7586×	`associate-l`
5400×	`*-commutative`
3947×	`add-sqr-sqrt`
3941×	`add-cube-cbrt`
765×	`associate-/r*`
380×	`associate-/r/`
224×	`sqrt-div`
199×	`associate-/l*`
143×	`flip3-+` `flip-+`
135×	`div-inv`
58×	`associate-/l/`
10×	`add-cbrt-cube` `add-exp-log`
7×	`clear-num` `frac-2neg`
5×	`pow1`
4×	`frac-add` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
1×	`sqrt-pow1` `pow1/2`

Counts

4 → 9719

Calls

4 calls:

1.3s	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
1.6s	(/ (+ (+ alpha beta) (+ (* 2 1) 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
587.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
594.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series953.0ms

Counts

4 → 12

Calls

4 calls:

312.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))))
423.0ms	(/ (+ (+ alpha beta) (+ (* 2 1) 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))))
104.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
115.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify9.6s

Counts

9731 → 9731

Iterations

Iter	Nodes
done	5001
2	4206
1	1738
0	1033

prune6.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.8b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.6b	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
4.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
4.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite4.0s

Algorithm

rewrite-expression-head

Rules

35126×	`*-un-lft-identity`
21045×	`distribute-lft-out`
20190×	`times-frac`
15159×	`sqrt-prod`
5612×	`add-sqr-sqrt`
5610×	`add-cube-cbrt`
3696×	`associate-l`
2440×	`*-commutative`
614×	`associate-/l*`
198×	`div-inv`
119×	`associate-/l/`
58×	`associate-/r/`
49×	`associate-/r*`
40×	`sqrt-div`
33×	`flip3-+` `flip-+`
21×	`add-exp-log`
18×	`add-cbrt-cube`
12×	`div-exp`
9×	`cbrt-undiv`
6×	`pow1`
5×	`clear-num` `frac-2neg`
4×	`insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`1-exp`

Counts

4 → 7865

Calls

4 calls:

1.2s	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
772.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
253.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
301.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series639.0ms

Counts

4 → 12

Calls

4 calls:

259.0ms	(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) 1) (sqrt (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
254.0ms	(/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ alpha beta) (* 2 1))))
73.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
53.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify9.0s

Counts

7877 → 7877

Iterations

Iter	Nodes
done	5000
1	3915
0	1694

prune12.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.8b

regimes138.0ms

Accuracy

55.7% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch101.0ms

Steps

Iters	Range		Point
9	7.775450676221288e+157	3.9765790759248505e+164	3.826019260484367e+164

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	20

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
369.0ms	8000×	pre	80	true