Details

sample51.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
14.0ms	256×	pre	80	true

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	554
2	111
1	33
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.6b

localize48.0ms

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))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.5s

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:

109.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
413.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
587.0ms	(/ (/ (/ (+ (+ (+ 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))
333.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)
172.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
199.0ms	(/ (/ (/ (+ (+ (+ 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))
105.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.8s

Counts

477 → 477

Iterations

Iter	Nodes
done	5001
1	1609
0	602

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize35.0ms

Local error

Found 3 expressions with local error:

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)))

3.4b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
827×	`*-un-lft-identity`
382×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
66×	`associate-/r/`
36×	`flip3-+` `flip-+`
31×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`frac-add` `associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `add-log-exp`

Counts

3 → 515

Calls

3 calls:

381.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

455.0ms

(/ (/ (/ (+ (+ (+ 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)))

298.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series597.0ms

Counts

3 → 9

Calls

3 calls:

235.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

235.0ms

(/ (/ (/ (+ (+ (+ 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)))

127.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.3s

Counts

524 → 524

Iterations

Iter	Nodes
done	5001
1	1682
0	613

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (sqrt (/ (/ (+ (+ (+ 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)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite9.2s

Algorithm

rewrite-expression-head

Rules

98889×	`times-frac`
64792×	`*-un-lft-identity`
38820×	`sqrt-prod`
32650×	`add-sqr-sqrt` `add-cube-cbrt`
18119×	`distribute-lft-out`
5246×	`associate-/r/`
2656×	`div-inv`
2597×	`flip3-+` `flip-+`
389×	`associate-/r*`
76×	`associate-/l*`
66×	`sqrt-div`
15×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
4×	`pow1` `clear-num` `frac-2neg` `frac-add` `add-log-exp`

Counts

4 → 21031

Calls

4 calls:

429.0ms	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
1.7s	(/ (sqrt (/ (/ (+ (+ (+ 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)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
302.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
295.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(/ (+ (+ alpha beta) (+ (* 2.0 1.0) 1.0)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))))
217.0ms	(/ (sqrt (/ (/ (+ (+ (+ 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)) (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))))
101.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
141.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify42.9s

Counts

21043 → 21043

Iterations

Iter	Nodes
done	16705
0	16705

prune2.1m

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize69.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.3b	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.4b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
9.2b	(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

rewrite801.0ms

Algorithm

rewrite-expression-head

Rules

161×	`times-frac`
132×	`sqrt-prod`
115×	`*-un-lft-identity`
96×	`add-sqr-sqrt`
85×	`add-cube-cbrt`
15×	`distribute-lft-out`
10×	`associate-/r/`
8×	`flip3-+` `flip-+`
7×	`pow1`
6×	`rem-sqrt-square` `add-cbrt-cube` `add-exp-log`
5×	`sqrt-div` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`associate-/r*` `sqrt-pow1` `pow1/2`
2×	`associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp`

Counts

4 → 168

Calls

4 calls:

116.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
120.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
337.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
218.0ms	(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
58.0ms	(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
103.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
225.0ms	(sqrt (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))

simplify3.5s

Counts

180 → 180

Iterations

Iter	Nodes
done	5000
2	3944
1	939
0	435

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

regimes156.0ms

Accuracy

56.4% (1.1b remaining)

Error of 2.5b against oracle of 1.4b and baseline of 3.8b

bsearch106.0ms

Steps

Iters	Range		Point
8	4.479708973753395e+157	2.5383605497524946e+161	1.4330656651092558e+161

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

797.0ms	8000×	body	80	valid
186.0ms	8000×	pre	80	true