Details

Time bar (total: 28.6s)

sample53.0ms

Algorithm
intervals
Results
14.0ms193×body80valid
9.0ms24×body1280valid
8.0ms256×pre80true
6.0ms22×body640valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify5.2s

Counts
1 → 1
Iterations
IterNodes
95824
94824
93820
92818
91812
90807
89805
88798
87795
86789
85786
84780
83777
82771
81768
80762
79759
78753
77750
76744
75741
74735
73732
72726
71723
70717
69714
68708
67705
66699
65696
64690
63687
62681
61678
60672
59669
58663
57660
56654
55651
54645
53642
52636
51633
50627
49624
48618
47615
46609
45606
44600
43597
42591
41588
40582
39579
38573
37570
36564
35561
34555
33552
32546
31543
30537
29534
28528
27525
26519
25516
24510
23507
22501
21498
20492
19489
18483
17480
16474
15471
14466
13455
12442
11411
10350
9254
8189
7164
6140
5112
469
350
233
120
010

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.6b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
58×*-un-lft-identity
26×add-sqr-sqrt
25×times-frac
19×distribute-lft-out
14×add-cube-cbrt
6×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-cbrt-cube add-exp-log add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 67
Calls
2 calls:
29.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
133.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series139.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
79.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify954.0ms

Counts
73 → 73
Iterations
IterNodes
32968
2956
1328
0126

prune692.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 14.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
1.6b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite667.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
34×add-sqr-sqrt
32×times-frac
24×add-cube-cbrt distribute-lft-out
11×add-log-exp
10×associate-/r*
8×add-cbrt-cube add-exp-log
6×associate-/l*
4×pow1 diff-log associate-/r/ insert-posit16 distribute-lft-out-- difference-of-squares
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp frac-sub flip-+ div-inv associate--r+
1×associate--r-
Counts
4 → 115
Calls
4 calls:
384.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
24.0ms
(/ alpha (+ (+ alpha beta) 2.0))
44.0ms
(/ beta (+ (+ alpha beta) 2.0))
213.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series354.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
91.0ms
(/ alpha (+ (+ alpha beta) 2.0))
52.0ms
(/ beta (+ (+ alpha beta) 2.0))
106.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify2.2s

Counts
127 → 127
Iterations
IterNodes
34669
21259
1454
0197

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.6b

localize82.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
0.1b
(* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha))))
0.1b
(/ (- (* (+ (* 1.0 1.0) (* (/ alpha (+ 2.0 (+ beta alpha))) (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) beta) (* (- (* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0)) (+ 2.0 (+ beta alpha)))) (* (+ 2.0 (+ beta alpha)) (+ (* 1.0 1.0) (* (/ alpha (+ 2.0 (+ beta alpha))) (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0)))))
1.6b
(- (* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0))

rewrite592.0ms

Algorithm
rewrite-expression-head
Rules
210×*-un-lft-identity
119×times-frac
81×distribute-lft-out
78×add-sqr-sqrt
63×add-cube-cbrt
62×add-cbrt-cube add-exp-log
42×associate-*r*
39×swap-sqr
30×pow1
28×associate-*l/
25×flip3-+ flip-+
23×prod-exp cbrt-unprod
22×associate-*l*
19×cbrt-undiv div-exp
18×frac-times associate-/r/ associate-/l/
16×frac-sub
10×associate-*r/
8×flip3-- flip--
7×pow-plus pow-prod-up
6×div-inv add-log-exp unswap-sqr
4×pow-prod-down insert-posit16
3×pow2 pow3 pow-sqr associate-/l*
2×*-commutative
1×difference-cubes clear-num associate-/r* sub-neg frac-2neg diff-log div-sub
Counts
4 → 244
Calls
4 calls:
101.0ms
(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
177.0ms
(* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha))))
121.0ms
(/ (- (* (+ (* 1.0 1.0) (* (/ alpha (+ 2.0 (+ beta alpha))) (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) beta) (* (- (* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0)) (+ 2.0 (+ beta alpha)))) (* (+ 2.0 (+ beta alpha)) (+ (* 1.0 1.0) (* (/ alpha (+ 2.0 (+ beta alpha))) (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0)))))
186.0ms
(- (* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0))

series848.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha))))
101.0ms
(* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha))))
501.0ms
(/ (- (* (+ (* 1.0 1.0) (* (/ alpha (+ 2.0 (+ beta alpha))) (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0))) beta) (* (- (* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0)) (+ 2.0 (+ beta alpha)))) (* (+ 2.0 (+ beta alpha)) (+ (* 1.0 1.0) (* (/ alpha (+ 2.0 (+ beta alpha))) (+ (/ alpha (+ 2.0 (+ beta alpha))) 1.0)))))
169.0ms
(- (* (* (/ alpha (+ 2.0 (+ beta alpha))) (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0))

simplify3.2s

Counts
256 → 256
Iterations
IterNodes
26220
11363
0371

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

localize115.0ms

Local error

Found 4 expressions with local error:

1.6b
(- (* (* (* (cbrt (/ alpha (+ 2.0 (+ beta alpha)))) (cbrt (/ alpha (+ 2.0 (+ beta alpha))))) (* (cbrt (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha))))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0))
8.3b
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
8.3b
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
8.3b
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))

rewrite835.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
63×cbrt-prod
45×times-frac
31×add-sqr-sqrt add-cube-cbrt
27×distribute-lft-out
6×associate-/r/ add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 106
Calls
4 calls:
784.0ms
(- (* (* (* (cbrt (/ alpha (+ 2.0 (+ beta alpha)))) (cbrt (/ alpha (+ 2.0 (+ beta alpha))))) (* (cbrt (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha))))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0))
17.0ms
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
15.0ms
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
17.0ms
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))

series808.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(- (* (* (* (cbrt (/ alpha (+ 2.0 (+ beta alpha)))) (cbrt (/ alpha (+ 2.0 (+ beta alpha))))) (* (cbrt (/ alpha (+ 2.0 (+ beta alpha)))) (/ alpha (+ 2.0 (+ beta alpha))))) (/ alpha (+ 2.0 (+ beta alpha)))) (* (* 1.0 1.0) 1.0))
231.0ms
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
191.0ms
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))
184.0ms
(cbrt (/ alpha (+ 2.0 (+ beta alpha))))

simplify1.7s

Counts
118 → 118
Iterations
IterNodes
33975
21086
1373
0160

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.5b

regimes158.0ms

Accuracy

75.8% (3.1b remaining)

Error of 5.9b against oracle of 2.9b and baseline of 15.5b

bsearch69.0ms

Steps
ItersRangePoint
7
5.7539564985828565e+19
9.677120307256084e+21
3.630174269413438e+21

simplify5.0ms

Iterations
IterNodes
230
130
027

end0.0ms

sample2.3s

Algorithm
intervals
Results
657.0ms723×body640valid
631.0ms5873×body80valid
336.0ms819×body1280valid
285.0ms8000×pre80true
173.0ms392×body320valid
55.0ms193×body160valid