Details

Time bar (total: 16.1s)

sample40.0ms

Algorithm
intervals
Results
7.0ms33×body1280valid
7.0ms169×body80valid
5.0ms33×body640valid
4.0ms256×pre80true
2.0ms12×body320valid
1.0ms9×body160valid

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5001
94613
81507
7644
6306
5164
474
353
234
120
010

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite218.0ms

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-+ associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 65
Calls
2 calls:
42.0ms
(/ (- beta alpha) (+ (+ alpha 2.0) beta))
172.0ms
(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

series153.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(/ (- beta alpha) (+ (+ alpha 2.0) beta))
86.0ms
(+ (/ (- beta alpha) (+ (+ alpha 2.0) beta)) 1.0)

simplify528.0ms

Counts
71 → 71
Iterations
IterNodes
done5002
21315
1326
0123

prune347.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.3b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
61×add-sqr-sqrt
56×times-frac
36×add-cube-cbrt
24×distribute-lft-out
13×associate-/r* associate-/l* distribute-lft-out--
10×add-cbrt-cube add-exp-log difference-of-squares
6×add-log-exp
4×pow1 associate-/r/ associate-/l/
3×cbrt-undiv clear-num frac-2neg flip3-- div-exp div-inv flip--
2×flip3-+ frac-sub flip-+
1×sub-neg diff-log div-sub
Counts
4 → 137
Calls
4 calls:
1.1s
(/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)
29.0ms
(/ beta (+ (+ alpha 2.0) beta))
23.0ms
(/ alpha (+ beta (+ alpha 2.0)))
175.0ms
(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series362.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ beta (+ alpha 2.0))) 1.0)) 2.0)
66.0ms
(/ beta (+ (+ alpha 2.0) beta))
57.0ms
(/ alpha (+ beta (+ alpha 2.0)))
130.0ms
(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify1.2s

Counts
149 → 149
Iterations
IterNodes
done5001
22730
1606
0251

prune822.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (+ alpha 2.0) beta))
0.7b
(cbrt (+ (+ alpha 2.0) beta))
0.7b
(cbrt (+ (+ alpha 2.0) beta))
2.0b
(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×cbrt-prod
12×add-sqr-sqrt
9×distribute-lft-out
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube add-exp-log
3×flip3-+ pow1/3 flip-+
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
16.0ms
(cbrt (+ (+ alpha 2.0) beta))
26.0ms
(cbrt (+ (+ alpha 2.0) beta))
14.0ms
(cbrt (+ (+ alpha 2.0) beta))
196.0ms
(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

series565.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(cbrt (+ (+ alpha 2.0) beta))
134.0ms
(cbrt (+ (+ alpha 2.0) beta))
169.0ms
(cbrt (+ (+ alpha 2.0) beta))
124.0ms
(- (/ alpha (+ beta (+ alpha 2.0))) 1.0)

simplify1.9s

Counts
72 → 72
Iterations
IterNodes
done5000
34312
2845
1285
0122

prune494.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.3b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ alpha (+ (+ alpha 2.0) beta))
0.8b
(exp (log (/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)) 2.0)))
2.0b
(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
10.8b
(log (/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)) 2.0))

rewrite997.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
72×add-sqr-sqrt
64×times-frac
50×log-prod
37×add-cube-cbrt
25×exp-sum
19×distribute-lft-out--
14×difference-of-squares
12×distribute-lft-out
9×add-exp-log
6×pow1 add-cbrt-cube add-log-exp
5×associate-/r*
4×exp-prod
3×div-inv associate-/l*
2×log-div div-exp rem-log-exp associate-/r/ log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ flip3-- exp-diff diff-log flip-+ flip-- rem-exp-log
Counts
4 → 126
Calls
4 calls:
29.0ms
(/ alpha (+ (+ alpha 2.0) beta))
391.0ms
(exp (log (/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)) 2.0)))
223.0ms
(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
349.0ms
(log (/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)) 2.0))

series473.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ alpha (+ (+ alpha 2.0) beta))
109.0ms
(exp (log (/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)) 2.0)))
106.0ms
(- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)
194.0ms
(log (/ (- (/ beta (+ (+ alpha 2.0) beta)) (- (/ alpha (+ (+ alpha 2.0) beta)) 1.0)) 2.0))

simplify896.0ms

Counts
138 → 138
Iterations
IterNodes
done5001
21815
1547
0266

prune854.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

regimes236.0ms

Accuracy

75.5% (3.2b remaining)

Error of 6.0b against oracle of 2.8b and baseline of 15.7b

bsearch57.0ms

Steps
ItersRangePoint
7
46374.558514477714
3809480.5813382245
417035.8774050207

simplify6.0ms

Iterations
IterNodes
done36
236
134
029

end0.0ms

sample1.7s

Algorithm
intervals
Results
619.0ms864×body1280valid
368.0ms5858×body80valid
204.0ms8000×pre80true
197.0ms666×body640valid
58.0ms392×body320valid
20.0ms220×body160valid