Details

Time bar (total: 17.5s)

sample39.0ms

Algorithm
intervals
Results
6.0ms169×body80valid
6.0ms33×body1280valid
5.0ms33×body640valid
4.0ms256×pre80true
1.0ms12×body320valid
1.0ms9×body160valid

simplify2.4s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.1b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite233.0ms

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:
48.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
180.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series179.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
102.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts
71 → 71
Iterations
IterNodes
done5001
21359
1326
0124

prune359.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 19.3b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
2.0b
(- (/ alpha (+ (+ alpha beta) 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 beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
30.0ms
(/ alpha (+ (+ alpha beta) 2.0))
54.0ms
(/ beta (+ (+ alpha beta) 2.0))
210.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series321.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
51.0ms
(/ alpha (+ (+ alpha beta) 2.0))
77.0ms
(/ beta (+ (+ alpha beta) 2.0))
94.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts
149 → 149
Iterations
IterNodes
done5002
22417
1563
0238

prune869.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.3b

localize76.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
9.1b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.1b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
9.1b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

rewrite332.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
63×cbrt-prod
46×times-frac
36×add-sqr-sqrt
31×add-cube-cbrt
27×distribute-lft-out
6×associate-/r/ add-log-exp
4×pow1 add-cbrt-cube add-exp-log
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 105
Calls
4 calls:
239.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
27.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
28.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
34.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

series760.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
218.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
227.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
206.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))

simplify958.0ms

Counts
117 → 117
Iterations
IterNodes
done5000
21047
1338
0161

prune842.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite960.0ms

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:
33.0ms
(/ beta (+ (+ alpha beta) 2.0))
339.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
242.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
335.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

series442.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ beta (+ (+ alpha beta) 2.0))
83.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
83.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
211.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))

simplify1.8s

Counts
138 → 138
Iterations
IterNodes
done5001
21836
1563
0269

prune792.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.3b

regimes267.0ms

Accuracy

75.5% (3.1b remaining)

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

bsearch51.0ms

Steps
ItersRangePoint
7
46374.558514477714
3809480.5813382245
417035.8774050207

simplify12.0ms

Iterations
IterNodes
done37
137
031

end0.0ms

sample1.4s

Algorithm
intervals
Results
340.0ms5858×body80valid
258.0ms8000×pre80true
239.0ms864×body1280valid
170.0ms666×body640valid
58.0ms392×body320valid
56.0ms220×body160valid