Details

Time bar (total: 21.9s)

sample33.0ms

Algorithm
intervals
Results
6.0ms37×body1280valid
6.0ms167×body80valid
4.0ms256×pre80true
3.0ms24×body640valid
2.0ms16×body320valid
1.0ms12×body160valid

simplify4.1s

Counts
1 → 1
Iterations
IterNodes
done5001
324930
314722
304510
294301
284120
273916
263715
253502
243325
233117
222909
212698
202516
192291
182012
171763
161558
151364
141138
13931
12742
11607
10526
9431
8318
7267
6197
5124
469
350
233
120
010

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.7b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite245.0ms

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:
64.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
175.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series152.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
83.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts
71 → 71
Iterations
IterNodes
done5003
21119
1326
0124

prune470.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 19.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
2.7b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
31×times-frac
28×add-sqr-sqrt
24×distribute-lft-out
23×add-cube-cbrt
10×associate-/r*
7×add-cbrt-cube add-exp-log
6×associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ div-inv difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 89
Calls
3 calls:
53.0ms
(/ beta (+ (+ alpha beta) 2.0))
57.0ms
(/ alpha (+ (+ alpha beta) 2.0))
250.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series272.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(/ beta (+ (+ alpha beta) 2.0))
68.0ms
(/ alpha (+ (+ alpha beta) 2.0))
137.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.5s

Counts
98 → 98
Iterations
IterNodes
done5022
34942
21047
1341
0153

prune580.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.3b
(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
0.4b
(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
12.3b
(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

rewrite845.0ms

Algorithm
rewrite-expression-head
Rules
560×*-un-lft-identity
505×times-frac
315×sqrt-prod
252×add-sqr-sqrt
228×add-cube-cbrt
198×distribute-lft-out
36×associate-/l*
24×associate-/r/
22×sqrt-div
21×associate-/r*
13×add-cbrt-cube add-exp-log
12×flip3-+ flip-+ div-inv
7×difference-of-squares
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1
3×clear-num frac-2neg
1×sub-neg flip3-- diff-log flip-- distribute-lft-out-- associate-/l/
Counts
4 → 401
Calls
4 calls:
28.0ms
(/ beta (+ (+ alpha beta) 2.0))
113.0ms
(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
54.0ms
(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
612.0ms
(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

series337.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ beta (+ (+ alpha beta) 2.0))
85.0ms
(/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0)))
97.0ms
(/ alpha (sqrt (+ (+ alpha beta) 2.0)))
99.0ms
(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

simplify2.2s

Counts
413 → 413
Iterations
IterNodes
done5008
22349
1911
0401

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.2b

localize68.0ms

Local error

Found 4 expressions with local error:

8.6b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.6b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
8.6b
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
12.3b
(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

rewrite605.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
63×cbrt-prod
55×add-sqr-sqrt times-frac
31×add-cube-cbrt
27×distribute-lft-out
7×difference-of-squares
6×associate-/r/ add-log-exp
5×sqrt-prod
4×pow1 add-cbrt-cube add-exp-log
3×cbrt-div flip3-+ pow1/3 flip-+ div-inv
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 110
Calls
4 calls:
20.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
14.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
16.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
547.0ms
(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

series775.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
208.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
225.0ms
(cbrt (/ beta (+ (+ alpha beta) 2.0)))
97.0ms
(- (/ (/ alpha (sqrt (+ (+ alpha beta) 2.0))) (sqrt (+ (+ alpha beta) 2.0))) 1.0)

simplify2.0s

Counts
122 → 122
Iterations
IterNodes
done5000
33162
2946
1352
0168

prune906.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.2b

regimes238.0ms

Accuracy

77.6% (2.8b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.8b

bsearch86.0ms

Steps
ItersRangePoint
7
22079.79486067198
654137.8667585424
644102.6150741008

simplify12.0ms

Iterations
IterNodes
done35
135
031

end0.0ms

sample1.2s

Algorithm
intervals
Results
333.0ms5877×body80valid
225.0ms711×body640valid
221.0ms838×body1280valid
165.0ms8000×pre80true
48.0ms388×body320valid
16.0ms186×body160valid