Details

Time bar (total: 17.4s)

sample34.0ms

Algorithm
intervals
Results
8.0ms191×body80valid
4.0ms24×body1280valid
4.0ms256×pre80true
4.0ms23×body640valid
2.0ms16×body320valid
0.0ms2×body160valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
12013
23413
35313
47413
516313
630213
762513
8143913
9437413
done500013

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
1.1b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite297.0ms

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-exp-log add-cbrt-cube add-log-exp
2×pow1 flip3-+ div-sub associate-/r/ flip-+ associate-/l/
1×cbrt-undiv +-commutative associate-+l- flip3-- frac-2neg div-exp clear-num sum-log flip-- div-inv
Counts
2 → 65
Calls
2 calls:
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
221.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series146.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
84.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify908.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (272.0ms)

IterNodesCost
01241134
13261074
213541014
done50011014

prune208.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.9b

localize19.0ms

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))
1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.8s

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-exp-log add-cbrt-cube difference-of-squares
6×add-log-exp
4×pow1 associate-/r/ associate-/l/
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ frac-sub flip-+
1×sub-neg diff-log div-sub
Counts
4 → 137
Calls
4 calls:
1.4s
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
44.0ms
(/ alpha (+ (+ alpha beta) 2.0))
59.0ms
(/ beta (+ (+ alpha beta) 2.0))
215.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series357.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
71.0ms
(/ alpha (+ (+ alpha beta) 2.0))
73.0ms
(/ beta (+ (+ alpha beta) 2.0))
105.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.5s

Counts
149 → 149
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02382750
15622646
224182494
done50012492

prune464.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt beta)
0.6b
(cbrt beta)
0.6b
(cbrt beta)
1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite244.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×cbrt-prod *-un-lft-identity
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- times-frac diff-log flip-- distribute-lft-out--
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
1.0ms
(cbrt beta)
240.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series922.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(cbrt beta)
265.0ms
(cbrt beta)
283.0ms
(cbrt beta)
112.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.1s

Counts
60 → 60
Iterations

Useful iterations: 3 (414.0ms)

IterNodesCost
081488
1171473
2472425
31857408
done5001408

prune227.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.0b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
6.9b
(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
6.9b
(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
20×*-un-lft-identity
14×sqrt-prod
8×sqrt-div distribute-lft-out-- add-log-exp difference-of-squares
6×pow1 add-cube-cbrt flip3-- flip--
4×add-exp-log times-frac frac-sub add-cbrt-cube
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 72
Calls
4 calls:
250.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
215.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
626.0ms
(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
694.0ms
(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series975.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
130.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
336.0ms
(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
423.0ms
(sqrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify675.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (195.0ms)

IterNodesCost
01322162
13222004
212401920
done50021920

prune709.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.0b

regimes178.0ms

Accuracy

99.2% (0.1b remaining)

Error of 3.2b against oracle of 3.1b and baseline of 16.5b

bsearch1.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
03388
13988
done3988

end0.0ms

sample1.5s

Algorithm
intervals
Results
370.0ms5793×body80valid
285.0ms8000×pre80true
282.0ms893×body1280valid
145.0ms713×body640valid
104.0ms415×body320valid
18.0ms186×body160valid