Details

Time bar (total: 27.9s)

sample54.0ms

Algorithm
intervals
Results
11.0ms194×body80valid
7.0ms23×body1280valid
6.0ms256×pre80true
5.0ms22×body640valid
2.0ms12×body320valid
1.0ms5×body160valid

simplify5.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize27.0ms

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)

rewrite430.0ms

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:
101.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
322.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series207.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
122.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.2s

Counts
71 → 71
Iterations

Useful iterations: 2 (318.0ms)

IterNodesCost
01241134
13261074
213541014
done50011014

prune449.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
1.5b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.3s

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-exp-log add-cbrt-cube
6×associate-/l*
4×pow1 diff-log associate-/r/ distribute-lft-out-- difference-of-squares
3×sub-neg flip3-- flip--
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num frac-sub flip-+ div-inv associate--r+
1×associate--r-
Counts
4 → 111
Calls
4 calls:
70.0ms
(/ alpha (+ (+ alpha beta) 2.0))
805.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
70.0ms
(/ beta (+ (+ alpha beta) 2.0))
369.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series435.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ alpha (+ (+ alpha beta) 2.0))
124.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
84.0ms
(/ beta (+ (+ alpha beta) 2.0))
145.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.6s

Counts
123 → 123
Iterations

Useful iterations: 2 (546.0ms)

IterNodesCost
01931936
14621814
219171730
done50001730

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize91.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.0b
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b
(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
1.5b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
245×*-un-lft-identity
177×associate-*r/
141×times-frac
131×add-sqr-sqrt
90×distribute-lft-out
83×flip3-+ flip-+
73×add-cube-cbrt
71×frac-times
66×frac-add associate-/l/
64×frac-sub
41×associate-*l/
39×unpow-prod-down cube-prod swap-sqr
38×associate-/r/
26×flip3-- flip--
24×add-exp-log add-cbrt-cube difference-of-squares
21×associate-*r* associate-*l*
12×pow1
11×sqr-pow
7×cbrt-undiv div-exp div-inv
6×add-log-exp
5×prod-exp cbrt-unprod distribute-lft-out--
4×unswap-sqr
3×pow-unpow associate-/l*
2×pow-exp rem-cube-cbrt
1×difference-cubes cube-div pow2 cube-mult pow-to-exp sub-neg pow-pow frac-2neg pow-plus diff-log unpow3 div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up
Counts
4 → 327
Calls
4 calls:
320.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
81.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
515.0ms
(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
844.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
136.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
782.0ms
(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
211.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.8s

Counts
339 → 339
Iterations

Useful iterations: done (1.8s)

IterNodesCost
050916735
1223015502
done500113374

prune3.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.6b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
1.5b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
11.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
32×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
14×log-prod
12×distribute-lft-out
8×log-div
7×add-exp-log exp-sum distribute-lft-out--
6×pow1 add-cbrt-cube add-log-exp difference-of-squares
5×flip3-- associate-/r* flip--
4×exp-prod exp-diff frac-sub
3×associate-/l*
2×associate-/r/ log-pow
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp rem-log-exp clear-num flip-+ div-inv rem-exp-log
Counts
4 → 95
Calls
4 calls:
75.0ms
(/ beta (+ (+ alpha beta) 2.0))
635.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
366.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
652.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

series571.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ beta (+ (+ alpha beta) 2.0))
114.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
130.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
237.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

simplify1.5s

Counts
107 → 107
Iterations

Useful iterations: 2 (496.0ms)

IterNodesCost
02112358
14772197
218722032
done50022032

prune731.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.6b

regimes324.0ms

Accuracy

75.3% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.6b

bsearch151.0ms

Steps
ItersRangePoint
9
10953890.001246931
1278537795488789.0
246471310145705.3

simplify13.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
040128
152128
done52128

end0.0ms

sample1.9s

Algorithm
intervals
Results
600.0ms5870×body80valid
309.0ms820×body1280valid
244.0ms8000×pre80true
237.0ms716×body640valid
77.0ms408×body320valid
24.0ms186×body160valid