Details

Time bar (total: 23.0s)

sample32.0ms

Algorithm
intervals
Results
6.0ms185×body80valid
5.0ms31×body1280valid
4.0ms256×pre80true
2.0ms20×body320valid
2.0ms13×body640valid
0.0ms7×body160valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.2b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite337.0ms

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:
81.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
252.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series167.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
85.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify815.0ms

Counts
71 → 71
Iterations

Useful iterations: 2 (210.0ms)

IterNodesCost
01241134
13261074
213541014
done50011014

prune375.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite889.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
23×add-sqr-sqrt
17×times-frac
13×add-cube-cbrt
12×distribute-lft-out
10×add-log-exp
5×add-exp-log associate-/r* add-cbrt-cube
4×diff-log distribute-lft-out-- difference-of-squares
3×pow1 sub-neg flip3-- flip-- associate-/l*
2×associate-/r/ frac-sub associate--r+
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv associate--r-
Counts
3 → 74
Calls
3 calls:
536.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
53.0ms
(/ beta (+ (+ alpha beta) 2.0))
297.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series269.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
81.0ms
(/ beta (+ (+ alpha beta) 2.0))
93.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify898.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (336.0ms)

IterNodesCost
01601464
13981385
216211315
done50011315

prune504.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize45.0ms

Local error

Found 4 expressions with local error:

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)))))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.2b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
376×*-un-lft-identity
211×times-frac
178×associate-*r/
172×add-sqr-sqrt
144×distribute-lft-out
102×add-cube-cbrt
85×flip3-+ flip-+
78×swap-sqr
72×frac-times
66×frac-add associate-/l/
64×frac-sub
42×associate-*r* associate-*l* associate-*l/ associate-/r/
33×add-exp-log add-cbrt-cube
26×flip3-- flip--
24×difference-of-squares
18×pow1 unpow-prod-down cube-prod
10×cbrt-undiv div-exp sqr-pow
9×prod-exp cbrt-unprod div-inv
8×unswap-sqr
6×add-log-exp
5×distribute-lft-out--
3×associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×difference-cubes sub-neg frac-2neg diff-log div-sub clear-num associate-/r*
Counts
4 → 374
Calls
4 calls:
348.0ms
(/ (- (* 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)))))
225.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
258.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
590.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series932.0ms

Counts
4 → 12
Calls
4 calls:
592.0ms
(/ (- (* 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)))))
94.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
102.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
144.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.1s

Counts
386 → 386
Iterations

Useful iterations: done (1.0s)

IterNodesCost
046818162
1192816726
done500115332

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 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) (+ 0 (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
0.1b
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
2.2b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
245×*-un-lft-identity
147×associate-*r/
141×times-frac
131×add-sqr-sqrt
90×distribute-lft-out
73×add-cube-cbrt
68×flip3-+ flip-+
66×associate-/l/
64×frac-sub
53×frac-times
48×frac-add
39×unpow-prod-down cube-prod swap-sqr
35×associate-*l/
26×flip3-- flip--
24×add-exp-log add-cbrt-cube difference-of-squares
21×associate-*r* associate-*l*
20×associate-/r/
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 → 309
Calls
4 calls:
306.0ms
(/ (- (* 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) (+ 0 (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
47.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
286.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
630.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series793.0ms

Counts
4 → 12
Calls
4 calls:
390.0ms
(/ (- (* 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) (+ 0 (* 1.0 (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
129.0ms
(pow (/ alpha (+ (+ alpha beta) 2.0)) 3)
97.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
176.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.2s

Counts
321 → 321
Iterations

Useful iterations: done (1.2s)

IterNodesCost
045613211
1194911798
done500010685

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

regimes473.0ms

Accuracy

94.9% (0.7b remaining)

Error of 3.5b against oracle of 2.8b and baseline of 16.0b

bsearch7.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03077
13477
done3477

end0.0ms

sample1.9s

Algorithm
intervals
Results
734.0ms855×body1280valid
339.0ms5893×body80valid
235.0ms8000×pre80true
161.0ms667×body640valid
54.0ms384×body320valid
19.0ms201×body160valid