Details

Time bar (total: 7.9m)

sample39.0ms

Algorithm
intervals
Results
8.0ms185×body80valid
5.0ms24×body1280valid
5.0ms256×pre80true
5.0ms28×body640valid
2.0ms16×body320valid
0.0ms3×body160valid

simplify963.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite322.0ms

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:
83.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
236.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series159.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
89.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.8s

Counts
71 → 71

prune199.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.8b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

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:
632.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
75.0ms
(/ alpha (+ (+ alpha beta) 2.0))
45.0ms
(/ beta (+ (+ alpha beta) 2.0))
254.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series388.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
83.0ms
(/ alpha (+ (+ alpha beta) 2.0))
91.0ms
(/ beta (+ (+ alpha beta) 2.0))
115.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify664.0ms

Counts
123 → 123

prune445.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.7b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.1b
(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
0.8b
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
376×*-un-lft-identity
211×times-frac
172×add-sqr-sqrt
144×distribute-lft-out
124×associate-*r/
102×add-cube-cbrt
85×flip3-+ flip-+
78×swap-sqr
72×frac-times
66×frac-add associate-/l/
64×frac-sub
48×associate-*l/
42×associate-*r* 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:
214.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
232.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
501.0ms
(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
616.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

series942.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
100.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
596.0ms
(/ (- (* beta (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (+ (+ alpha beta) 2.0) (- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
156.0ms
(- (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))

simplify1.2s

Counts
386 → 386

prune2.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

localize216.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
0.1b
(* (* (+ (+ (pow (/ alpha (+ (+ alpha beta) 2.0)) 6) (pow 1.0 6)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))) (+ (* (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (- (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (/ alpha (+ (+ alpha beta) 2.0))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
0.1b
(* (* beta (+ (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 3))) (+ (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) (+ (* (pow 1.0 3) (pow 1.0 3)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))
0.8b
(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

rewrite17.3s

Algorithm
rewrite-expression-head
Rules
40575×frac-times
36593×associate-*r/
22302×frac-add
20376×flip3-+ flip-+
17351×associate-*l/
11577×cube-div
7290×frac-sub
1216×flip3-- flip--
254×add-sqr-sqrt
221×unpow-prod-down cube-prod
140×difference-of-squares
73×sqr-pow
48×*-un-lft-identity
40×times-frac
34×add-exp-log add-cbrt-cube
29×pow1
21×distribute-lft-out--
15×prod-exp cbrt-unprod
12×pow-prod-down
6×add-cube-cbrt pow-pow add-log-exp
5×distribute-rgt-in distribute-lft-in pow-exp rem-cube-cbrt
4×cbrt-undiv div-exp associate-*r*
3×pow-unpow
2×associate-*l* *-commutative
1×difference-cubes pow2 cube-mult pow-to-exp sub-neg pow-plus diff-log unpow3 pow-sqr pow-prod-up
Counts
4 → 11269
Calls
4 calls:
74.0ms
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
8.5s
(* (* (+ (+ (pow (/ alpha (+ (+ alpha beta) 2.0)) 6) (pow 1.0 6)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))) (+ (* (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (- (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (/ alpha (+ (+ alpha beta) 2.0))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
1.2s
(* (* beta (+ (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 3))) (+ (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) (+ (* (pow 1.0 3) (pow 1.0 3)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))
1.4s
(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

series2.5s

Counts
4 → 12
Calls
4 calls:
149.0ms
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
394.0ms
(* (* (+ (+ (pow (/ alpha (+ (+ alpha beta) 2.0)) 6) (pow 1.0 6)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))) (+ (* (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (- (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (/ alpha (+ (+ alpha beta) 2.0))))) (* (+ (* 1.0 (+ 1.0 (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (+ alpha beta) 2.0)))
1.8s
(* (* beta (+ (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (+ (* 1.0 1.0) (* (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 3))) (+ (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow (/ alpha (+ (+ alpha beta) 2.0)) 3)) (+ (* (pow 1.0 3) (pow 1.0 3)) (* (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3)))))
168.0ms
(- (pow (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) 3) (pow (pow 1.0 3) 3))

simplify1.5m

Counts
11281 → 11281

prune5.8m

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.6b

regimes156.0ms

Accuracy

75.8% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 15.7b

bsearch83.0ms

Steps
ItersRangePoint
9
3344124399.4880223
5893413222975757.0
12778882773963.467

simplify740.0ms

end0.0ms

sample961.0ms

Algorithm
intervals
Results
238.0ms5847×body80valid
217.0ms831×body1280valid
136.0ms705×body640valid
102.0ms8000×pre80true
37.0ms404×body320valid
13.0ms213×body160valid