Details

Time bar (total: 2.5m)

sample54.0ms

Algorithm
intervals
Results
13.0ms197×body80valid
8.0ms24×body1280valid
7.0ms256×pre80true
5.0ms17×body640valid
3.0ms12×body320valid
1.0ms6×body160valid

simplify167.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
167.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize33.0ms

Local error

Found 2 expressions with local error:

2.1b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite169.0ms

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-+ insert-posit16 associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log frac-2neg flip3-- div-exp associate-+l- div-inv flip--
Counts
2 → 67
Calls
2 calls:
Slowest
121.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
46.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series156.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
85.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
71.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.9s

Counts
74 → 73
Calls
74 calls:
Slowest
441.0ms
(- (+ 1.0 (* 0.5 beta)) (* 0.5 alpha))
269.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
268.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
226.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
179.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune696.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

localize20.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ alpha (+ (+ alpha beta) 2.0))
0.0b
(/ beta (+ (+ alpha beta) 2.0))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.1s

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-cbrt-cube add-exp-log difference-of-squares
6×add-log-exp
4×pow1 associate-/r/ insert-posit16 associate-/l/
3×cbrt-undiv clear-num frac-2neg flip3-- div-exp div-inv flip--
2×flip3-+ frac-sub flip-+
1×sub-neg diff-log div-sub
Counts
4 → 141
Calls
4 calls:
Slowest
901.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
138.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
44.0ms
(/ beta (+ (+ alpha beta) 2.0))
23.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series367.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
92.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
78.0ms
(/ alpha (+ (+ alpha beta) 2.0))
67.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify10.1s

Counts
155 → 153
Calls
155 calls:
Slowest
506.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
379.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
313.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
298.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
276.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.8b

localize48.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
0.0b
(/ (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))

rewrite800.0ms

Algorithm
rewrite-expression-head
Rules
186×*-un-lft-identity
103×times-frac
72×distribute-lft-out
66×add-sqr-sqrt
54×add-cube-cbrt
51×associate-*r/
39×swap-sqr
38×flip3-+ flip-+
32×frac-sub
25×add-cbrt-cube add-exp-log
21×frac-times associate-*r* associate-*l*
18×associate-/l/
16×associate-/r/
15×flip3-- flip--
11×pow1 associate-*l/
8×add-log-exp
7×cbrt-undiv div-exp prod-exp cbrt-unprod
5×div-inv
4×sub-neg insert-posit16 associate--r+ unswap-sqr
3×distribute-rgt-in distribute-lft-in associate-/l*
2×diff-log associate--l+
1×pow2 clear-num associate-/r* frac-2neg pow-plus div-sub pow-prod-down pow-sqr *-commutative pow-prod-up difference-of-squares
Counts
4 → 210
Calls
4 calls:
Slowest
490.0ms
(/ (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
154.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
111.0ms
(- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
39.0ms
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))

series677.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
292.0ms
(/ (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
175.0ms
(- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))
129.0ms
(- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))
81.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))

simplify48.7s

Counts
240 → 222
Calls
240 calls:
Slowest
2.1s
(/ (* (* (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))) (- (* beta (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) (* (+ (+ alpha beta) 2.0) (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))))) (* (* (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* 2.0 (* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))))
1.1s
(- (* (* beta (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (+ (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (* (* (/ 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)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3)))))
1.1s
(- (* (* beta (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (+ (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (* (* (/ 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)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3)))))
1.1s
(- (* (* beta (+ (pow (/ alpha (+ (+ alpha beta) 2.0)) 3) (pow 1.0 3))) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (* (+ (* (/ 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) (- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0))))))
1.0s
(- (* (* beta (- (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0))) (* (- (+ alpha beta) 2.0) (+ (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* 1.0 1.0)))) (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (* (- (* (+ alpha beta) (+ alpha beta)) (* 2.0 2.0)) (- (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* 1.0 1.0) (* 1.0 1.0))))))

prune3.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize94.0ms

Local error

Found 4 expressions with local error:

2.1b
(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))
0.1b
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
0.1b
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
0.1b
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))

rewrite492.0ms

Algorithm
rewrite-expression-head
Rules
187×*-un-lft-identity
159×add-cbrt-cube add-exp-log
130×pow1
100×times-frac
73×add-sqr-sqrt prod-exp cbrt-unprod
72×distribute-lft-out
53×add-cube-cbrt
48×cbrt-undiv div-exp
40×swap-sqr
38×pow-prod-up
25×pow-prod-down
24×pow-sqr
22×associate-*r* associate-*l*
20×pow-plus
19×frac-times
16×difference-of-squares
15×pow2
13×associate-*l/ associate-*r/
9×unpow-prod-down cube-prod sqr-pow
8×associate-/r/
6×pow-pow add-log-exp
5×pow-exp rem-cube-cbrt unswap-sqr
4×flip3-+ flip-+ insert-posit16 div-inv
3×cube-div pow-unpow
2×*-commutative
1×cube-mult pow-to-exp difference-cubes sub-neg flip3-- diff-log unpow3 flip-- distribute-lft-out--
Counts
4 → 298
Calls
4 calls:
Slowest
275.0ms
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
146.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))
38.0ms
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
20.0ms
(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))

series477.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(- (pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3) (pow (* 1.0 1.0) 3))
114.0ms
(pow (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) 3)
110.0ms
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
90.0ms
(* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0)))

simplify1.2m

Counts
372 → 310
Calls
372 calls:
Slowest
958.0ms
(* (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))
904.0ms
(* (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))) (* (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))
888.0ms
(* (* (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))) (* (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0))) (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))))
883.0ms
(* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))))
770.0ms
(* (* (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))) (* (/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0))) (* (* (/ alpha (+ (+ alpha beta) 2.0)) (/ alpha (+ (+ alpha beta) 2.0))) (/ alpha (+ (+ alpha beta) 2.0)))))

prune5.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

regimes215.0ms

Accuracy

64.1% (4.5b remaining)

Error of 7.6b against oracle of 3.1b and baseline of 15.6b

bsearch317.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
559.0ms5860×body80valid
456.0ms206×body160valid
434.0ms858×body1280valid
321.0ms8000×pre80true
251.0ms690×body640valid
118.0ms386×body320valid