Details

Time bar (total: 34.6s)

sample54.0ms

Algorithm
intervals
Results
13.0ms187×body80valid
11.0ms31×body1280valid
8.0ms256×pre80true
6.0ms24×body640valid
2.0ms9×body320valid
1.0ms5×body160valid

simplify186.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
186.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.4b

localize37.0ms

Local error

Found 2 expressions with local error:

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

rewrite166.0ms

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
117.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
47.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series173.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
105.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
68.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.4s

Counts
74 → 73
Calls
74 calls:
Slowest
235.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
211.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
178.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
176.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
171.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))

prune703.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.7b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite568.0ms

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-cbrt-cube add-exp-log
6×associate-/l*
4×pow1 diff-log associate-/r/ insert-posit16 distribute-lft-out-- difference-of-squares
3×sub-neg flip3-- flip--
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp frac-sub flip-+ div-inv associate--r+
1×associate--r-
Counts
4 → 115
Calls
4 calls:
Slowest
355.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
149.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
40.0ms
(/ beta (+ (+ alpha beta) 2.0))
22.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series287.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
76.0ms
(/ beta (+ (+ alpha beta) 2.0))
64.0ms
(- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
63.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify6.0s

Counts
114 → 127
Calls
114 calls:
Slowest
367.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
341.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
267.0ms
(- (* 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))))
245.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
239.0ms
(* (+ (+ alpha beta) 2.0) (+ (/ alpha (+ (+ alpha beta) 2.0)) 1.0))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize58.0ms

Local error

Found 4 expressions with local error:

10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
0.0b
(/ beta (+ (+ alpha beta) 2.0))

rewrite685.0ms

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×exp-sum add-exp-log distribute-lft-out--
6×pow1 add-cbrt-cube add-log-exp difference-of-squares
5×associate-/r* flip3-- flip--
4×exp-prod exp-diff frac-sub insert-posit16
3×associate-/l*
2×associate-/r/ log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-exp rem-log-exp flip-+ div-inv rem-exp-log
Counts
4 → 99
Calls
4 calls:
Slowest
242.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
232.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
164.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
44.0ms
(/ beta (+ (+ alpha beta) 2.0))

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
129.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
104.0ms
(exp (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))))
66.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify6.7s

Counts
87 → 111
Calls
87 calls:
Slowest
566.0ms
(exp (log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))))
489.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
335.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
300.0ms
(exp (log (- (* 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))))))
269.0ms
(log (- (* 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)))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

localize44.0ms

Local error

Found 4 expressions with local error:

10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
10.2b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.0b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite952.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity
21×log-prod
12×log-div
10×distribute-lft-out--
8×difference-of-squares
7×pow1 flip3-- add-exp-log add-cube-cbrt flip--
6×frac-sub add-log-exp
4×times-frac add-cbrt-cube insert-posit16
3×rem-log-exp log-pow
1×sub-neg diff-log
Counts
4 → 79
Calls
4 calls:
Slowest
275.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
261.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
247.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
168.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series663.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
180.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
172.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
116.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify6.7s

Counts
54 → 91
Calls
54 calls:
Slowest
930.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
482.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
412.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
259.0ms
(log (- (* 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)))))
258.0ms
(log (- (* 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)))))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.6b

regimes232.0ms

Accuracy

77.4% (3.0b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.5b

bsearch115.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
665.0ms5777×body80valid
543.0ms915×body1280valid
387.0ms8000×pre80true
317.0ms752×body640valid
102.0ms359×body320valid
37.0ms197×body160valid