Details

Time bar (total: 43.9s)

sample53.0ms

Algorithm
intervals
Results
12.0ms175×body80valid
10.0ms32×body1280valid
8.0ms256×pre80true
6.0ms23×body640valid
4.0ms20×body320valid
1.0ms6×body160valid

simplify136.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
136.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite180.0ms

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
122.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
56.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series155.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
80.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))
75.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify3.8s

Counts
74 → 73
Calls
74 calls:
Slowest
310.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
265.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
211.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
200.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
194.0ms
(* (exp (/ (- beta alpha) (+ (+ alpha beta) 2.0))) (exp 1.0))

prune633.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.2s

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
948.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
148.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
32.0ms
(/ alpha (+ (+ alpha beta) 2.0))
30.0ms
(/ beta (+ (+ alpha beta) 2.0))

series325.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
90.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
67.0ms
(/ beta (+ (+ alpha beta) 2.0))
60.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify10.0s

Counts
155 → 153
Calls
155 calls:
Slowest
513.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
400.0ms
(- (* 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))))
259.0ms
(- (* 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))))
238.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize54.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))
0.7b
(cbrt (+ (+ alpha beta) 2.0))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
15×cbrt-prod
12×add-sqr-sqrt
9×distribute-lft-out
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-cbrt-cube add-exp-log insert-posit16
3×flip3-+ pow1/3 flip-+
2×difference-of-squares
1×sub-neg times-frac flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
Slowest
140.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
18.0ms
(cbrt (+ (+ alpha beta) 2.0))
12.0ms
(cbrt (+ (+ alpha beta) 2.0))
10.0ms
(cbrt (+ (+ alpha beta) 2.0))

series485.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(cbrt (+ (+ alpha beta) 2.0))
127.0ms
(cbrt (+ (+ alpha beta) 2.0))
124.0ms
(cbrt (+ (+ alpha beta) 2.0))
91.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify4.0s

Counts
39 → 76
Calls
39 calls:
Slowest
272.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
255.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
251.0ms
(+ (pow 2.0 1/3) (+ (* 0.16666666666666666 (* (pow 2.0 1/3) beta)) (* 1/3 (* (pow 0.25 1/3) alpha))))
250.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
239.0ms
(+ (pow 2.0 1/3) (+ (* 0.16666666666666666 (* (pow 2.0 1/3) beta)) (* 1/3 (* (pow 0.25 1/3) alpha))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize42.0ms

Local error

Found 4 expressions with local error:

9.3b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
2.2b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.7b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
94×add-sqr-sqrt
91×*-un-lft-identity
74×times-frac
50×log-prod
39×add-cube-cbrt
31×distribute-lft-out--
25×exp-sum
22×difference-of-squares
9×add-exp-log
7×associate-/l*
6×pow1 add-cbrt-cube add-log-exp
4×exp-prod insert-posit16 associate-/l/
3×associate-/r* flip3-- div-inv flip--
2×log-div div-exp rem-log-exp log-pow frac-sub
1×cbrt-undiv clear-num sub-neg frac-2neg exp-diff diff-log div-sub rem-exp-log
Counts
4 → 141
Calls
4 calls:
Slowest
920.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
332.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
256.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
162.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series522.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
208.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
111.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
110.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
93.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))

simplify14.1s

Counts
132 → 153
Calls
132 calls:
Slowest
532.0ms
(- (+ (* 2.0 (/ 1 (pow beta 2))) 1.0) (* 1.0 (/ 1 beta)))
474.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
392.0ms
(exp (* (cbrt (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))) (cbrt (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))))
335.0ms
(exp (log (/ (* (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (cbrt (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))) (* (cbrt 2.0) (cbrt 2.0)))))
278.0ms
(- (* 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))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

regimes290.0ms

Accuracy

98.4% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 15.9b

bsearch14.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
596.0ms5814×body80valid
428.0ms824×body1280valid
270.0ms8000×pre80true
267.0ms756×body640valid
163.0ms430×body320valid
28.0ms176×body160valid