Details

Time bar (total: 36.6s)

sample53.0ms

Algorithm
intervals
Results
13.0ms185×body80valid
11.0ms31×body1280valid
8.0ms256×pre80true
6.0ms23×body640valid
2.0ms9×body320valid
1.0ms8×body160valid

simplify150.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
150.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize33.0ms

Local error

Found 2 expressions with local error:

1.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite184.0ms

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
138.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
44.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series156.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
87.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
69.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.8s

Counts
74 → 73
Calls
74 calls:
Slowest
576.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
248.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
231.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
202.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))
188.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune650.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ 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
917.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
141.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
36.0ms
(/ alpha (+ (+ alpha beta) 2.0))
35.0ms
(/ beta (+ (+ alpha beta) 2.0))

series336.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
88.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
81.0ms
(/ alpha (+ (+ alpha beta) 2.0))
59.0ms
(/ beta (+ (+ alpha beta) 2.0))

simplify9.8s

Counts
155 → 153
Calls
155 calls:
Slowest
441.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
394.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
343.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
246.0ms
(- (* 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
(- (* (/ beta (+ (+ alpha beta) 2.0)) (/ beta (+ (+ alpha beta) 2.0))) (* (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.5b

localize82.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ 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))

rewrite190.0ms

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
152.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
17.0ms
(cbrt (+ (+ alpha beta) 2.0))
10.0ms
(cbrt (+ (+ alpha beta) 2.0))
10.0ms
(cbrt (+ (+ alpha beta) 2.0))

series546.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
161.0ms
(cbrt (+ (+ alpha beta) 2.0))
152.0ms
(cbrt (+ (+ alpha beta) 2.0))
141.0ms
(cbrt (+ (+ alpha beta) 2.0))
92.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify3.8s

Counts
39 → 76
Calls
39 calls:
Slowest
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)))
229.0ms
(+ (pow 2.0 1/3) (+ (* 0.16666666666666666 (* (pow 2.0 1/3) beta)) (* 1/3 (* (pow 0.25 1/3) alpha))))
222.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))
214.0ms
(+ (pow 2.0 1/3) (+ (* 0.16666666666666666 (* (pow 2.0 1/3) beta)) (* 1/3 (* (pow 0.25 1/3) alpha))))
211.0ms
(- (+ (pow (/ 1 alpha) -1/3) (* 0.6666666666666666 (pow (/ 1 (pow alpha 2)) 1/3))) (* 0.4444444444444444 (pow (/ 1 (pow alpha 5)) 1/3)))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.5b

localize35.0ms

Local error

Found 4 expressions with local error:

11.1b
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
1.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
1.7b
(- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))
0.6b
(exp (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
33×add-sqr-sqrt
24×log-prod
18×distribute-lft-out--
14×associate--l+
13×pow1
10×difference-of-squares
9×exp-sum log-pow add-cube-cbrt
8×log-div exp-prod
7×add-log-exp
6×flip3-- flip--
5×add-exp-log
4×associate--l- times-frac add-cbrt-cube frac-sub insert-posit16
3×sub-neg diff-log associate--r+
2×rem-exp-log
1×exp-diff rem-log-exp
Counts
4 → 97
Calls
4 calls:
Slowest
300.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
297.0ms
(exp (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))
285.0ms
(- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))
142.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series986.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
462.0ms
(- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))
278.0ms
(exp (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))
155.0ms
(log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
90.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify7.1s

Counts
71 → 109
Calls
71 calls:
Slowest
426.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
386.0ms
(log (- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3)))
290.0ms
(exp (* (cbrt (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0))) (cbrt (- (log (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))) (log 2.0)))))
287.0ms
(- (+ (log 1.0) (* 0.5 beta)) (+ (log 2.0) (* 0.5 alpha)))
236.0ms
(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)))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

regimes201.0ms

Accuracy

72.4% (3.5b remaining)

Error of 6.7b against oracle of 3.2b and baseline of 15.8b

bsearch25.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
725.0ms736×body640valid
611.0ms5835×body80valid
451.0ms843×body1280valid
352.0ms8000×pre80true
98.0ms379×body320valid
36.0ms207×body160valid