Details

Time bar (total: 47.7s)

sample52.0ms

Algorithm
intervals
Results
13.0ms183×body80valid
9.0ms29×body1280valid
8.0ms256×pre80true
6.0ms22×body640valid
2.0ms14×body160valid
2.0ms8×body320valid

simplify143.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
143.0ms
(/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize41.0ms

Local error

Found 2 expressions with local error:

2.9b
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
0.0b
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

rewrite198.0ms

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
153.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
43.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

series136.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
78.0ms
(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)
58.0ms
(/ (- beta alpha) (+ (+ alpha beta) 2.0))

simplify3.4s

Counts
74 → 73
Calls
74 calls:
Slowest
240.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
236.0ms
(/ (* (* (- beta alpha) (- beta alpha)) (- beta alpha)) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))
196.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.5 alpha)))
191.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 1) (* 2.0 (/ 1 beta)))
182.0ms
(- (+ (* 4.0 (/ 1 (pow beta 2))) 2.0) (* 2.0 (/ 1 beta)))

prune713.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.3b

localize40.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ 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)

rewrite1.2s

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
979.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
156.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
47.0ms
(/ beta (+ (+ alpha beta) 2.0))
45.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series370.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
111.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
71.0ms
(/ beta (+ (+ alpha beta) 2.0))
65.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify10.7s

Counts
155 → 153
Calls
155 calls:
Slowest
547.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
346.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
294.0ms
(- (* 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))))
251.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
249.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize50.0ms

Local error

Found 4 expressions with local error:

9.8b
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
2.9b
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
0.5b
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
0.0b
(/ alpha (+ (+ alpha beta) 2.0))

rewrite768.0ms

Algorithm
rewrite-expression-head
Rules
89×*-un-lft-identity
72×add-sqr-sqrt
64×times-frac
50×log-prod
37×add-cube-cbrt
25×exp-sum
19×distribute-lft-out--
14×difference-of-squares
12×distribute-lft-out
9×add-exp-log
6×pow1 add-cbrt-cube add-log-exp
5×associate-/r*
4×exp-prod insert-posit16
3×div-inv associate-/l*
2×log-div div-exp rem-log-exp associate-/r/ log-pow
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ flip3-- exp-diff diff-log flip-+ flip-- rem-exp-log
Counts
4 → 130
Calls
4 calls:
Slowest
304.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
276.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
150.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
33.0ms
(/ alpha (+ (+ alpha beta) 2.0))

series466.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
188.0ms
(log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0))
108.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
105.0ms
(exp (log (/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)))
65.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify9.8s

Counts
118 → 142
Calls
118 calls:
Slowest
438.0ms
(/ (cbrt alpha) (+ (+ alpha beta) 2.0))
364.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
331.0ms
(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)))))
325.0ms
(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)))))
282.0ms
(/ (* (* alpha alpha) alpha) (* (* (+ (+ alpha beta) 2.0) (+ (+ alpha beta) 2.0)) (+ (+ alpha beta) 2.0)))

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.0b

localize37.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ 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
886.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
177.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
41.0ms
(/ alpha (+ (+ alpha beta) 2.0))
36.0ms
(/ beta (+ (+ alpha beta) 2.0))

series339.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)
101.0ms
(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
70.0ms
(/ beta (+ (+ alpha beta) 2.0))
64.0ms
(/ alpha (+ (+ alpha beta) 2.0))

simplify10.6s

Counts
155 → 153
Calls
155 calls:
Slowest
546.0ms
(- (pow (/ beta (+ (+ alpha beta) 2.0)) 3) (pow (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0) 3))
349.0ms
(- (* 0.5 beta) (+ (* 0.25 (pow beta 2)) (* 0.25 (* beta alpha))))
349.0ms
(- (* 0.5 alpha) (+ (* 0.25 (pow alpha 2)) (* 0.25 (* beta alpha))))
274.0ms
(+ (* (+ alpha beta) (+ alpha beta)) (- (* 2.0 2.0) (* (+ alpha beta) 2.0)))
250.0ms
(- (* 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))))

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.0b

regimes183.0ms

Accuracy

77.6% (2.9b remaining)

Error of 6.1b against oracle of 3.3b and baseline of 16.0b

bsearch124.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
725.0ms738×body640valid
720.0ms5792×body80valid
380.0ms837×body1280valid
325.0ms8000×pre80true
116.0ms420×body320valid
38.0ms213×body160valid