Details

Time bar (total: 37.1s)

sample68.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
7.0ms256×pre80true

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01753
112153
2195953
done500153

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.5b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
45.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite990.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
143.0ms
(* i (+ (+ alpha beta) i))
160.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
417.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
245.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.7s

Counts
4 → 12
Calls
4 calls:
27.0ms
(* i (+ (+ alpha beta) i))
181.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.2s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
276.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify869.0ms

Counts
201 → 201
Iterations

Useful iterations: done (856.0ms)

IterNodesCost
034511544
done500010704

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 36.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
37.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
309.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
455.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
79.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
238.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.2s

Counts
4 → 12
Calls
4 calls:
401.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
454.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
164.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
196.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify3.6s

Counts
264 → 264
Iterations

Useful iterations: done (3.6s)

IterNodesCost
039811487
1339911158
done500110688

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
37.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
4160×times-frac
3009×*-un-lft-identity
1593×add-sqr-sqrt
1529×add-cube-cbrt
810×distribute-lft-out
171×div-inv
147×associate-/r/
101×associate-/r*
67×flip3-+ flip-+
43×add-exp-log
36×associate-/l*
34×add-cbrt-cube
32×difference-of-squares
29×div-exp
20×cbrt-undiv
16×sqrt-prod distribute-lft-out--
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
3×1-exp
1×flip3-- flip--
Counts
4 → 1484
Calls
4 calls:
334.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
344.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
206.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
264.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
322.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
528.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
125.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))
163.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.4s

Counts
1496 → 1496
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0172083112
done500077544

prune6.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
0.2b
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.2b
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
0.3b
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
4175×times-frac
3109×*-un-lft-identity
1550×add-sqr-sqrt
1534×add-cube-cbrt
877×distribute-lft-out
169×div-inv
142×associate-/r/
119×associate-/r*
65×flip3-+ flip-+
43×add-exp-log
34×add-cbrt-cube
29×div-exp
25×associate-/l*
20×cbrt-undiv
8×difference-of-squares
7×associate-/l/
4×pow1 frac-2neg clear-num sqrt-prod distribute-lft-out-- add-log-exp
3×1-exp
1×flip3-- flip--
Counts
4 → 1494
Calls
4 calls:
567.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
239.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
335.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
168.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

series990.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i))))
224.0ms
(/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
365.0ms
(/ (/ i 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))))
115.0ms
(/ (+ (+ alpha beta) i) (+ (+ alpha beta) (* 2.0 i)))

simplify1.4s

Counts
1506 → 1506
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0162182109
done500176067

prune6.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.8b

regimes364.0ms

Accuracy

46.7% (8.8b remaining)

Error of 10.9b against oracle of 2.1b and baseline of 18.6b

bsearch53.0ms

Steps
ItersRangePoint
4
1.795372052662639e+144
2.9011180149917516e+144
2.3136904725044102e+144

simplify14.0ms

Iterations

Useful iterations: done (14.0ms)

IterNodesCost
043136
160128
done60126

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s8000×body80valid
274.0ms8000×pre80true