Details

Time bar (total: 29.8s)

sample54.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
6.0ms256×pre80true

simplify48.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05826
128326
2162026
3500326
done500326

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.1b
(/ (/ (* (* 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))
46.5b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite713.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
18×associate-*l/
16×pow1
14×associate-/l* difference-of-squares
9×associate-/l/
7×div-inv
6×associate-*r*
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
159.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
118.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
265.0ms
(/ (/ (* (* 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))
159.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.3s

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
114.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
879.0ms
(/ (/ (* (* 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))
195.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify70.0ms

Counts
212 → 212
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012495670
150015161
done50015161

prune627.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 31.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
366×times-frac
300×add-sqr-sqrt
235×*-un-lft-identity
155×add-cube-cbrt
96×associate-*r*
70×add-exp-log add-cbrt-cube
62×difference-of-squares
44×associate-/r/
42×associate-*l*
33×cbrt-undiv div-exp
31×sqrt-prod distribute-lft-out--
22×flip3-+ flip-+ div-inv
19×associate-/l*
16×prod-exp cbrt-unprod
12×associate-/r*
9×distribute-lft-out
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
307.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
896.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
75.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
151.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.9s

Counts
4 → 12
Calls
4 calls:
355.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
95.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify120.0ms

Counts
376 → 376
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0168310749
150019903
done50019903

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.8b

localize23.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
33.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite938.0ms

Algorithm
rewrite-expression-head
Rules
11777×times-frac
6537×add-sqr-sqrt
5431×*-un-lft-identity
4327×add-cube-cbrt
3150×sqrt-prod
1104×difference-of-squares
552×distribute-lft-out--
313×div-inv
302×associate-/r/
152×associate-/r*
142×flip3-+ flip-+
39×add-exp-log
30×add-cbrt-cube
26×div-exp
23×associate-/l*
17×cbrt-undiv
6×pow1
4×sqrt-div add-log-exp
3×1-exp associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num
1×prod-exp cbrt-unprod
Counts
4 → 3531
Calls
4 calls:
293.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
76.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
9.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
9.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series583.0ms

Counts
4 → 12
Calls
4 calls:
357.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i)))))
96.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
61.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
69.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.6s

Counts
3543 → 3543
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05001182857
done5001182857

prune9.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 31.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
32.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
33.2b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
1669×times-frac
1103×add-sqr-sqrt
864×*-un-lft-identity
630×add-cube-cbrt
290×associate-*r*
220×add-exp-log
210×difference-of-squares
128×div-exp
107×associate-/r/
105×sqrt-prod distribute-lft-out--
101×associate-/r*
100×add-cbrt-cube
58×div-inv
53×cbrt-undiv
51×flip3-+ prod-exp flip-+
42×associate-*l*
21×cbrt-unprod
15×rec-exp 1-exp
14×unswap-sqr
9×distribute-lft-out
7×pow1 associate-/l*
4×associate-/l/ add-log-exp
3×frac-2neg associate-*r/ clear-num
1×frac-times pow-flip pow-prod-down associate-*l/ un-div-inv *-commutative inv-pow
Counts
4 → 879
Calls
4 calls:
206.0ms
(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
1.0s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
76.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
158.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.1s

Counts
4 → 12
Calls
4 calls:
558.0ms
(/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify281.0ms

Counts
891 → 891
Iterations

Useful iterations: 1 (61.0ms)

IterNodesCost
0338628125
1500226725
done500226725

prune2.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 31.8b

regimes128.0ms

Accuracy

36.1% (2.5b remaining)

Error of 36.5b against oracle of 34.0b and baseline of 37.9b

bsearch60.0ms

Steps
ItersRangePoint
8
1.5160333269998001e+200
3.4778725636249246e+203
1.1193682871354866e+201

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04047
14047
done4047

end0.0ms

sample781.0ms

Algorithm
intervals
Results
401.0ms8000×body80valid
118.0ms8000×pre80true