Details

Time bar (total: 9.2s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
3.0ms256×pre80true

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05826
128326
2162026
3500326
done500326

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 56.7b

localize19.0ms

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))))
36.4b
(/ (/ (* (* 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))
49.0b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite636.0ms

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:
143.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
104.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
235.0ms
(/ (/ (* (* 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))
143.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
110.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
822.0ms
(/ (/ (* (* 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))
181.0ms
(/ (* (* 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 (29.0ms)

IterNodesCost
012495670
150015161
done50015161

prune605.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 33.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.2b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
33.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite684.0ms

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:
202.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
268.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
66.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
136.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series811.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
342.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
126.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify74.0ms

Counts
264 → 264
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010985877
150015622
done50015622

prune818.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.2b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
33.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.4b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite543.0ms

Algorithm
rewrite-expression-head
Rules
81×times-frac
73×*-un-lft-identity
61×add-sqr-sqrt
45×add-cube-cbrt
24×add-exp-log
22×add-cbrt-cube
18×associate-/r/
16×associate-/r* associate-/l*
10×flip3-+ div-exp flip-+ distribute-lft-out
9×cbrt-undiv div-inv
8×difference-of-squares
5×pow1 associate-/l/
4×frac-2neg clear-num sqrt-prod distribute-lft-out-- add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×rec-exp flip3-- pow-flip 1-exp flip-- inv-pow
Counts
4 → 169
Calls
4 calls:
129.0ms
(/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
203.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
67.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
138.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series589.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
255.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
86.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify112.0ms

Counts
181 → 181
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07712666
140572463
250012437
done50012437

prune530.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 33.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.3b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.3b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
72×add-sqr-sqrt
57×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
14×difference-of-squares
12×associate-/r*
11×add-exp-log add-cbrt-cube
8×sqrt-div
7×associate-/l* distribute-lft-out--
6×pow1
5×flip3-+ flip-+
4×associate-/r/ associate-/l/ add-log-exp
3×cbrt-undiv div-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ clear-num div-inv
1×sqrt-undiv flip3-- prod-exp flip-- cbrt-unprod
Counts
4 → 141
Calls
4 calls:
139.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
68.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
8.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
8.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series491.0ms

Counts
4 → 12
Calls
4 calls:
280.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
57.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
62.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify71.0ms

Counts
153 → 153
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05512690
123772513
250022475
done50022475

prune644.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 33.3b

regimes142.0ms

Accuracy

35.1% (2.3b remaining)

Error of 36.6b against oracle of 34.3b and baseline of 37.8b

bsearch48.0ms

Steps
ItersRangePoint
7
4.3937702386440575e+210
1.1253432725521615e+212
4.4417126888079337e+210

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03730
13730
done3730

end0.0ms

sample731.0ms

Algorithm
intervals
Results
357.0ms8000×body80valid
117.0ms8000×pre80true