Details

Time bar (total: 9.0s)

sample42.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
5.0ms256×pre80true

simplify36.0ms

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

localize17.0ms

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))))

rewrite622.0ms

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:
139.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
102.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
232.0ms
(/ (/ (* (* 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))
137.0ms
(/ (* (* 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:
62.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
109.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
849.0ms
(/ (/ (* (* 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))
194.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify69.0ms

Counts
212 → 212
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012495670
150015161
done50015161

prune618.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 33.3b

localize18.0ms

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)))

rewrite667.0ms

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:
197.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
263.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
64.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
130.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series795.0ms

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)))
330.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
124.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify73.0ms

Counts
264 → 264
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010985877
150015622
done50015622

prune807.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 33.3b

localize19.0ms

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)))

rewrite531.0ms

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:
127.0ms
(/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
199.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
65.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
133.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series583.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
252.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
91.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
123.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify102.0ms

Counts
181 → 181
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07712666
140572463
250012437
done50012437

prune537.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 33.3b

localize23.0ms

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))))

rewrite226.0ms

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:
136.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
65.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
11.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
8.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series494.0ms

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)))
59.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
64.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify69.0ms

Counts
153 → 153
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05512690
123772513
250022475
done50022475

prune503.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 33.3b

regimes148.0ms

Accuracy

35.1% (2.3b remaining)

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

bsearch53.0ms

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

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04147
14147
done4147

end0.0ms

sample709.0ms

Algorithm
intervals
Results
340.0ms8000×body80valid
117.0ms8000×pre80true