Details

Time bar (total: 23.0s)

sample51.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
5.0ms256×pre80true

simplify895.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01753
15853
228253
3177353
done500053

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize49.0ms

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))))
39.4b
(/ (/ (* (* 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))
46.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite745.0ms

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:
150.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
130.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
270.0ms
(/ (/ (* (* 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))
185.0ms
(/ (* (* 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:
79.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
137.0ms
(* (* 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))
207.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify706.0ms

Counts
212 → 212
Iterations

Useful iterations: done (690.0ms)

IterNodesCost
035812169
1133511471
done500210171

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.3b

localize64.0ms

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)))
38.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
38.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite920.0ms

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:
255.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
349.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
181.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
123.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series1.0s

Counts
4 → 12
Calls
4 calls:
304.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
459.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
146.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
109.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify564.0ms

Counts
264 → 264
Iterations

Useful iterations: done (542.0ms)

IterNodesCost
039811487
1113711156
done500010702

prune1.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 37.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
38.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
38.3b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
38.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite863.0ms

Algorithm
rewrite-expression-head
Rules
192×times-frac
173×add-sqr-sqrt
135×*-un-lft-identity
124×sqrt-prod
97×add-cube-cbrt
38×difference-of-squares
25×associate-/l*
22×associate-/r/
19×distribute-lft-out--
15×add-exp-log associate-/r* add-cbrt-cube
13×flip3-+ flip-+
11×div-inv
7×associate-/l/
5×cbrt-undiv div-exp
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/
1×flip3-- sqrt-div prod-exp flip-- cbrt-unprod
Counts
4 → 234
Calls
4 calls:
308.0ms
(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
230.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
206.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series2.2s

Counts
4 → 12
Calls
4 calls:
1.7s
(/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
186.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
193.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
149.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify2.2s

Counts
246 → 246
Iterations

Useful iterations: done (2.2s)

IterNodesCost
037710971
185810561
2411210065
done500010055

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 37.3b

localize49.0ms

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))))
38.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.1b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.3b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

rewrite340.0ms

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:
193.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
9.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
8.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
116.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
377.0ms
(/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (sqrt (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
70.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
66.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
121.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))

simplify1.6s

Counts
153 → 153
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02405041
15784594
228134453
done50004447

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 37.3b

regimes367.0ms

Accuracy

36.2% (2.6b remaining)

Error of 36.4b against oracle of 33.8b and baseline of 37.8b

bsearch89.0ms

Steps
ItersRangePoint
6
3.998441498091938e+207
4.743012469806171e+208
4.07062621862513e+207

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02684
13684
done3684

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s8000×body80valid
328.0ms8000×pre80true