Details

Time bar (total: 44.1s)

sample36.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
5.0ms256×pre80true

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
017485
158485
2267485
31566485
done5013485

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
35.8b
(/ (/ (* (* 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))
47.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×*-un-lft-identity add-cube-cbrt
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 clear-num frac-2neg distribute-lft-in *-commutative
1×pow2 pow-plus flip3-- pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
138.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
101.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
316.0ms
(/ (/ (* (* 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))
162.0ms
(/ (* (* 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:
84.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
149.0ms
(* (* 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))
283.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify2.7s

Counts
212 → 212
Iterations

Useful iterations: done (2.6s)

IterNodesCost
0358140846
11310123115
done5001122274

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 33.4b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (* 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))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
264×times-frac
191×add-sqr-sqrt
178×*-un-lft-identity
110×add-cube-cbrt
96×associate-*r*
74×add-cbrt-cube add-exp-log
42×associate-*l*
40×associate-/r/
35×cbrt-undiv div-exp
30×difference-of-squares
21×flip3-+ flip-+
20×div-inv
19×distribute-lft-out
17×prod-exp cbrt-unprod
15×sqrt-prod distribute-lft-out--
13×associate-/l*
10×associate-/r*
6×pow1 unswap-sqr
5×associate-/l/
4×add-log-exp
3×clear-num frac-2neg associate-*r/
1×frac-times flip3-- pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 304
Calls
4 calls:
257.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
995.0ms
(* (/ (/ (* 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))))
79.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
161.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.0s

Counts
4 → 12
Calls
4 calls:
354.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.3s
(* (/ (/ (* 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))))
106.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
182.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify3.7s

Counts
316 → 316
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0463205283
11635192497
done5001189716

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 33.3b

localize38.0ms

Local error

Found 4 expressions with local error:

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)))
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))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
85×add-cbrt-cube add-exp-log
79×times-frac
63×*-un-lft-identity
61×add-sqr-sqrt
42×associate-*l*
41×add-cube-cbrt
40×cbrt-undiv div-exp
21×prod-exp cbrt-unprod
18×associate-/r/
15×associate-*r*
12×associate-/r*
10×flip3-+ flip-+
9×div-inv distribute-lft-out
7×associate-/l/
6×pow1
5×associate-/l*
4×associate-*r/ add-log-exp difference-of-squares unswap-sqr
3×clear-num frac-2neg
2×frac-times associate-*l/ sqrt-prod distribute-lft-out--
1×flip3-- pow-prod-down *-commutative flip--
Counts
4 → 191
Calls
4 calls:
440.0ms
(/ (* (/ (/ (* 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)))
580.0ms
(* (/ (/ (* 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))))
88.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
122.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.5s

Counts
4 → 12
Calls
4 calls:
3.4s
(/ (* (/ (/ (* 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)))
811.0ms
(* (/ (/ (* 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))))
137.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
200.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.9s

Counts
203 → 203
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0339120821
11164113402
done5000111628

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 33.3b

localize66.0ms

Local error

Found 4 expressions with local error:

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))))
0.2b
(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
33.8b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
34.5b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
220×add-exp-log
136×add-cbrt-cube
91×times-frac div-exp
87×prod-exp
73×add-sqr-sqrt *-un-lft-identity
54×cbrt-undiv
49×add-cube-cbrt cbrt-unprod
43×associate-*l*
39×associate-*r*
18×associate-/r/
11×pow1
10×flip3-+ flip-+
9×rec-exp 1-exp div-inv distribute-lft-out
6×frac-times associate-/r* associate-*l/ associate-*r/ difference-of-squares
4×pow-prod-down associate-/l* add-log-exp unswap-sqr associate-/l/
3×sqrt-prod distribute-lft-out--
2×clear-num frac-2neg *-commutative
1×flip3-- un-div-inv flip--
Counts
4 → 242
Calls
4 calls:
618.0ms
(* (/ (/ (* 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))))
1.0s
(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
80.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
145.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.4s

Counts
4 → 12
Calls
4 calls:
788.0ms
(* (/ (/ (* 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))))
3.3s
(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
114.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
170.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify4.5s

Counts
254 → 254
Iterations

Useful iterations: done (4.5s)

IterNodesCost
0409167915
11373150957
done5001145631

prune1.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 33.3b

regimes279.0ms

Accuracy

30.5% (2.6b remaining)

Error of 36.8b against oracle of 34.2b and baseline of 37.9b

bsearch98.0ms

Steps
ItersRangePoint
9
3.1364010932508096e+181
5.1808368891769336e+188
3.204294196618706e+184

simplify11.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
026778
137778
done37778

end0.0ms

sample1.4s

Algorithm
intervals
Results
906.0ms8000×body80valid
213.0ms8000×pre80true