Details

Time bar (total: 35.3s)

sample93.0ms

Algorithm
intervals
Results
52.0ms256×body80valid
14.0ms256×pre80true

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done2093
42093
31567
2267
158
017

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.0b
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
45.5b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite747.0ms

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 insert-posit16 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 → 204
Calls
4 calls:
192.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
117.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
243.0ms
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
187.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.7s

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
164.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0))
316.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify1.6s

Counts
216 → 216
Iterations
IterNodes
done2012
22012
11313
0360

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.3b

localize419.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

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-cbrt-cube add-exp-log
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×insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r/
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 368
Calls
4 calls:
289.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
836.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
53.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
112.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series4.1s

Counts
4 → 12
Calls
4 calls:
499.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
127.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
175.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.9s

Counts
380 → 380
Iterations
IterNodes
done2002
22002
11707
0503

prune2.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 32.3b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (* (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
70×times-frac
58×*-un-lft-identity
45×add-cbrt-cube add-exp-log
43×add-sqr-sqrt
42×associate-*l*
40×add-cube-cbrt
16×associate-/r/
15×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
11×flip3-+ flip-+
9×pow1 associate-/r* distribute-lft-out
8×sqrt-div div-inv
7×associate-*r/ associate-/l*
6×associate-/l/
5×frac-times
4×insert-posit16 add-log-exp
3×clear-num frac-2neg pow-prod-down associate-*l/
2×unswap-sqr
1×associate-*r* *-commutative
Counts
4 → 169
Calls
4 calls:
920.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (* (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))))
84.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
176.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
158.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.8s

Counts
4 → 12
Calls
4 calls:
3.4s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (* (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) (sqrt (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))))
143.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
157.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
153.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.5s

Counts
181 → 181
Iterations
IterNodes
done2004
22004
1884
0278

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.3b

localize89.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
32.9b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
33.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
78×*-un-lft-identity
58×add-sqr-sqrt add-cube-cbrt
40×sqrt-prod
24×associate-/r/
22×add-cbrt-cube add-exp-log
16×associate-/r* associate-/l*
15×flip3-+ flip-+
12×div-inv
10×distribute-lft-out
9×cbrt-undiv div-exp
7×associate-/l/
4×pow1 clear-num frac-2neg insert-posit16 add-log-exp
2×sqrt-div prod-exp associate-*r/ cbrt-unprod
Counts
4 → 189
Calls
4 calls:
251.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
69.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
206.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
195.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series1.3s

Counts
4 → 12
Calls
4 calls:
749.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (sqrt (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
142.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
171.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
195.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.6s

Counts
201 → 201
Iterations
IterNodes
done2007
22007
1830
0299

prune2.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 32.3b

regimes271.0ms

Accuracy

43.5% (1.6b remaining)

Error of 35.4b against oracle of 33.8b and baseline of 36.6b

bsearch91.0ms

Steps
ItersRangePoint
7
1.552345887359089e+214
8.527333628447613e+215
1.5767353599681066e+214

simplify8.0ms

Iterations
IterNodes
done41
141
030

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.7s8000×body80valid
438.0ms8000×pre80true