Details

Time bar (total: 32.9s)

sample28.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
4.0ms256×pre80true

simplify640.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01753
15853
228253
3159153
done500053

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (+ (+ alpha beta) i))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.3b
(/ (/ (* (* 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))
46.6b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite569.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
50×associate-/r/
49×flip3-+ flip-+
42×add-sqr-sqrt
32×frac-times
31×*-un-lft-identity
30×associate-*r/
26×add-cube-cbrt
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-*l/
14×associate-/l* difference-of-squares
11×pow1
9×associate-/l/
8×associate-*r*
7×div-inv
5×associate-/r*
4×associate-*l* pow-prod-down add-log-exp
3×distribute-lft-out
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 189
Calls
4 calls:
72.0ms
(* i (+ (+ alpha beta) i))
105.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
237.0ms
(/ (/ (* (* 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:
23.0ms
(* i (+ (+ alpha beta) i))
109.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
855.0ms
(/ (/ (* (* 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))
189.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify714.0ms

Counts
201 → 201
Iterations

Useful iterations: done (705.0ms)

IterNodesCost
034511544
1116510760
done50009674

prune580.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (* 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))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
31.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 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-exp-log add-cbrt-cube
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×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×flip3-- flip--
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 364
Calls
4 calls:
278.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
816.0ms
(* (/ (/ (* 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))))
67.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
136.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts
4 → 12
Calls
4 calls:
335.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.2s
(* (/ (/ (* 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))))
89.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
127.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify652.0ms

Counts
376 → 376
Iterations

Useful iterations: done (631.0ms)

IterNodesCost
050121013
1161220455
done500018795

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
0.1b
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ 1 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
31.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
8237×times-frac
4696×add-sqr-sqrt
3788×*-un-lft-identity
2936×add-cube-cbrt
1240×associate-*r*
810×difference-of-squares
535×add-exp-log
405×sqrt-prod distribute-lft-out--
389×div-inv
383×div-exp
367×associate-/r/
190×add-cbrt-cube
171×flip3-+ flip-+
113×cbrt-undiv
111×prod-exp
101×associate-/r*
75×1-exp
42×associate-*l*
36×cbrt-unprod
32×unswap-sqr
30×rec-exp
17×associate-/l*
9×distribute-lft-out
6×pow1
5×associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 2880
Calls
4 calls:
208.0ms
(/ (/ 1 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
1.6s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ 1 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
67.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
137.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.8s

Counts
4 → 12
Calls
4 calls:
348.0ms
(/ (/ 1 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))
2.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ 1 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
125.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify2.7s

Counts
2892 → 2892
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02815198997
done5000185912

prune7.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 31.1b

localize31.0ms

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))) (sqrt (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))))
31.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
32.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
818×times-frac
549×add-sqr-sqrt
425×*-un-lft-identity
349×sqrt-prod
311×add-cube-cbrt
293×associate-*r*
90×difference-of-squares
56×associate-/r/
45×distribute-lft-out--
42×associate-*l*
30×div-inv
29×flip3-+ flip-+
27×add-exp-log add-cbrt-cube
16×unswap-sqr
9×cbrt-undiv div-exp associate-/r* distribute-lft-out
7×associate-/l*
6×pow1 prod-exp cbrt-unprod associate-/l/
4×add-log-exp
3×frac-2neg associate-*r/ clear-num
2×sqrt-div
1×frac-times pow-prod-down associate-*l/ *-commutative
Counts
4 → 458
Calls
4 calls:
976.0ms
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))))
66.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
132.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
136.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series2.6s

Counts
4 → 12
Calls
4 calls:
2.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (sqrt (/ 1 (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))))))
92.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
127.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))
129.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.2s

Counts
470 → 470
Iterations

Useful iterations: done (1.1s)

IterNodesCost
094627486
1240726075
done500024974

prune2.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 31.1b

regimes157.0ms

Accuracy

35.5% (2.5b remaining)

Error of 36.8b against oracle of 34.3b and baseline of 38.2b

bsearch52.0ms

Steps
ItersRangePoint
7
1.7703642706139512e+221
1.2100692140006563e+223
1.7918517454980545e+221

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
031101
14299
done4299

end0.0ms

sample704.0ms

Algorithm
intervals
Results
333.0ms8000×body80valid
116.0ms8000×pre80true