Details

Time bar (total: 36.9s)

sample49.0ms

Algorithm
intervals
Results
20.0ms256×body80valid
6.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01753
15853
228253
3159153
done500053

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.8b

localize34.0ms

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))))
35.2b
(/ (/ (* (* 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))
44.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite865.0ms

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:
109.0ms
(* i (+ (+ alpha beta) i))
167.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
366.0ms
(/ (/ (* (* 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))
213.0ms
(/ (* (* 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:
47.0ms
(* i (+ (+ alpha beta) i))
171.0ms
(* (* 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))
329.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify1.2s

Counts
201 → 201
Iterations

Useful iterations: done (1.2s)

IterNodesCost
034511544
1116510760
done50009674

prune899.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 32.2b

localize23.0ms

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))))
32.7b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.8s

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:
350.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.1s
(* (/ (/ (* 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))))
94.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
180.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.6s

Counts
4 → 12
Calls
4 calls:
449.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
2.9s
(* (/ (/ (* 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))))
108.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
178.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify997.0ms

Counts
376 → 376
Iterations

Useful iterations: done (977.0ms)

IterNodesCost
050121013
1161220455
done500018795

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 32.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
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) (* 2.0 i)) (+ (+ alpha beta) 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))))
32.9b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite2.5s

Algorithm
rewrite-expression-head
Rules
1055×times-frac
808×*-un-lft-identity
588×add-sqr-sqrt
410×add-cube-cbrt
278×associate-*l*
188×distribute-lft-out
96×associate-*r*
67×add-exp-log add-cbrt-cube
64×associate-/r/
62×difference-of-squares
35×cbrt-undiv div-exp
34×div-inv
31×sqrt-prod distribute-lft-out--
30×flip3-+ flip-+
21×associate-/l*
14×associate-/r*
12×prod-exp cbrt-unprod unswap-sqr
6×pow1
5×associate-/l/
4×add-log-exp
3×frac-2neg clear-num
2×flip3-- flip--
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 620
Calls
4 calls:
155.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
424.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.7s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) 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))))
178.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series4.2s

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))
486.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.4s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) 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))))
208.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.6s

Counts
632 → 632
Iterations

Useful iterations: done (1.5s)

IterNodesCost
079335881
1259635339
done500133697

prune2.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
0.0b
(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.0b
(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
0.0b
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
1688×times-frac
1426×*-un-lft-identity
705×add-sqr-sqrt
661×add-cube-cbrt
428×distribute-lft-out
278×associate-*l*
80×associate-/r/
74×associate-/l*
52×add-exp-log add-cbrt-cube
45×div-inv
35×flip3-+ flip-+
30×associate-/r*
26×cbrt-undiv div-exp
24×associate-*r*
8×prod-exp cbrt-unprod unswap-sqr
6×pow1 difference-of-squares
4×add-log-exp
3×frac-2neg clear-num sqrt-prod associate-/l/ distribute-lft-out--
1×frac-times flip3-- associate-*r/ pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 842
Calls
4 calls:
1.2s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
353.0ms
(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
80.0ms
(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
130.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))

series1.3s

Counts
4 → 12
Calls
4 calls:
676.0ms
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* 0.25 alpha) (+ (* 0.5 i) (* 0.25 beta))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
393.0ms
(/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
148.0ms
(/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i)))
110.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))

simplify1.9s

Counts
854 → 854
Iterations

Useful iterations: done (1.8s)

IterNodesCost
081939668
1250338585
done500237431

prune4.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.6b

regimes328.0ms

Accuracy

40.8% (9.6b remaining)

Error of 11.5b against oracle of 1.9b and baseline of 18.1b

bsearch85.0ms

Steps
ItersRangePoint
7
3.091949947182249e+101
1.2621807769510458e+103
1.2436173149267944e+103

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
035112
150112
done50112

end0.0ms

sample1.6s

Algorithm
intervals
Results
981.0ms8000×body80valid
220.0ms8000×pre80true