Details

Time bar (total: 41.3s)

sample97.0ms

Algorithm
intervals
Results
55.0ms256×body80valid
15.0ms256×pre80true

simplify4.7s

Counts
1 → 1
Iterations
IterNodes
412205
31883
2352
192
017

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.0b

localize67.0ms

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))))
37.1b
(/ (/ (* (* 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))
44.5b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
61×add-cbrt-cube add-exp-log
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 insert-posit16 add-log-exp
3×distribute-lft-out
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in *-commutative
1×flip3-- flip-- unswap-sqr
Counts
4 → 193
Calls
4 calls:
47.0ms
(* i (+ (+ alpha beta) i))
98.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
201.0ms
(/ (/ (* (* 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))
155.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
25.0ms
(* i (+ (+ alpha beta) i))
153.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.0s
(/ (/ (* (* 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))
283.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.6s

Counts
205 → 205
Iterations
IterNodes
28453
11826
0351

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 36.1b

localize62.0ms

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))))
36.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite1.2s

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:
258.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
721.0ms
(* (/ (/ (* 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))))
86.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
123.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.8s

Counts
4 → 12
Calls
4 calls:
458.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.0s
(* (/ (/ (* 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))))
134.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
191.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify1.2s

Counts
380 → 380
Iterations
IterNodes
12579
0503

prune6.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.0b

localize65.0ms

Local error

Found 4 expressions with local error:

36.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
37.6b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
15×add-cbrt-cube add-exp-log
12×associate-/r*
10×associate-/l*
8×flip3-+ associate-/r/ flip-+ associate-/l/
5×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg insert-posit16 div-inv add-log-exp
2×associate-*r/
1×prod-exp cbrt-unprod
Counts
4 → 122
Calls
4 calls:
70.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
132.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
155.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
142.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series634.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
169.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
157.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
183.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify616.0ms

Counts
134 → 134
Iterations
IterNodes
22047
1594
0126

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 36.0b

localize130.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
36.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
37.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
37.5b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
221×times-frac
201×*-un-lft-identity
111×add-sqr-sqrt
109×add-cube-cbrt
106×sqrt-prod
46×distribute-lft-out
23×associate-/l*
16×add-exp-log
14×add-cbrt-cube
8×associate-/r* div-inv
7×div-exp
6×pow1
5×cbrt-undiv flip3-+ flip-+
4×sqrt-div associate-/r/ insert-posit16 add-log-exp
3×associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r/
1×1-exp prod-exp cbrt-unprod
Counts
4 → 214
Calls
4 calls:
102.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
45.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
18.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
12.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
1.3s
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
155.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
90.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
67.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.5s

Counts
226 → 226
Iterations
IterNodes
23545
11441
0353

prune4.8s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 36.0b

regimes261.0ms

Accuracy

29.9% (2.2b remaining)

Error of 36.5b against oracle of 34.3b and baseline of 37.4b

bsearch103.0ms

Steps
ItersRangePoint
8
3.695319009802177e+172
2.2761401880509482e+175
5.313821326912652e+172

simplify20.0ms

Iterations
IterNodes
237
137
027

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.9s8000×body80valid
429.0ms8000×pre80true