Details

Time bar (total: 47.6s)

sample52.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
8.0ms256×pre80true

simplify4.1s

Counts
1 → 1
Iterations
IterNodes
411034
31567
2267
158
017

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize36.0ms

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))))
34.9b
(/ (/ (* (* 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))
46.2b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

rewrite651.0ms

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:
132.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
121.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
244.0ms
(/ (/ (* (* 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))
150.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))
151.0ms
(* (* 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))
248.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))))

simplify3.3s

Counts
216 → 216
Iterations
IterNodes
27459
11304
0360

prune3.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 34.5b

localize53.0ms

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))))
34.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b
(/ (+ (* 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:
252.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
771.0ms
(* (/ (/ (* 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))))
61.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
125.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series3.9s

Counts
4 → 12
Calls
4 calls:
439.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))
3.1s
(* (/ (/ (* 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))))
128.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
154.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify4.7s

Counts
380 → 380
Iterations
IterNodes
27081
11692
0503

prune6.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 34.4b

localize115.0ms

Local error

Found 4 expressions with local error:

34.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
34.8b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

rewrite568.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
18×add-cbrt-cube add-exp-log
12×associate-/r*
8×flip3-+ associate-/r/ flip-+ associate-/l* associate-/l/
6×cbrt-undiv div-exp
4×pow1 clear-num frac-2neg associate-*r/ insert-posit16 div-inv add-log-exp
2×prod-exp cbrt-unprod
Counts
4 → 116
Calls
4 calls:
94.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
70.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
213.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
189.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

series558.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
116.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
153.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))
141.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))

simplify3.6s

Counts
128 → 128
Iterations
IterNodes
39537
21579
1366
0126

prune3.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 34.4b

localize72.0ms

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))))
34.5b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
34.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
34.7b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite224.0ms

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:
115.0ms
(/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (+ (sqrt (+ (+ alpha beta) (* 2 i))) (sqrt (sqrt 1.0))))
86.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
7.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series1.7s

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))))
126.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i)))
88.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
105.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.4s

Counts
226 → 226
Iterations
IterNodes
22802
1895
0353

prune4.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 34.4b

regimes229.0ms

Accuracy

0% (2.6b remaining)

Error of 36.4b against oracle of 33.8b and baseline of 36.4b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
234
134
025

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.7s8000×body80valid
396.0ms8000×pre80true