Details

Time bar (total: 18.8s)

sample48.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
5.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01753
15853
228253
3177353
done500053

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.7b
(/ (/ (* (* 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))
45.4b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite895.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-cbrt-cube
58×times-frac
54×flip3-+ flip-+
50×associate-/r/
44×add-sqr-sqrt
36×frac-times
30×associate-*r/
28×add-cube-cbrt *-un-lft-identity
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 add-log-exp
3×swap-sqr
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num *-commutative
1×pow2 flip3-- pow-plus pow-sqr pow-prod-up flip-- unswap-sqr
Counts
4 → 200
Calls
4 calls:
147.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
182.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
334.0ms
(/ (/ (* (* 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))
220.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
127.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.0s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
221.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify742.0ms

Counts
212 → 212
Iterations

Useful iterations: done (727.0ms)

IterNodesCost
035812169
1133511471
done500210171

prune925.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
0.3b
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
37.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite883.0ms

Algorithm
rewrite-expression-head
Rules
216×times-frac
163×add-sqr-sqrt
151×*-un-lft-identity
99×add-cube-cbrt
32×associate-/r/ difference-of-squares
28×associate-/l*
25×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
16×associate-/r* sqrt-prod div-inv distribute-lft-out--
11×cbrt-undiv div-exp
10×distribute-lft-out
6×associate-/l/
4×pow1 frac-2neg clear-num add-log-exp
2×associate-*r/ prod-exp cbrt-unprod
1×flip3-- flip--
Counts
4 → 252
Calls
4 calls:
344.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
248.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
93.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
182.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
384.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
388.0ms
(/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
140.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
159.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify554.0ms

Counts
264 → 264
Iterations

Useful iterations: done (530.0ms)

IterNodesCost
039811487
1115611156
done500010706

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 36.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
37.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
37.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite513.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
70×*-un-lft-identity
45×sqrt-prod
44×add-sqr-sqrt add-cube-cbrt
18×add-exp-log associate-/r/ add-cbrt-cube
17×associate-/l*
13×associate-/r* distribute-lft-out
12×flip3-+ flip-+
9×div-inv
7×associate-/l/
6×cbrt-undiv div-exp
4×pow1 frac-2neg associate-*r/ clear-num add-log-exp
2×prod-exp cbrt-unprod
1×sqrt-div
Counts
4 → 160
Calls
4 calls:
195.0ms
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
75.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
78.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
158.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series701.0ms

Counts
4 → 12
Calls
4 calls:
308.0ms
(/ (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
120.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
130.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
143.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify1.9s

Counts
172 → 172
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02725622
16585333
235095071
done50005065

prune999.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 36.6b

localize61.0ms

Local error

Found 4 expressions with local error:

37.6b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
38.9b
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.9b
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
38.9b
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×cbrt-div
5×flip3-+ flip-+
4×pow1 add-log-exp
3×times-frac pow1/3 associate-/r*
2×cbrt-undiv associate-*r/ div-exp associate-/r/ associate-/l/
1×frac-2neg prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 64
Calls
4 calls:
101.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
6.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
5.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
5.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series969.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
274.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
290.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
295.0ms
(cbrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01241584
13861522
220561375
done50001359

prune567.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 36.6b

regimes205.0ms

Accuracy

3.2% (3.7b remaining)

Error of 38.3b against oracle of 34.5b and baseline of 38.4b

bsearch221.0ms

Steps
ItersRangePoint
2
2.9890207141089673e+150
3.2088919848491803e+150
3.1814080760066536e+150
8
5.522922348167397e+137
5.889816599354321e+140
2.677113738334714e+139
7
1.1669666060540711e+85
2.123166983468196e+86
1.980179602823052e+86

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
039184
149184
done49184

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s8000×body80valid
312.0ms8000×pre80true