Details

Time bar (total: 1.1m)

sample68.0ms

Algorithm
intervals
Results
28.0ms256×body80valid
8.0ms256×pre80true

simplify839.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
31753
2282
158
017

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 40.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)
5.6b
(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
30.8b
(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
35.7b
(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

rewrite850.0ms

Algorithm
rewrite-expression-head
Rules
395×times-frac
242×*-un-lft-identity
170×add-sqr-sqrt
144×add-cube-cbrt
52×add-cbrt-cube add-exp-log
51×distribute-lft-out
45×associate-/r/
33×div-inv
26×cbrt-undiv div-exp associate-*l*
25×associate-/l*
21×associate-*l/ difference-of-squares
14×associate-/r*
13×flip3-+ flip-+
8×prod-exp cbrt-unprod
6×pow1
5×associate-/l/
4×add-log-exp
3×clear-num frac-2neg associate-*r*
2×unswap-sqr
1×flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 326
Calls
4 calls:
173.0ms
(* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)
306.0ms
(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
199.0ms
(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
138.0ms
(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

series1.3s

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)
495.0ms
(/ (/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha)) (/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i)))
445.0ms
(/ (- (* (+ (+ (* 2.0 i) beta) alpha) (+ (+ (* 2.0 i) beta) alpha)) 1.0) (* (/ (+ (+ alpha beta) i) (+ (+ (* 2.0 i) beta) alpha)) i))
194.0ms
(/ (+ (* (+ (+ alpha beta) i) i) (* beta alpha)) (+ (+ (* 2.0 i) beta) alpha))

simplify888.0ms

Counts
338 → 338
Iterations
IterNodes
done5001
11740
0536

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 35.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
0.3b
(* (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0)))))) (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i)))
35.7b
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))
35.7b
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

rewrite12.5s

Algorithm
rewrite-expression-head
Rules
12647×times-frac
9655×*-un-lft-identity
4735×add-sqr-sqrt
4338×add-cube-cbrt
3430×sqrt-prod
2885×distribute-lft-out
1748×associate-*l*
680×associate-/r/
404×associate-*r*
384×div-inv
319×flip3-+ flip-+
91×associate-/r*
71×add-cbrt-cube add-exp-log
70×unswap-sqr
63×distribute-lft-out--
38×cbrt-undiv div-exp
27×associate-/l*
12×prod-exp cbrt-unprod
6×pow1
5×associate-/l/
4×add-log-exp
3×clear-num frac-2neg
1×frac-times sqrt-div pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 4193
Calls
4 calls:
331.0ms
(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
11.1s
(* (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0)))))) (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i)))
100.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))
95.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

series4.8s

Counts
4 → 12
Calls
4 calls:
843.0ms
(/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0))))))
3.6s
(* (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ (* i 2.0) (+ beta (+ alpha (sqrt 1.0)))) (/ (+ beta (+ alpha i)) (+ alpha (+ beta (* i 2.0)))))) (/ (sqrt (/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))) (/ (+ alpha (- (+ beta (* i 2.0)) (sqrt 1.0))) i)))
167.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))
170.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

simplify2.2s

Counts
4205 → 4205
Iterations
IterNodes
done5001
03113

prune30.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 35.2b

localize94.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (sqrt (+ (+ alpha beta) (* i 2.0))))
35.6b
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
35.6b
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
35.7b
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
48×sqrt-prod
45×times-frac
44×add-sqr-sqrt
42×*-un-lft-identity add-cube-cbrt
9×associate-/r* associate-/l*
8×add-cbrt-cube sqrt-div add-exp-log
6×pow1 flip3-+ flip-+
4×associate-/r/ add-log-exp associate-/l/
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
1×sqrt-undiv
Counts
4 → 126
Calls
4 calls:
101.0ms
(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (sqrt (+ (+ alpha beta) (* i 2.0))))
48.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
29.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
98.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))

series769.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(/ (sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta))) (sqrt (+ (+ alpha beta) (* i 2.0))))
190.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
226.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
149.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ (+ alpha beta) (* i 2.0)))

simplify1.2s

Counts
138 → 138
Iterations
IterNodes
done5000
22591
1499
0209

prune2.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 35.2b

localize116.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (+ alpha beta) (* i 2.0))) (cbrt (+ (+ alpha beta) (* i 2.0))))
35.6b
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
35.6b
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
35.7b
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
31×*-un-lft-identity
23×add-cube-cbrt
16×cbrt-prod
13×pow1
12×cbrt-div times-frac
10×flip3-+ flip-+
8×add-exp-log
6×add-cbrt-cube pow1/3 swap-sqr associate-*r* associate-*l* sqrt-prod
4×frac-times associate-/r* sqrt-div distribute-lft-out add-log-exp unswap-sqr
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ associate-/r/ pow-sqr pow-prod-up associate-/l/
1×pow2 cbrt-undiv clear-num frac-2neg pow-plus div-exp prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 113
Calls
4 calls:
148.0ms
(* (cbrt (+ (+ alpha beta) (* i 2.0))) (cbrt (+ (+ alpha beta) (* i 2.0))))
54.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
29.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
86.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

series910.0ms

Counts
4 → 12
Calls
4 calls:
344.0ms
(* (cbrt (+ (+ alpha beta) (* i 2.0))) (cbrt (+ (+ alpha beta) (* i 2.0))))
217.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
190.0ms
(sqrt (+ (* i (+ beta (+ alpha i))) (* alpha beta)))
159.0ms
(/ (+ (* i (+ beta (+ alpha i))) (* alpha beta)) (+ alpha (+ beta (* i 2.0))))

simplify1.1s

Counts
125 → 125
Iterations
IterNodes
done5001
22767
1537
0208

prune1.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 35.2b

regimes292.0ms

Accuracy

34.3% (2.5b remaining)

Error of 36.5b against oracle of 33.9b and baseline of 37.8b

bsearch1.0ms

Steps
ItersRangePoint
0
7.857719149395794e+212
8.267328660381287e+212
8.06252390488854e+212

simplify11.0ms

Iterations
IterNodes
done79
379
275
171
051

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s8000×body80valid
264.0ms8000×pre80true