Details

Time bar (total: 26.5s)

sample56.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
7.0ms256×pre80true

simplify918.0ms

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: 53.5b

localize25.0ms

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))))
38.4b
(/ (/ (* (* 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))
45.3b
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

rewrite847.0ms

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:
210.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
154.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
296.0ms
(/ (/ (* (* 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))
178.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

series1.6s

Counts
4 → 12
Calls
4 calls:
73.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
145.0ms
(* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
1.1s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
250.0ms
(/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))))

simplify627.0ms

Counts
212 → 212
Iterations

Useful iterations: done (615.0ms)

IterNodesCost
035812169
1133511471
done500210171

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 35.8b

localize48.0ms

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))))
35.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.9s

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:
434.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
1.2s
(* (/ (/ (* 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))))
96.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
221.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.8s

Counts
4 → 12
Calls
4 calls:
442.0ms
(/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.1s
(* (/ (/ (* 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))))
122.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
180.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify837.0ms

Counts
376 → 376
Iterations

Useful iterations: done (816.0ms)

IterNodesCost
050121013
1178520471
done500118911

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 35.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
35.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
36.0b
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
25×times-frac
24×associate-*r*
23×add-cube-cbrt *-un-lft-identity sqrt-prod
14×add-exp-log add-cbrt-cube
8×pow1 sqrt-div
7×flip3-+ flip-+
6×associate-*l* unswap-sqr
4×associate-/r/ add-log-exp
3×cbrt-undiv associate-*r/ div-exp prod-exp associate-/r* cbrt-unprod
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ div-inv associate-/l/
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 109
Calls
4 calls:
130.0ms
(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
94.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
26.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
13.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

series434.0ms

Counts
4 → 12
Calls
4 calls:
186.0ms
(* (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))
114.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
66.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))
68.0ms
(sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i))))

simplify1.7s

Counts
121 → 121
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01903629
15883381
234952793
done50002684

prune519.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 35.8b

localize46.0ms

Local error

Found 4 expressions with local error:

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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
0.2b
(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
35.4b
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
36.1b
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
215×add-exp-log
125×add-cbrt-cube
94×times-frac
88×div-exp
86×prod-exp
78×add-sqr-sqrt
75×*-un-lft-identity
57×associate-*l*
49×add-cube-cbrt
48×cbrt-undiv
46×cbrt-unprod
25×associate-*r*
18×associate-/r/
11×pow1
10×rec-exp flip3-+ 1-exp flip-+
9×associate-*r/ div-inv distribute-lft-out
7×frac-times
6×associate-/r* difference-of-squares unswap-sqr
4×pow-prod-down associate-*l/ associate-/l/ associate-/l* add-log-exp
3×sqrt-prod un-div-inv distribute-lft-out--
2×frac-2neg clear-num *-commutative
1×flip3-- flip--
Counts
4 → 244
Calls
4 calls:
871.0ms
(* (/ (/ (* 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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
478.0ms
(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
96.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
169.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

series3.9s

Counts
4 → 12
Calls
4 calls:
3.1s
(* (/ (/ (* 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))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))))
451.0ms
(* (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (/ 1 (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
128.0ms
(/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))
170.0ms
(/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))

simplify891.0ms

Counts
256 → 256
Iterations

Useful iterations: done (875.0ms)

IterNodesCost
041213918
1149013252
done500010473

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 35.8b

regimes221.0ms

Accuracy

37.4% (2.2b remaining)

Error of 36.8b against oracle of 34.5b and baseline of 38.1b

bsearch81.0ms

Steps
ItersRangePoint
7
4.208907867440382e+224
1.6005123975973089e+226
4.284299083279605e+224

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
030110
140110
done40110

end0.0ms

sample2.1s

Algorithm
intervals
Results
936.0ms8000×body80valid
744.0ms8000×pre80true