Details

Time bar (total: 14.2s)

sample34.0ms

Algorithm
intervals
Results
8.0ms207×body80valid
7.0ms256×pre80true
3.0ms17×body1280valid
2.0ms13×body640valid
1.0ms13×body320valid
0.0ms6×body160valid

simplify545.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210129
340829
4143729
done500029

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
90.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
295.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series583.0ms

Counts
3 → 9
Calls
3 calls:
232.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
271.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify943.0ms

Counts
120 → 120
Iterations

Useful iterations: 2 (317.0ms)

IterNodesCost
02254035
16773821
230773577
done50003577

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.8b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite687.0ms

Algorithm
rewrite-expression-head
Rules
603×times-frac
484×*-un-lft-identity
408×add-sqr-sqrt
260×add-cube-cbrt
219×sqrt-prod
153×associate-*r*
67×distribute-lft-out
45×distribute-lft-out-- difference-of-squares
38×associate-/r/
34×associate-*l*
32×add-exp-log add-cbrt-cube
25×associate-/l*
21×flip3-+ flip-+
19×div-inv
15×unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 485
Calls
4 calls:
391.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
97.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
70.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
90.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
420.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
225.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
137.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
277.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify689.0ms

Counts
497 → 497
Iterations

Useful iterations: done (667.0ms)

IterNodesCost
056820612
1173219182
done500118202

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(/ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.3b
(+ (/ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite659.0ms

Algorithm
rewrite-expression-head
Rules
111×*-un-lft-identity
85×times-frac
76×add-sqr-sqrt
51×add-cube-cbrt
46×sqrt-prod
36×add-exp-log add-cbrt-cube
34×associate-*l*
27×distribute-lft-out
21×associate-*r*
14×cbrt-undiv div-exp associate-/r*
8×prod-exp associate-/r/ cbrt-unprod
6×pow1 flip3-+ sqrt-div flip-+ add-log-exp unswap-sqr
5×associate-/l/ associate-/l*
4×div-inv
3×distribute-lft-out-- difference-of-squares
2×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
1×+-commutative pow-prod-down sum-log *-commutative
Counts
4 → 188
Calls
4 calls:
190.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
112.0ms
(/ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
70.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
277.0ms
(+ (/ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series952.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
231.0ms
(/ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
139.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
277.0ms
(+ (/ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.1s

Counts
200 → 200
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03166936
19176442
235715443
done50005441

prune543.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
0.4b
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
8.3b
(+ (* (* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite828.0ms

Algorithm
rewrite-expression-head
Rules
412×times-frac
332×*-un-lft-identity
323×add-sqr-sqrt
254×sqrt-prod
186×add-cube-cbrt
46×associate-*r*
43×distribute-lft-out
36×associate-*l*
35×add-exp-log
28×unswap-sqr
24×associate-/r/ associate-/l* distribute-lft-out-- difference-of-squares
23×add-cbrt-cube
17×associate-/r*
14×sqrt-div
13×flip3-+ div-exp flip-+
12×div-inv
9×pow1
8×cbrt-undiv prod-exp
6×add-log-exp
5×pow-flip
4×sqrt-pow1 cbrt-unprod
3×rec-exp 1-exp
2×frac-2neg pow1/2 div-sub clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative associate-/l/ inv-pow
Counts
4 → 403
Calls
4 calls:
98.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
293.0ms
(* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
67.0ms
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
344.0ms
(+ (* (* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series824.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
142.0ms
(* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
179.0ms
(/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
282.0ms
(+ (* (* (/ 1 (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) (/ (+ alpha beta) (sqrt (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify676.0ms

Counts
415 → 415
Iterations

Useful iterations: done (654.0ms)

IterNodesCost
059116301
1157414987
done500114018

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

regimes194.0ms

Accuracy

17% (5.4b remaining)

Error of 11.0b against oracle of 5.5b and baseline of 12.1b

bsearch71.0ms

Steps
ItersRangePoint
7
1.4116812876132222e+209
2.791389625835243e+210
1.5371929371909745e+209

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
034143
141143
done41143

end0.0ms

sample806.0ms

Algorithm
intervals
Results
247.0ms6387×body80valid
130.0ms8000×pre80true
104.0ms532×body1280valid
84.0ms529×body640valid
39.0ms341×body320valid
16.0ms211×body160valid