Details

Time bar (total: 9.8s)

sample52.0ms

Algorithm
intervals
Results
17.0ms202×body80valid
6.0ms256×pre80true
5.0ms20×body640valid
4.0ms12×body1280valid
2.0ms9×body320valid
2.0ms13×body160valid

simplify500.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
13129
210129
341329
4145529
done500129

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 22.3b

Counts
2 → 1

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
3.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.2b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite75.0ms

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:
22.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
16.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series181.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
90.0ms
(+ (/ (/ (* (+ 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)))

simplify755.0ms

Counts
120 → 120
Iterations

Useful iterations: done (750.0ms)

IterNodesCost
02254035
16953842
232733598
done50003577

prune495.0ms

Filtered
89 candidates to 120 candidates (-34.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1119120
Fresh000
Picked101
Done000
Total1129121

Merged error: 6.3b

Counts
121 → 9

localize16.0ms

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)))
8.6b
(+ (* (/ (+ 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)

rewrite250.0ms

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:
124.0ms
(* (/ (+ 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))))
24.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
45.0ms
(+ (* (/ (+ 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)

series253.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (/ (+ 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))))
49.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
41.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
94.0ms
(+ (* (/ (+ 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)

simplify477.0ms

Counts
497 → 497
Iterations

Useful iterations: done (448.0ms)

IterNodesCost
057620636
1177119444
done500018834

prune1.3s

Filtered
273 candidates to 497 candidates (-82.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4934497
Fresh358
Picked101
Done000
Total4979506

Merged error: 6.3b

Counts
506 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1 (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
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.0b
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
8.8b
(+ (* (+ alpha beta) (* (/ 1 (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)

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
344×times-frac
273×add-sqr-sqrt
251×*-un-lft-identity
154×associate-*r*
141×add-cube-cbrt
132×sqrt-prod
100×add-exp-log
56×add-cbrt-cube
38×div-exp
37×prod-exp
31×associate-*l*
29×distribute-lft-out
25×unswap-sqr
21×distribute-lft-out-- difference-of-squares
20×associate-/r/
19×cbrt-undiv cbrt-unprod
15×flip3-+ flip-+
13×pow1
10×frac-times div-inv
7×rec-exp 1-exp associate-*r/ associate-/r*
6×sqrt-div associate-*l/ add-log-exp
4×pow-prod-down
3×pow-flip associate-/l*
2×*-commutative
1×+-commutative frac-2neg sqrt-pow1 pow1/2 clear-num sum-log inv-pow
Counts
4 → 343
Calls
4 calls:
111.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
13.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
53.0ms
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
46.0ms
(+ (* (+ alpha beta) (* (/ 1 (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)

series245.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
38.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
70.0ms
(* (+ alpha beta) (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))
94.0ms
(+ (* (+ alpha beta) (* (/ 1 (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)

simplify449.0ms

Counts
355 → 355
Iterations

Useful iterations: done (432.0ms)

IterNodesCost
051614684
1170513488
done500012505

prune842.0ms

Filtered
186 candidates to 355 candidates (-90.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New3532355
Fresh268
Picked011
Done000
Total3559364

Merged error: 6.3b

Counts
364 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ alpha beta) (/ 1 (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
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
8.4b
(+ (* (* (+ alpha beta) (/ 1 (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)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
313×times-frac
261×*-un-lft-identity
211×add-sqr-sqrt
151×add-cube-cbrt
118×sqrt-prod
30×distribute-lft-out
27×associate-*r*
24×associate-/l* distribute-lft-out-- difference-of-squares
22×add-exp-log associate-/r/
16×add-cbrt-cube
14×flip3-+ associate-/r* flip-+
11×div-inv
8×pow1
7×div-exp
6×sqrt-div add-log-exp
5×cbrt-undiv unswap-sqr
4×associate-*l* prod-exp
3×pow-flip
2×frac-times rec-exp frac-2neg 1-exp div-sub associate-*l/ clear-num cbrt-unprod
1×+-commutative sqrt-pow1 pow1/2 associate-*r/ pow-prod-down sum-log un-div-inv *-commutative associate-/l/ inv-pow
Counts
4 → 312
Calls
4 calls:
21.0ms
(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
24.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
12.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
48.0ms
(+ (* (* (+ alpha beta) (/ 1 (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)

series221.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (+ alpha beta) (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
53.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
35.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
93.0ms
(+ (* (* (+ alpha beta) (/ 1 (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)

simplify383.0ms

Counts
324 → 324
Iterations

Useful iterations: done (367.0ms)

IterNodesCost
050511600
1130510805
done500010526

prune792.0ms

Filtered
181 candidates to 324 candidates (-79.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New3213324
Fresh077
Picked011
Done101
Total32211333

Merged error: 6.3b

Counts
333 → 11

regimes638.0ms

Accuracy

73.7% (1.6b remaining)

Error of 7.7b against oracle of 6.1b and baseline of 12.3b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
035131
144131
done44131

end0.0ms

sample1.4s

Algorithm
intervals
Results
407.0ms6367×body80valid
184.0ms8000×pre80true
171.0ms534×body1280valid
136.0ms549×body640valid
61.0ms328×body320valid
30.0ms222×body160valid

Profiling

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