Details

Time bar (total: 25.4s)

sample38.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
9.0ms256×pre80true

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01435
13335
211035
348235
4240035
done500135

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.4b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
804×times-frac
584×*-un-lft-identity
340×add-sqr-sqrt add-cube-cbrt
122×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 463
Calls
4 calls:
7.0ms
(+ (+ alpha beta) (* beta alpha))
22.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
20.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series67.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (+ alpha beta) (* beta alpha))
26.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
24.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify589.0ms

Counts
475 → 475
Iterations

Useful iterations: done (558.0ms)

IterNodesCost
060525900
1151125129
done500024972

prune1.3s

Filtered
283 candidates to 475 candidates (-67.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New4669475
Fresh000
Picked101
Done000
Total4679476

Merged error: 0.5b

Counts
476 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
243×times-frac
191×*-un-lft-identity
154×add-sqr-sqrt
124×add-cube-cbrt
60×associate-*l*
54×add-exp-log
34×add-cbrt-cube
32×distribute-lft-out
25×associate-/l*
24×div-exp associate-/r/
18×associate-*r*
14×cbrt-undiv
13×flip3-+ flip-+
12×prod-exp div-inv
10×associate-/r*
9×unswap-sqr
7×pow1
6×cbrt-unprod
4×rec-exp 1-exp add-log-exp
3×frac-2neg clear-num associate-/l/
1×frac-times pow-flip associate-*r/ pow-prod-down associate-*l/ un-div-inv *-commutative inv-pow
Counts
4 → 282
Calls
4 calls:
10.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
22.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
52.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series69.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
22.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
28.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.5s

Counts
294 → 294
Iterations

Useful iterations: 2 (809.0ms)

IterNodesCost
036911010
1113510514
235989455
done50009455

prune702.0ms

Filtered
192 candidates to 294 candidates (-53.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2940294
Fresh088
Picked011
Done000
Total2949303

Merged error: 0.5b

Counts
303 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.2b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite432.0ms

Algorithm
rewrite-expression-head
Rules
1471×times-frac
1040×*-un-lft-identity
673×add-sqr-sqrt
627×sqrt-prod
590×add-cube-cbrt
258×associate-*r*
225×distribute-lft-out
88×associate-/r/
71×associate-/l*
63×associate-*l*
46×flip3-+ flip-+
44×div-inv
20×unswap-sqr
15×add-exp-log add-cbrt-cube
10×associate-/r*
6×pow1
5×associate-/l/
4×cbrt-undiv div-exp add-log-exp
3×frac-2neg sqrt-div clear-num
2×prod-exp cbrt-unprod
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 761
Calls
4 calls:
41.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
271.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
16.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
17.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series80.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
26.0ms
(* (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (/ (sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
13.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.4s

Counts
773 → 773
Iterations

Useful iterations: done (1.3s)

IterNodesCost
090748746
1195246528
done500046441

prune5.0s

Filtered
466 candidates to 773 candidates (-65.9%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New7730773
Fresh077
Picked011
Done011
Total7739782

Merged error: 0.5b

Counts
782 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.0b
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.1b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite739.0ms

Algorithm
rewrite-expression-head
Rules
3775×times-frac
2447×*-un-lft-identity
1680×add-sqr-sqrt
1505×add-cube-cbrt
1316×sqrt-prod
606×associate-*r*
471×distribute-lft-out
150×associate-/l*
78×associate-/r/
60×sqrt-div
48×associate-*l*
45×add-exp-log add-cbrt-cube
41×flip3-+ flip-+
39×div-inv
35×unswap-sqr
22×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
4×associate-/r* add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 1522
Calls
4 calls:
69.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
459.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
8.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
9.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series123.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
26.0ms
(* (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (/ (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
10.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
11.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify3.4s

Counts
1534 → 1534
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01334100799
1426893325
done500192533

prune7.3s

Filtered
617 candidates to 1534 candidates (-148.6%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New153401534
Fresh066
Picked011
Done022
Total153491543

Merged error: 0.5b

Counts
1543 → 9

regimes149.0ms

Accuracy

49.7% (1.3b remaining)

Error of 2.3b against oracle of 1.0b and baseline of 3.6b

bsearch18.0ms

Steps
ItersRangePoint
7
7.177480459497802e+164
8.235032861842214e+166
1.892887342950917e+165

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02974
14274
done4274

end0.0ms

sample895.0ms

Algorithm
intervals
Results
517.0ms8000×body80valid
131.0ms8000×pre80true

Profiling

Loading profile data...