Details

Time bar (total: 13.0s)

sample30.0ms

Algorithm
intervals
Results
9.0ms59×body640valid
5.0ms133×body80valid
4.0ms34×body320valid
4.0ms19×body1280valid
1.0ms11×body160valid

simplify6.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
11815
23115
34115
45215
55915
67515
79615
812015
913815
1014515
1115015
1216015
1316715
1417215
1518215
1618915
1719415
1820415
1921115
2021615
2122615
2223315
2323815
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2928215
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3129915
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3432115
3532615
3633615
3734315
3834815
3935815
4036515
4137015
4238015
4338715
4439215
4540215
4640915
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4943115
5043615
5144615
5245315
5345815
5446815
5547515
5648015
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5849715
5950215
6051215
6151915
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6353415
6454115
6554615
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6856815
6957815
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482360415
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485362615
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487364315
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493368715
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500373615
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502375315
503375815
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506378015
507379015
508379715
509380215
510381215
511381915
512382415
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514384115
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530395615
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536400015
537401015
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544406115
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553412715
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557415415
558416415
559417115
560417615
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564420815
565421515
566422015
567423015
568423715
569424215
570425215
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625465515
626466015
627467015
628467715
629468215
630469215
631469915
632470415
633471415
634472115
635472615
636473615
637474315
638474815
639475815
640476515
641477015
642478015
643478715
644479215
645480215
646480915
647481415
648482415
649483115
650483615
651484615
652485315
653485815
654486815
655487515
656488015
657489015
658489715
659490215
660491215
661491915
662492415
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664494115
665494615
666495615
667496315
668496815
669497815
670498515
671499015
done500015

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 9.9b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (+ x 1.0))
2.1b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
associate-/r*
add-exp-log add-cbrt-cube difference-of-squares
associate-/l*
pow1 associate-/r/
flip3-- frac-add flip--
cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
6.0ms
(/ 1.0 (- x 1.0))
20.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
6.0ms
(/ 1.0 (+ x 1.0))
35.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series20.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 1.0 (- x 1.0))
4.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.0ms
(/ 1.0 (+ x 1.0))
11.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify941.0ms

Counts
126 → 126
Iterations

Useful iterations: 3 (423.0ms)

IterNodesCost
02121832
15051716
214671630
345091608
done50001608

prune221.0ms

Filtered
92 candidates to 126 candidates (-37.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1224126
Fresh000
Picked101
Done000
Total1234127

Merged error: 0.5b

Counts
127 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
0.3b
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
2.1b
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
12.7b
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
340×*-un-lft-identity
225×times-frac
176×add-sqr-sqrt
150×frac-sub
101×distribute-lft-out--
94×frac-times
65×add-cube-cbrt
64×flip3-- flip--
52×associate-*r/ associate-*l/
51×difference-of-squares
47×associate-/l/
41×swap-sqr
31×associate-*r* associate-*l*
20×add-exp-log add-cbrt-cube
18×pow1
16×distribute-lft-out
13×associate-/r/
11×associate-/r*
add-log-exp
cbrt-undiv sub-neg div-exp prod-exp cbrt-unprod div-inv unswap-sqr
distribute-rgt-in distribute-lft-in associate--l+ associate-/l*
pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
frac-2neg diff-log div-sub clear-num
Counts
4 → 352
Calls
4 calls:
21.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
45.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
45.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
81.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
8.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
13.0ms
(- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0))))
34.0ms
(/ (- (* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x))) (* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))) (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))

simplify496.0ms

Counts
364 → 364
Iterations

Useful iterations: done (477.0ms)

IterNodesCost
057416482
1168115203
done500114485

prune1.8s

Filtered
227 candidates to 364 candidates (-60.4%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3631364
Fresh033
Picked011
Done000
Total3635368

Merged error: 0.5b

Counts
368 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.2b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
1.6b
(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
14.8b
(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
add-cube-cbrt add-log-exp
pow1
associate-*l* associate-*l/
flip3-+ times-frac associate-*r* flip-+ associate-/l*
cbrt-undiv flip3-- div-sub div-exp prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/ distribute-lft-out
+-commutative associate-+l- sub-neg frac-2neg diff-log pow-prod-down frac-add clear-num associate-/r* sum-log *-commutative div-inv unswap-sqr
Counts
4 → 73
Calls
4 calls:
6.0ms
(* (+ x 1.0) x)
4.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
21.0ms
(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
10.0ms
(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

series28.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* (+ x 1.0) x)
4.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
14.0ms
(+ (/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x)) (/ 1.0 (- x 1.0)))
5.0ms
(/ (- (* 1.0 x) (* (+ x 1.0) 2.0)) (* (+ x 1.0) x))

simplify532.0ms

Counts
85 → 85
Iterations

Useful iterations: done (530.0ms)

IterNodesCost
01531549
14621479
217801111
done50001105

prune130.0ms

Filtered
64 candidates to 85 candidates (-32.8%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New85085
Fresh033
Picked011
Done011
Total85590

Merged error: 0.5b

Counts
90 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (pow x 7)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))))
0.1b
(/ 2.0 (pow x 5))
0.1b
(/ 2.0 (pow x 7))
0.6b
(/ 2.0 (pow x 3))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
78×*-un-lft-identity
64×add-sqr-sqrt add-cube-cbrt
36×unpow-prod-down
26×associate-/r*
19×add-exp-log
12×cube-prod sqr-pow
11×distribute-lft-out
10×add-cbrt-cube
div-exp associate-/l* add-log-exp
div-inv
pow1 cube-mult unpow3 frac-add
cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num sum-log
flip3-+ flip-+
+-commutative associate-+r+
Counts
4 → 177
Calls
4 calls:
63.0ms
(+ (/ 2.0 (pow x 7)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))))
5.0ms
(/ 2.0 (pow x 5))
5.0ms
(/ 2.0 (pow x 7))
8.0ms
(/ 2.0 (pow x 3))

series21.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (/ 2.0 (pow x 7)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))))
5.0ms
(/ 2.0 (pow x 5))
6.0ms
(/ 2.0 (pow x 7))
4.0ms
(/ 2.0 (pow x 3))

simplify522.0ms

Counts
189 → 189
Iterations

Useful iterations: 2 (176.0ms)

IterNodesCost
02862461
16402164
220732074
done50002074

prune369.0ms

Filtered
122 candidates to 189 candidates (-54.9%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New1863189
Fresh112
Picked011
Done022
Total1877194

Merged error: 0.0b

Counts
194 → 7

regimes59.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 26.0b

bsearch30.0ms

Steps
ItersRangePoint
9
0.009971872296741319
901.3230478674768
128.9853277188641
9
-174458.2165831976
-0.46594774775336223
-111.66855799925936

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02967
13949
done3949

end0.0ms

sample882.0ms

Algorithm
intervals
Results
292.0ms1823×body640valid
180.0ms4225×body80valid
105.0ms546×body1280valid
105.0ms908×body320valid
39.0ms500×body160valid

Profiling

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