Details

Time bar (total: 8.2s)

sample29.0ms

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

simplify73.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
11815
23115
34115
45215
55915
66815
78615
810715
911715
done11715

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

localize12.0ms

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)))

rewrite65.0ms

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
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
6.0ms
(/ 1.0 (- x 1.0))
18.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
6.0ms
(/ 1.0 (+ x 1.0))
31.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series22.0ms

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))
14.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.8s

Counts
126 → 126
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02121832
14961716
212801630
337311608
done50001607

prune219.0ms

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))))

rewrite212.0ms

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*
6×add-log-exp
5×cbrt-undiv sub-neg div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×distribute-rgt-in distribute-lft-in associate--l+ associate-/l*
2×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up
1×frac-2neg diff-log div-sub clear-num
Counts
4 → 352
Calls
4 calls:
23.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
39.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
44.0ms
(- (* (- (/ 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))))
80.0ms
(/ (- (* (- (/ 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))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ 1.0 (- x 1.0)) (/ 1.0 (- x 1.0)))
4.0ms
(* (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))
12.0ms
(- (* (- (/ 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))))
33.0ms
(/ (- (* (- (/ 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))))

simplify593.0ms

Counts
364 → 364
Iterations

Useful iterations: done (568.0ms)

IterNodesCost
057416482
1164615203
done500214467

prune1.7s

Filtered
225 candidates to 364 candidates (-61.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3631364
Fresh033
Picked011
Done000
Total3635368

Merged error: 0.5b

Counts
368 → 5

localize11.0ms

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))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×pow1
4×associate-*l* associate-*l/
3×flip3-+ times-frac associate-*r* flip-+ associate-/l*
2×cbrt-undiv flip3-- div-sub div-exp prod-exp associate-/r/ flip-- cbrt-unprod associate-/l/ distribute-lft-out
1×+-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))
25.0ms
(+ (/ (- (* 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))

simplify1.0s

Counts
85 → 85
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01531549
14581479
216531111
done50001101

prune126.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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
9×div-exp associate-/l* add-log-exp
6×div-inv
4×pow1 cube-mult unpow3 frac-add
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num sum-log
2×flip3-+ flip-+
1×+-commutative associate-+r+
Counts
4 → 177
Calls
4 calls:
60.0ms
(+ (/ 2.0 (pow x 5)) (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 7))))
5.0ms
(/ 2.0 (pow x 5))
5.0ms
(/ 2.0 (pow x 7))
6.0ms
(/ 2.0 (pow x 3))

series21.0ms

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

simplify737.0ms

Counts
189 → 189
Iterations

Useful iterations: 2 (325.0ms)

IterNodesCost
02862461
16292164
218362074
done50012074

prune355.0ms

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

regimes57.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch28.0ms

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

sample835.0ms

Algorithm
intervals
Results
274.0ms1823×body640valid
168.0ms4225×body80valid
105.0ms908×body320valid
104.0ms546×body1280valid
37.0ms500×body160valid

Profiling

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