Details

Time bar (total: 17.8s)

sample31.0ms

Algorithm
intervals
Results
8.0ms46×body1280valid
6.0ms44×body640valid
5.0ms130×body80valid
2.0ms21×body320valid
1.0ms15×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
75813
87913
918313
1053513
11170613
12358413
done500013

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ 1.0 x) (- x 1.0))
3.8b
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
52×times-frac
45×add-sqr-sqrt
23×add-cube-cbrt
18×distribute-lft-out distribute-lft-out--
9×associate-/r* difference-of-squares
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
4×associate-/r/
3×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num flip-- flip-+ div-inv associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 104
Calls
3 calls:
12.0ms
(/ x (+ x 1.0))
29.0ms
(/ (+ 1.0 x) (- x 1.0))
99.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series263.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(/ x (+ x 1.0))
46.0ms
(/ (+ 1.0 x) (- x 1.0))
160.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify1.1s

Counts
113 → 113
Iterations

Useful iterations: 2 (322.0ms)

IterNodesCost
01861584
14481503
219021427
done50001427

prune280.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 1.0 x) (- x 1.0))
0.0b
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0))))
0.0b
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
3.8b
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0))))

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
363×*-un-lft-identity
212×times-frac
109×distribute-lft-out
91×add-sqr-sqrt
69×add-cube-cbrt
25×distribute-lft-out--
24×swap-sqr
20×add-exp-log add-cbrt-cube
19×difference-of-squares
18×associate-*r* associate-*l* frac-sub
17×associate-/r*
13×frac-times associate-*r/ associate-*l/ associate-/r/ associate-/l/
11×pow1
8×associate-/l*
6×cbrt-undiv flip3-+ div-exp flip-+ div-inv add-log-exp
4×prod-exp cbrt-unprod unswap-sqr
3×flip3-- flip--
2×frac-2neg clear-num
1×pow2 sub-neg pow-plus diff-log div-sub pow-prod-down frac-add pow-sqr *-commutative pow-prod-up
Counts
4 → 246
Calls
4 calls:
27.0ms
(/ (+ 1.0 x) (- x 1.0))
208.0ms
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0))))
97.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
30.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0))))

series823.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (+ 1.0 x) (- x 1.0))
423.0ms
(/ (- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0)))) (+ (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0))))
64.0ms
(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
280.0ms
(- (* (/ x (+ x 1.0)) (/ x (+ x 1.0))) (* (/ (+ 1.0 x) (- x 1.0)) (/ (+ 1.0 x) (- x 1.0))))

simplify693.0ms

Counts
258 → 258
Iterations

Useful iterations: done (676.0ms)

IterNodesCost
03588387
111247832
done50007370

prune553.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))
0.0b
(* (* x (/ x (+ x 1.0))) (- x 1.0))
0.0b
(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))) (* (+ (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0))) (* (+ x 1.0) (- x 1.0))))
18.1b
(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0)))))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
286×frac-times
279×associate-*r/
170×frac-sub
153×flip3-+ flip-+
134×associate-*l/
87×associate-/l/
84×flip3-- flip--
35×associate-/r/
31×add-exp-log add-cbrt-cube
14×pow1
13×prod-exp cbrt-unprod
12×*-un-lft-identity
10×add-sqr-sqrt
9×frac-add
8×add-cube-cbrt
6×associate-*r* pow-prod-down add-log-exp
5×cbrt-undiv sub-neg div-exp associate-*l*
4×distribute-rgt-in distribute-lft-in associate--l+
3×times-frac associate-/l*
2×*-commutative
1×frac-2neg diff-log div-sub clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 316
Calls
4 calls:
87.0ms
(* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))
61.0ms
(* (* x (/ x (+ x 1.0))) (- x 1.0))
375.0ms
(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))) (* (+ (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0))) (* (+ x 1.0) (- x 1.0))))
88.0ms
(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0)))))

series917.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))
54.0ms
(* (* x (/ x (+ x 1.0))) (- x 1.0))
529.0ms
(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))) (* (+ (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0))) (* (+ x 1.0) (- x 1.0))))
251.0ms
(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0)))))

simplify1.3s

Counts
328 → 328
Iterations

Useful iterations: done (1.2s)

IterNodesCost
070916208
1263715483
done500014839

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* x (/ x (+ x 1.0))) (- x 1.0))
0.0b
(* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))
0.0b
(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))) (* (+ x 1.0) (- x 1.0)))
18.1b
(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0)))))

rewrite643.0ms

Algorithm
rewrite-expression-head
Rules
265×associate-*r/
250×frac-times
170×frac-sub
135×flip3-+ flip-+
125×associate-*l/
87×associate-/l/
75×flip3-- flip--
27×add-exp-log add-cbrt-cube
14×pow1
12×*-un-lft-identity
11×prod-exp cbrt-unprod
10×add-sqr-sqrt
8×add-cube-cbrt associate-/r/
6×associate-*r* pow-prod-down add-log-exp
5×sub-neg associate-*l*
4×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate--l+
3×times-frac associate-/l*
2×*-commutative
1×frac-2neg diff-log div-sub clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 287
Calls
4 calls:
82.0ms
(* (* x (/ x (+ x 1.0))) (- x 1.0))
118.0ms
(* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))
280.0ms
(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))) (* (+ x 1.0) (- x 1.0)))
118.0ms
(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0)))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* x (/ x (+ x 1.0))) (- x 1.0))
102.0ms
(* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))
366.0ms
(/ (- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0))))) (* (+ x 1.0) (- x 1.0)))
241.0ms
(- (* (* x (/ x (+ x 1.0))) (- x 1.0)) (* (+ x 1.0) (* (+ 1.0 x) (/ (+ 1.0 x) (- x 1.0)))))

simplify1.3s

Counts
299 → 299
Iterations

Useful iterations: done (1.2s)

IterNodesCost
062312632
1234711938
done500211376

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes63.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.1b

bsearch119.0ms

Steps
ItersRangePoint
8
1575.9184687212278
8587103.50349991
11003.158265916662
10
-1.3980170606481126e+18
-1333.496421940221
-11446.426080740146

simplify18.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
03491
15176
26076
36376
done6376

end0.0ms

sample1.1s

Algorithm
intervals
Results
337.0ms1699×body1280valid
233.0ms4137×body80valid
233.0ms1218×body640valid
66.0ms344×body160valid
63.0ms602×body320valid