Details

Time bar (total: 26.1s)

sample58.0ms

Algorithm
intervals
Results
18.0ms66×body640valid
9.0ms129×body80valid
7.0ms32×body320valid
6.0ms17×body1280valid
2.0ms12×body160valid

simplify171.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11815
23115
34115
45015
55515
66415
78215
89915
910915
done10915

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.4b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite605.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
32×times-frac
24×add-sqr-sqrt
13×distribute-lft-out
12×add-cube-cbrt
10×distribute-lft-out-- add-log-exp
5×add-exp-log add-cbrt-cube
4×associate-/r* difference-of-squares
3×pow1 frac-add associate-/l*
2×sub-neg associate-+l+ flip3-- flip3-+ diff-log sum-log associate-/r/ frac-sub flip-- flip-+
1×cbrt-undiv +-commutative associate-+l- frac-2neg div-exp clear-num div-inv
Counts
3 → 77
Calls
3 calls:
27.0ms
(/ 1.0 (+ x 1.0))
95.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
476.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series409.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(/ 1.0 (+ x 1.0))
51.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
325.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify2.1s

Counts
86 → 86
Iterations

Useful iterations: 3 (908.0ms)

IterNodesCost
01661401
14051318
211071250
333711228
done50001228

prune323.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ 1.0 (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
18.9b
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite853.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
48×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt add-cube-cbrt
15×cbrt-div
10×distribute-lft-out
9×frac-add add-log-exp
7×frac-sub
6×associate-/r/
5×frac-times associate-*l/
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 associate-*r/ div-inv
2×associate-+l+ sum-log
1×+-commutative associate-+l- sub-neg flip3-- diff-log flip--
Counts
4 → 106
Calls
4 calls:
6.0ms
(cbrt (/ 1.0 (+ x 1.0)))
11.0ms
(cbrt (/ 1.0 (+ x 1.0)))
12.0ms
(cbrt (/ 1.0 (+ x 1.0)))
819.0ms
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series926.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(cbrt (/ 1.0 (+ x 1.0)))
180.0ms
(cbrt (/ 1.0 (+ x 1.0)))
229.0ms
(cbrt (/ 1.0 (+ x 1.0)))
330.0ms
(+ (- (* (* (cbrt (/ 1.0 (+ x 1.0))) (cbrt (/ 1.0 (+ x 1.0)))) (cbrt (/ 1.0 (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.2s

Counts
118 → 118
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02432845
15752750
216602113
done50012005

prune466.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.4b
(cbrt (/ 1.0 (+ x 1.0)))
9.7b
(/ (+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
24.1b
(+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
2088×associate-*l/
1777×cbrt-div
800×frac-times
778×associate-*r/
699×flip3-+ flip-+
512×frac-add
384×frac-sub
258×associate-/l/
233×flip3-- flip--
42×cbrt-prod *-un-lft-identity
30×add-sqr-sqrt
28×associate-/r/
22×add-cube-cbrt
20×add-exp-log
16×add-cbrt-cube
15×times-frac
11×pow1
9×swap-sqr distribute-lft-out
7×pow1/3 associate-*r* associate-*l* prod-exp cbrt-unprod
6×add-log-exp
4×cbrt-undiv associate-+l+ div-exp unswap-sqr
3×associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in pow-prod-down pow-sqr pow-prod-up div-inv
1×+-commutative pow2 frac-2neg pow-plus clear-num associate-/r* sum-log *-commutative
Counts
4 → 660
Calls
4 calls:
70.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
11.0ms
(cbrt (/ 1.0 (+ x 1.0)))
632.0ms
(/ (+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
262.0ms
(+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))

series2.4s

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
220.0ms
(cbrt (/ 1.0 (+ x 1.0)))
1.4s
(/ (+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0)) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) (- x 1.0)))
684.0ms
(+ (* (- x 1.0) (- (* (* (pow 1.0 2/3) (cbrt (/ 1.0 (+ x 1.0)))) x) (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) 2.0))) (* (* (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) x) 1.0))

simplify2.6s

Counts
672 → 672
Iterations

Useful iterations: done (2.5s)

IterNodesCost
0153160444
1495856533
done500256452

prune8.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3)))
0.1b
(/ 2.0 (pow x 5))
0.4b
(/ 2.0 (pow x 7))
0.4b
(/ 2.0 (pow x 3))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
71×*-un-lft-identity
63×add-sqr-sqrt add-cube-cbrt
36×unpow-prod-down
26×associate-/r*
19×add-exp-log
12×cube-prod sqr-pow
10×add-cbrt-cube
9×div-exp associate-/l*
6×add-log-exp
5×div-inv distribute-lft-out
4×pow1 cube-mult unpow3
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×+-commutative flip3-+ frac-add sum-log flip-+
Counts
4 → 172
Calls
4 calls:
119.0ms
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3)))
14.0ms
(/ 2.0 (pow x 5))
11.0ms
(/ 2.0 (pow x 7))
9.0ms
(/ 2.0 (pow x 3))

series431.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(+ (/ 2.0 (pow x 5)) (/ 2.0 (pow x 3)))
85.0ms
(/ 2.0 (pow x 5))
88.0ms
(/ 2.0 (pow x 7))
68.0ms
(/ 2.0 (pow x 3))

simplify1.5s

Counts
184 → 184
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02552079
14841812
213451744
done50011742

prune652.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes57.0ms

Accuracy

99.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 23.7b

bsearch232.0ms

Steps
ItersRangePoint
9
0.21963308938311268
137362616.0762091
101.6588453171347
11
-2445851338.3862987
-4.2674702477225e-16
-101.77579100982673

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
038104
15286
done5286

end0.0ms

sample1.6s

Algorithm
intervals
Results
590.0ms1861×body640valid
244.0ms961×body320valid
242.0ms4132×body80valid
223.0ms570×body1280valid
109.0ms480×body160valid