Details

Time bar (total: 40.8s)

sample23.0ms

Algorithm
intervals
Results
7.0ms68×body640valid
4.0ms133×body80valid
2.0ms26×body320valid
2.0ms14×body1280valid
1.0ms15×body160valid

simplify87.0ms

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: 10.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
0.0b
(/ 1.0 (- x 1.0))
2.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
35×times-frac
33×add-sqr-sqrt
14×distribute-lft-out--
13×add-cube-cbrt
10×add-log-exp
9×distribute-lft-out
8×difference-of-squares
5×add-exp-log associate-/r* add-cbrt-cube
3×pow1 flip3-- frac-add flip-- associate-/l*
2×sub-neg associate-+l+ diff-log sum-log associate-/r/ frac-sub
1×cbrt-undiv +-commutative associate-+l- frac-2neg flip3-+ div-exp clear-num flip-+ div-inv
Counts
3 → 81
Calls
3 calls:
58.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
11.0ms
(/ 1.0 (- x 1.0))
267.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series500.0ms

Counts
3 → 9
Calls
3 calls:
45.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
28.0ms
(/ 1.0 (- x 1.0))
426.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify1.6s

Counts
90 → 90
Iterations

Useful iterations: 3 (724.0ms)

IterNodesCost
01791458
14231375
211471305
334301285
done50001285

prune191.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
2.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
2.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
435×*-un-lft-identity
156×times-frac
100×distribute-lft-out
89×distribute-lft-out--
76×cbrt-prod
60×cbrt-div
45×frac-add
30×swap-sqr
25×frac-times
20×add-sqr-sqrt
19×add-log-exp
15×flip3-- flip3-+ frac-sub flip-- flip-+
12×add-cube-cbrt associate-*r* associate-*l*
11×pow1
6×add-exp-log associate-+l+ pow1/3 sum-log
5×associate-*r/ associate-*l/
4×add-cbrt-cube unswap-sqr
3×+-commutative associate-+l- sub-neg diff-log
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 183
Calls
4 calls:
1.3s
(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
262.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
265.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
268.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
490.0ms
(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
224.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
216.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
220.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify705.0ms

Counts
195 → 195
Iterations

Useful iterations: done (689.0ms)

IterNodesCost
02508410
15297841
214967581
done50006624

prune425.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

2.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
6.4b
(/ (* (cbrt (- (* (- (/ 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))))) (cbrt (- (* (- (/ 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)))))) (* (cbrt (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))))
13.5b
(cbrt (- (* (- (/ 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)))))
13.5b
(cbrt (- (* (- (/ 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)))))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
6811×frac-sub
6350×frac-times
4666×cbrt-div
2475×flip3-- flip--
2404×associate-*r/ associate-*l/
2303×associate-/l/
39×*-un-lft-identity
35×associate-/r/
16×add-exp-log
13×times-frac
9×add-log-exp
8×cbrt-prod add-cbrt-cube distribute-lft-out
7×distribute-lft-out--
6×add-sqr-sqrt add-cube-cbrt
4×pow1 cbrt-undiv div-exp prod-exp cbrt-unprod
3×frac-add
2×associate-+l+ pow1/3 sum-log difference-of-squares
1×+-commutative associate-+l- sub-neg frac-2neg flip3-+ diff-log clear-num associate-/r* flip-+ div-inv associate-/l*
Counts
4 → 2501
Calls
4 calls:
268.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
893.0ms
(/ (* (cbrt (- (* (- (/ 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))))) (cbrt (- (* (- (/ 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)))))) (* (cbrt (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))))
111.0ms
(cbrt (- (* (- (/ 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)))))
116.0ms
(cbrt (- (* (- (/ 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)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
225.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
949.0ms
(/ (* (cbrt (- (* (- (/ 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))))) (cbrt (- (* (- (/ 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)))))) (* (cbrt (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (- (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))))
416.0ms
(cbrt (- (* (- (/ 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)))))
412.0ms
(cbrt (- (* (- (/ 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)))))

simplify1.6s

Counts
2513 → 2513
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01928240187
done5000227147

prune25.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
19.1b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ (sqrt 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (sqrt 1.0) (cbrt (- x 1.0)))))

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
9×frac-add add-log-exp
7×add-cube-cbrt
6×cbrt-div flip3-- flip--
4×pow1 add-exp-log add-cbrt-cube
3×frac-times pow1/3 associate-*r/ associate-*l/ frac-sub distribute-lft-out-- difference-of-squares
2×associate-+l+ sum-log
1×+-commutative associate-+l- sub-neg flip3-+ diff-log flip-+
Counts
4 → 69
Calls
4 calls:
4.0ms
(cbrt (- x 1.0))
4.0ms
(cbrt (- x 1.0))
5.0ms
(cbrt (- x 1.0))
234.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ (sqrt 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (sqrt 1.0) (cbrt (- x 1.0)))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(cbrt (- x 1.0))
96.0ms
(cbrt (- x 1.0))
91.0ms
(cbrt (- x 1.0))
141.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (/ (sqrt 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (sqrt 1.0) (cbrt (- x 1.0)))))

simplify824.0ms

Counts
81 → 81
Iterations

Useful iterations: done (821.0ms)

IterNodesCost
01992140
15351900
216621599
done50011438

prune222.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 26.3b

bsearch105.0ms

Steps
ItersRangePoint
11
6.1632953816490534e-12
2923699147.8271213
108.85805631382505
10
-21283307590.397102
-3.152803306627408e-07
-97.6859664947938

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
03272
14056
done4056

end0.0ms

sample560.0ms

Algorithm
intervals
Results
183.0ms1878×body640valid
107.0ms4173×body80valid
73.0ms579×body1280valid
67.0ms912×body320valid
24.0ms459×body160valid