Details

Time bar (total: 15.1s)

sample33.0ms

Algorithm
intervals
Results
8.0ms53×body1280valid
7.0ms46×body640valid
5.0ms126×body80valid
2.0ms19×body320valid
1.0ms12×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: 30.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ 1.0 x) (- x 1.0))
3.6b
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

rewrite174.0ms

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:
16.0ms
(/ x (+ x 1.0))
41.0ms
(/ (+ 1.0 x) (- x 1.0))
109.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

series310.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(/ x (+ x 1.0))
60.0ms
(/ (+ 1.0 x) (- x 1.0))
198.0ms
(- (/ x (+ x 1.0)) (/ (+ 1.0 x) (- x 1.0)))

simplify885.0ms

Counts
113 → 113
Iterations

Useful iterations: 2 (296.0ms)

IterNodesCost
01861584
14481503
219021427
done50001427

prune332.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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)) (cbrt (- x 1.0)))
18.4b
(- (/ x (+ x 1.0)) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ 1.0 x) (cbrt (- x 1.0)))))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
38×cbrt-prod
34×add-sqr-sqrt
32×*-un-lft-identity
16×cbrt-div
14×add-cube-cbrt
11×pow1
10×swap-sqr
9×flip3-- flip--
8×pow1/3 associate-*r* associate-*l* distribute-lft-out--
6×add-exp-log add-log-exp difference-of-squares
5×frac-times
4×add-cbrt-cube unswap-sqr
3×associate-*r/ associate-*l/ frac-sub
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus diff-log prod-exp *-commutative cbrt-unprod
Counts
4 → 101
Calls
4 calls:
12.0ms
(cbrt (- x 1.0))
8.0ms
(cbrt (- x 1.0))
68.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
99.0ms
(- (/ x (+ x 1.0)) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ 1.0 x) (cbrt (- x 1.0)))))

series716.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(cbrt (- x 1.0))
133.0ms
(cbrt (- x 1.0))
175.0ms
(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
254.0ms
(- (/ x (+ x 1.0)) (* (/ 1 (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (+ 1.0 x) (cbrt (- x 1.0)))))

simplify2.0s

Counts
113 → 113
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02212038
15721880
228181711
done50001685

prune319.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
0.3b
(/ 1.0 (* x x))
0.5b
(/ 3.0 (pow x 3))
5.0b
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
59×*-un-lft-identity
53×times-frac
37×add-sqr-sqrt
35×add-cube-cbrt
16×add-log-exp
14×add-exp-log
13×associate-/r*
12×unpow-prod-down cube-prod
11×add-cbrt-cube
9×unpow3
7×distribute-lft-out
6×associate-/l*
5×div-exp
4×pow1 cube-mult distribute-rgt-out diff-log div-inv distribute-lft-out-- sqr-pow
3×cbrt-undiv sum-log frac-sub distribute-neg-frac
2×distribute-rgt-neg-in frac-2neg flip3-+ neg-log frac-add clear-num flip-+
1×+-commutative associate--l- neg-sub0 pow-to-exp sub-neg flip3-- distribute-rgt1-in pow-exp prod-exp flip-- cbrt-unprod associate--r+ difference-of-squares
Counts
4 → 133
Calls
4 calls:
75.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
13.0ms
(/ 1.0 (* x x))
14.0ms
(/ 3.0 (pow x 3))
262.0ms
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

series264.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(+ (/ 3.0 x) (/ 3.0 (pow x 3)))
39.0ms
(/ 1.0 (* x x))
48.0ms
(/ 3.0 (pow x 3))
54.0ms
(- (- (/ 1.0 (* x x))) (+ (/ 3.0 x) (/ 3.0 (pow x 3))))

simplify2.5s

Counts
145 → 145
Iterations

Useful iterations: 2 (954.0ms)

IterNodesCost
02151986
16051746
246631650
done50001650

prune333.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* 3.0 x) 1.0)
0.0b
(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
4×sum-log
2×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
1×associate-+r+
Counts
2 → 24
Calls
2 calls:
12.0ms
(+ (* 3.0 x) 1.0)
34.0ms
(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

series83.0ms

Counts
2 → 6
Calls
2 calls:
44.0ms
(+ (* 3.0 x) 1.0)
39.0ms
(+ (* 1.0 (pow x 2)) (+ (* 3.0 x) 1.0))

simplify2.5s

Counts
30 → 30
Iterations

Useful iterations: 3 (826.0ms)

IterNodesCost
050397
1167375
2675345
33985311
done5002311

prune74.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch94.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
7392.742446615246
10
-2676750800.736259
-2.9526231381329305e-09
-14718.562895208246

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02966
13851
done3851

end0.0ms

sample1.5s

Algorithm
intervals
Results
721.0ms1745×body1280valid
274.0ms4091×body80valid
169.0ms1240×body640valid
97.0ms627×body320valid
20.0ms297×body160valid