Details

Time bar (total: 6.6s)

sample22.0ms

Algorithm
intervals
Results
6.0ms60×body640valid
4.0ms136×body80valid
2.0ms18×body1280valid
2.0ms26×body320valid
1.0ms16×body160valid

simplify77.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
11815
23115
34115
45215
56515
68015
710315
812315
914115
done14115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite234.0ms

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:
5.0ms
(/ 1.0 (- x 1.0))
5.0ms
(/ 1.0 (+ x 1.0))
36.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
182.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ 1.0 (- x 1.0))
24.0ms
(/ 1.0 (+ x 1.0))
43.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
207.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify504.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (133.0ms)

IterNodesCost
02131832
15081716
216201630
done50001630

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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))
17.1b
(+ (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×cbrt-prod
9×add-log-exp
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
5×frac-add
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+ distribute-lft-out
3×pow1/3 frac-sub
2×associate-+l+ sum-log
1×+-commutative frac-times associate-+l- sub-neg flip3-- diff-log associate-*r/ associate-*l/ flip--
Counts
4 → 63
Calls
4 calls:
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
2.0ms
(cbrt (+ x 1.0))
320.0ms
(+ (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series509.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(cbrt (+ x 1.0))
88.0ms
(cbrt (+ x 1.0))
87.0ms
(cbrt (+ x 1.0))
244.0ms
(+ (- (* (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt 1.0) (cbrt (+ x 1.0)))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify475.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
01741944
14651891
215481326
done50001326

prune265.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(- (* 1.0 x) (* (+ x 1.0) 2.0))
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
17.3b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
46×associate-*l/
16×flip3-- frac-add flip--
13×flip3-+ flip-+
12×frac-times
11×pow1 add-exp-log add-sqr-sqrt *-un-lft-identity add-cbrt-cube
8×associate-*r* add-log-exp
7×add-cube-cbrt
6×associate-*r/
5×sub-neg associate-*l*
4×distribute-rgt-in associate-+l+ distribute-lft-in pow-prod-down prod-exp cbrt-unprod
2×*-commutative
1×+-commutative diff-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 96
Calls
4 calls:
10.0ms
(* (+ x 1.0) x)
2.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
20.0ms
(* (* (+ x 1.0) x) (- x 1.0))
11.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series182.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (+ x 1.0) x)
36.0ms
(- (* 1.0 x) (* (+ x 1.0) 2.0))
98.0ms
(* (* (+ x 1.0) x) (- x 1.0))
1.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify1.3s

Counts
108 → 108
Iterations

Useful iterations: 2 (248.0ms)

IterNodesCost
02242834
17662668
239772528
done50002528

prune301.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
0.2b
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log add-cbrt-cube
18×associate-*l/
12×add-sqr-sqrt *-un-lft-identity
10×pow1
8×frac-times add-cube-cbrt associate-*r* associate-/r/
7×flip3-+ prod-exp cbrt-unprod flip-+
6×flip3-- flip--
5×associate-*l*
4×associate-*r/ pow-prod-down
3×cbrt-undiv times-frac div-exp associate-/l* add-log-exp
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative
1×frac-2neg clear-num associate-/r* div-inv distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
3 → 84
Calls
3 calls:
10.0ms
(* (+ x 1.0) x)
20.0ms
(* (* (+ x 1.0) x) (- x 1.0))
17.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

series231.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* (+ x 1.0) x)
96.0ms
(* (* (+ x 1.0) x) (- x 1.0))
93.0ms
(/ 2.0 (* (* (+ x 1.0) x) (- x 1.0)))

simplify746.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (170.0ms)

IterNodesCost
01541283
14311247
220321075
done50001075

prune173.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01013
11513
done1513

end0.0ms

sample621.0ms

Algorithm
intervals
Results
210.0ms1837×body640valid
124.0ms4155×body80valid
80.0ms976×body320valid
75.0ms550×body1280valid
27.0ms482×body160valid