Details

Time bar (total: 6.8s)

sample23.0ms

Algorithm
intervals
Results
6.0ms63×body640valid
3.0ms123×body80valid
3.0ms36×body320valid
2.0ms17×body1280valid
1.0ms17×body160valid

simplify17.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0187
1317
2437
3577
4737
5927
61267
71587
82077
92097
102097
done2097

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize12.0ms

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))
3.5b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite356.0ms

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:
11.0ms
(/ 1.0 (- x 1.0))
11.0ms
(/ 1.0 (+ x 1.0))
59.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
271.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series308.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ 1.0 (- x 1.0))
24.0ms
(/ 1.0 (+ x 1.0))
47.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
210.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify46.0ms

Counts
126 → 126
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0496865
11681827
25002816
done5002816

prune246.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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)))
21.7b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

rewrite288.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
49×add-sqr-sqrt *-un-lft-identity
45×times-frac
39×cbrt-div
31×add-cube-cbrt
21×frac-add
15×frac-times associate-*l/
10×flip3-- flip--
9×associate-*r/ distribute-lft-out-- add-log-exp difference-of-squares
7×frac-sub
6×associate-/r/
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 div-inv
2×associate-+l+ sum-log
1×+-commutative associate-+l- sub-neg flip3-+ diff-log flip-+
Counts
4 → 126
Calls
4 calls:
6.0ms
(cbrt (/ 1.0 (- x 1.0)))
6.0ms
(cbrt (/ 1.0 (- x 1.0)))
6.0ms
(cbrt (/ 1.0 (- x 1.0)))
264.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

series624.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(cbrt (/ 1.0 (- x 1.0)))
132.0ms
(cbrt (/ 1.0 (- x 1.0)))
123.0ms
(cbrt (/ 1.0 (- x 1.0)))
247.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (* (* (cbrt (/ 1.0 (- x 1.0))) (cbrt (/ 1.0 (- x 1.0)))) (cbrt (/ 1.0 (- x 1.0)))))

simplify61.0ms

Counts
138 → 138
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
06482052
119581908
250011778
done50011778

prune397.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b
(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))
2.5b
(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
4.1b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))
13.2b
(/ (* (+ (/ 1.0 (+ x 1.0)) (- (- (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))) (- (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) (/ 2.0 x)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
197×*-un-lft-identity
102×times-frac
61×distribute-lft-out--
49×add-sqr-sqrt
38×distribute-lft-out
35×associate-/l/
32×frac-sub
26×frac-add
25×frac-times
22×add-cube-cbrt
18×flip--
16×flip3-- flip-+
14×flip3-+
13×add-log-exp
11×associate-/r*
10×difference-of-squares
9×add-exp-log associate-/r/ add-cbrt-cube
6×distribute-neg-frac
5×associate-*r/ associate-*l/ div-inv
4×pow1
3×diff-log
2×cbrt-undiv sub-neg div-exp sum-log
1×+-commutative frac-2neg prod-exp associate--l+ clear-num cbrt-unprod associate-/l*
Counts
4 → 161
Calls
4 calls:
64.0ms
(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))
499.0ms
(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
74.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))
1.1s
(/ (* (+ (/ 1.0 (+ x 1.0)) (- (- (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))) (- (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) (/ 2.0 x)))

series778.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))
227.0ms
(- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))
173.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))
220.0ms
(/ (* (+ (/ 1.0 (+ x 1.0)) (- (- (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (- (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0))) (/ 2.0 x))) (- (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))) (/ 2.0 x)))

simplify49.0ms

Counts
173 → 173
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09913037
150022839
done50022839

prune491.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x 1.0) x)
0.0b
(* (+ x 1.0) x)
0.0b
(* (* (+ x 1.0) x) (- x 1.0))
18.8b
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
48×associate-*l/
16×frac-add
15×add-sqr-sqrt flip3-- *-un-lft-identity flip--
14×flip3-+ flip-+
13×pow1 add-exp-log add-cbrt-cube
12×frac-times
11×associate-*r*
9×add-cube-cbrt associate-*l*
6×associate-*r/ add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
4×distribute-rgt-in sub-neg associate-+l+ distribute-lft-in
3×*-commutative
2×distribute-lft-out unswap-sqr
1×+-commutative sum-log distribute-lft-out-- difference-of-squares
Counts
4 → 105
Calls
4 calls:
20.0ms
(* (+ x 1.0) x)
21.0ms
(* (+ x 1.0) x)
43.0ms
(* (* (+ x 1.0) x) (- x 1.0))
32.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

series196.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (+ x 1.0) x)
50.0ms
(* (+ x 1.0) x)
101.0ms
(* (* (+ x 1.0) x) (- x 1.0))
2.0ms
(+ (* (- (* 1.0 x) (* (+ x 1.0) 2.0)) (- x 1.0)) (* (* (+ x 1.0) x) 1.0))

simplify117.0ms

Counts
117 → 117
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07511323
144271240
250031240
done50031240

prune314.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes21.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0115
1115
done115

end0.0ms

sample612.0ms

Algorithm
intervals
Results
196.0ms1881×body640valid
115.0ms4156×body80valid
75.0ms935×body320valid
71.0ms553×body1280valid
27.0ms476×body160valid