Details

Time bar (total: 21.4s)

sample42.0ms

Algorithm
intervals
Results
13.0ms136×body80valid
10.0ms66×body640valid
4.0ms12×body1280valid
4.0ms31×body320valid
1.0ms12×body160valid

simplify3.7s

Counts
1 → 1
Iterations
IterNodes
done5001
104810
91188
8437
7210
6162
5135
489
341
231
118
010

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize28.0ms

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))
1.8b
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

rewrite269.0ms

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-cbrt-cube add-exp-log difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv associate-+r+ clear-num sum-log sub-neg frac-2neg flip3-+ diff-log div-exp frac-sub flip-+ div-inv
1×+-commutative associate-+r-
Counts
4 → 114
Calls
4 calls:
10.0ms
(/ 1.0 (+ x 1.0))
9.0ms
(/ 1.0 (- x 1.0))
58.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
186.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

series833.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1.0 (+ x 1.0))
381.0ms
(/ 1.0 (- x 1.0))
70.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
336.0ms
(+ (/ 1.0 (- x 1.0)) (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)))

simplify1.1s

Counts
126 → 126
Iterations
IterNodes
done5001
22093
1537
0211

prune547.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
2.7b
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
4.3b
(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
16.6b
(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
370×*-un-lft-identity
239×times-frac
150×add-sqr-sqrt
87×distribute-lft-out--
68×distribute-lft-out
56×frac-sub
53×difference-of-squares
33×add-cube-cbrt
28×flip3-- flip--
27×frac-times
17×associate-/l/
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×associate-/r* associate-*l/ associate-*r/
8×add-cbrt-cube add-exp-log add-log-exp
6×sub-neg associate-/l*
5×associate-/r/
4×distribute-rgt-in distribute-lft-in associate--r+
3×frac-add div-inv
2×diff-log
1×pow2 cbrt-undiv clear-num frac-2neg flip3-+ pow-plus div-sub div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ unswap-sqr
Counts
4 → 238
Calls
4 calls:
377.0ms
(* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
124.0ms
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
214.0ms
(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
937.0ms
(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x)))

series1.7s

Counts
4 → 12
Calls
4 calls:
112.0ms
(* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))
249.0ms
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
303.0ms
(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
992.0ms
(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))) (/ 2.0 x)))

simplify578.0ms

Counts
250 → 250
Iterations
IterNodes
done5001
11216
0406

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
2.7b
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
4.3b
(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
16.6b
(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (* (* (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))) (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))))) (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))))) (/ 2.0 x)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
144×cbrt-div
107×*-un-lft-identity
99×frac-times
96×frac-sub
89×times-frac
80×add-sqr-sqrt
68×flip3-- flip--
65×associate-/r/
63×frac-add
40×distribute-lft-out--
33×associate-*l/
31×add-cube-cbrt
23×difference-of-squares
21×associate-*r/
17×associate-/l/
12×distribute-lft-out
10×add-log-exp
6×add-cbrt-cube add-exp-log associate-/l*
5×sub-neg div-inv
4×pow1 associate--r+
3×associate-/r* diff-log
2×distribute-rgt-in distribute-lft-in
1×cbrt-undiv clear-num frac-2neg flip3-+ div-sub div-exp flip-+
Counts
4 → 218
Calls
4 calls:
122.0ms
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
122.0ms
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
207.0ms
(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
1.4s
(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (* (* (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))) (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))))) (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))))) (/ 2.0 x)))

series2.0s

Counts
4 → 12
Calls
4 calls:
284.0ms
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
268.0ms
(- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))
350.0ms
(- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x))))
1.1s
(/ (- (/ (/ (* 1.0 1.0) (- x 1.0)) (- x 1.0)) (* (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)) (- (/ 1.0 (+ 1.0 x)) (/ 2.0 x)))) (+ (* (* (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x)))) (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))))) (cbrt (- (/ 1.0 (- x 1.0)) (/ 1.0 (+ 1.0 x))))) (/ 2.0 x)))

simplify770.0ms

Counts
230 → 230
Iterations
IterNodes
done5001
11859
0675

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x))))
0.0b
(- (* x 1.0) (* 2.0 (+ 1.0 x)))
0.0b
(* (* (- x 1.0) x) (+ 1.0 x))
16.5b
(+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0)))

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
30×associate-*l/
24×associate-*r/
22×flip3-- flip--
16×frac-times frac-add
12×flip3-+ flip-+
11×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log
8×add-log-exp
7×associate-*r* add-cube-cbrt
6×distribute-rgt-in distribute-lft-in associate-*l*
5×sub-neg
4×associate-+l+ pow-prod-down prod-exp cbrt-unprod
2×*-commutative associate--r+
1×+-commutative sum-log diff-log distribute-lft-out distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 106
Calls
4 calls:
35.0ms
(* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x))))
6.0ms
(- (* x 1.0) (* 2.0 (+ 1.0 x)))
45.0ms
(* (* (- x 1.0) x) (+ 1.0 x))
42.0ms
(+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x))))
62.0ms
(- (* x 1.0) (* 2.0 (+ 1.0 x)))
165.0ms
(* (* (- x 1.0) x) (+ 1.0 x))
2.0ms
(+ (* (- x 1.0) (- (* x 1.0) (* 2.0 (+ 1.0 x)))) (* x (* (+ 1.0 x) 1.0)))

simplify376.0ms

Counts
118 → 118
Iterations
IterNodes
done5001
1843
0234

prune736.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
done11
111
08

end0.0ms

sample1.8s

Algorithm
intervals
Results
637.0ms954×body320valid
453.0ms1831×body640valid
348.0ms4219×body80valid
145.0ms546×body1280valid
48.0ms453×body160valid