Details

Time bar (total: 12.0s)

sample36.0ms

Algorithm
intervals
Results
9.0ms284×body80nan
5.0ms47×body640valid
4.0ms36×body1280valid
4.0ms141×body80valid
2.0ms24×body320valid
0.0ms8×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv frac-2neg sqrt-div div-exp clear-num associate-/r/
1×sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 117
Calls
3 calls:
12.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
62.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series250.0ms

Counts
3 → 9
Calls
3 calls:
76.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
137.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
126 → 126
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02011764
14111621
29571551
323671528
done50011517

prune268.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.3b
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
2.8b
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
124×*-un-lft-identity
105×times-frac
65×add-sqr-sqrt
53×add-cube-cbrt
52×sqrt-prod
35×distribute-lft-out
27×associate-/r*
13×add-exp-log add-cbrt-cube
9×div-inv
8×distribute-lft-out--
7×associate-/l*
6×add-log-exp
5×associate-/r/
4×pow1 cbrt-undiv div-exp difference-of-squares
3×frac-2neg associate-*r/ clear-num associate-/l/
2×flip3-- flip3-+ sqrt-div frac-sub flip-- flip-+
1×sub-neg diff-log frac-add prod-exp cbrt-unprod
Counts
4 → 158
Calls
4 calls:
12.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
147.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
38.0ms
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

series801.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 1.0 (sqrt (+ x 1.0)))
37.0ms
(/ 1.0 (sqrt x))
427.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
259.0ms
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

simplify1.2s

Counts
170 → 170
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03393045
18222803
225572592
done50022590

prune399.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
0.2b
(/ 1.0 (sqrt x))
1.9b
(- (* 1.0 (+ x 1.0)) (* x 1.0))
4.6b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite375.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
37×times-frac
32×add-exp-log add-cbrt-cube
26×add-sqr-sqrt add-cube-cbrt
24×sqrt-prod
22×associate-*r/
14×flip3-+ associate-*l* flip-+ distribute-lft-out
12×frac-times prod-exp cbrt-unprod
11×associate-/r/
9×pow1
7×cbrt-undiv div-exp associate-/r*
6×associate-*l/ frac-add add-log-exp
5×distribute-rgt-in distribute-lft-in
4×div-inv associate-/l*
3×pow-prod-down
2×flip3-- frac-2neg associate--l+ clear-num flip-- associate-/l/
1×sub-neg diff-log associate-*r* *-commutative
Counts
4 → 135
Calls
4 calls:
108.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
7.0ms
(/ 1.0 (sqrt x))
14.0ms
(- (* 1.0 (+ x 1.0)) (* x 1.0))
241.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series822.0ms

Counts
4 → 12
Calls
4 calls:
486.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
37.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (* 1.0 (+ x 1.0)) (* x 1.0))
297.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify1.8s

Counts
147 → 147
Iterations

Useful iterations: 2 (785.0ms)

IterNodesCost
03333744
110073614
246252955
done50002955

prune395.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.9b
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
4.6b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite346.0ms

Algorithm
rewrite-expression-head
Rules
73×*-un-lft-identity
58×times-frac
42×add-sqr-sqrt add-cube-cbrt
40×sqrt-prod
34×add-exp-log add-cbrt-cube
20×associate-*r/
18×distribute-lft-out
15×flip3-+ flip-+
14×associate-*l* associate-/r*
13×associate-/r/
12×frac-times prod-exp cbrt-unprod
9×pow1
8×cbrt-undiv div-exp
7×associate-/l*
6×associate-*l/ frac-add
5×div-inv
4×distribute-rgt-in distribute-lft-in add-log-exp
3×frac-2neg pow-prod-down clear-num
2×sqrt-div
1×associate-*r* *-commutative
Counts
4 → 164
Calls
4 calls:
13.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
83.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
237.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series905.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
486.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
297.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify1.6s

Counts
176 → 176
Iterations

Useful iterations: 2 (710.0ms)

IterNodesCost
03593687
19883475
241123014
done50003014

prune419.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

regimes27.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
11621
done1621

end0.0ms

sample911.0ms

Algorithm
intervals
Results
180.0ms1787×body640valid
170.0ms8130×body80nan
140.0ms1123×body1280valid
109.0ms4167×body80valid
44.0ms623×body320valid
17.0ms300×body160valid