Details

Time bar (total: 19.0s)

sample73.0ms

Algorithm
intervals
Results
14.0ms69×body640valid
12.0ms17×body320valid
11.0ms252×body80nan
8.0ms32×body1280valid
7.0ms125×body80valid
1.0ms13×body160valid

simplify7.0ms

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: 21.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
3.4b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite148.0ms

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:
13.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
123.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series351.0ms

Counts
3 → 9
Calls
3 calls:
106.0ms
(/ 1.0 (sqrt (+ x 1.0)))
51.0ms
(/ 1.0 (sqrt x))
193.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.9s

Counts
126 → 126
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02011764
14111621
29571551
323671528
done50011517

prune481.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.2b
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.3b
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

rewrite369.0ms

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:
26.0ms
(/ 1.0 (sqrt (+ x 1.0)))
13.0ms
(/ 1.0 (sqrt x))
258.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
55.0ms
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

series910.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ 1.0 (sqrt (+ x 1.0)))
48.0ms
(/ 1.0 (sqrt x))
675.0ms
(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ x 1.0)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
86.0ms
(- (/ 1.0 x) (/ 1.0 (+ x 1.0)))

simplify2.1s

Counts
170 → 170
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03393045
18222803
225572592
done50022590

prune592.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize36.0ms

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))
2.4b
(- (* 1.0 (+ x 1.0)) (* x 1.0))
4.8b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite545.0ms

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:
143.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
8.0ms
(/ 1.0 (sqrt x))
15.0ms
(- (* 1.0 (+ x 1.0)) (* x 1.0))
370.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
616.0ms
(/ (* 1.0 (- (* 1.0 (+ x 1.0)) (* x 1.0))) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
53.0ms
(/ 1.0 (sqrt x))
1.0ms
(- (* 1.0 (+ x 1.0)) (* x 1.0))
431.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify2.8s

Counts
147 → 147
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
03333744
110073614
246252955
done50002955

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.6b
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
4.8b
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

rewrite456.0ms

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:
14.0ms
(/ 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))))
339.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ 1.0 (sqrt (+ x 1.0)))
53.0ms
(/ 1.0 (sqrt x))
660.0ms
(/ (* 1.0 1.0) (* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0))))
446.0ms
(* (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))) (* x (+ x 1.0)))

simplify2.5s

Counts
176 → 176
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
03593687
19883475
241123014
done50003014

prune488.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

regimes42.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01221
11621
done1621

end0.0ms

sample1.8s

Algorithm
intervals
Results
557.0ms1050×body1280valid
393.0ms1918×body640valid
301.0ms8150×body80nan
143.0ms4128×body80valid
126.0ms601×body320valid
20.0ms303×body160valid