Details

Time bar (total: 23.2s)

sample243.0ms

Algorithm
intervals
Results
66.0ms84×body1280valid
32.0ms53×body640valid
24.0ms22×body640nan
22.0ms21×body1280nan
16.0ms28×body10240exit
15.0ms144×body80valid
15.0ms41×body320valid
12.0ms176×body80nan
5.0ms13×body320nan
4.0ms18×body160valid
1.0ms4×body160nan

simplify879.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
51231
4238
381
234
117
08

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.3b
(pow x (/ 1.0 n))
1.1b
(pow (+ 1.0 x) (/ 1.0 n))
2.1b
(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite116.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
28×*-un-lft-identity
26×pow-unpow
19×add-cube-cbrt
18×times-frac
17×unpow-prod-down
9×difference-of-squares
8×sqr-pow
5×pow1 add-exp-log add-log-exp
3×add-cbrt-cube distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
3 → 79
Calls
3 calls:
6.0ms
(pow x (/ 1.0 n))
10.0ms
(pow (+ 1.0 x) (/ 1.0 n))
95.0ms
(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

series690.0ms

Counts
3 → 9
Calls
3 calls:
88.0ms
(pow x (/ 1.0 n))
227.0ms
(pow (+ 1.0 x) (/ 1.0 n))
374.0ms
(- (pow (+ 1.0 x) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.0s

Counts
88 → 88
Iterations
IterNodes
done5001
22071
1544
0189

prune584.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.4b

localize63.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow x (/ 1.0 n))
1.1b
(pow (+ x 1.0) (/ 1.0 n))
1.1b
(pow (+ x 1.0) (/ 1.0 n))
2.1b
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
41×*-un-lft-identity
39×pow-unpow
30×sqrt-prod
28×add-cube-cbrt
27×times-frac
23×unpow-prod-down
16×difference-of-squares
11×sqr-pow
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube distribute-lft-out--
3×pow-to-exp pow-pow pow-exp div-inv distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
4 → 115
Calls
4 calls:
6.0ms
(pow x (/ 1.0 n))
14.0ms
(pow (+ x 1.0) (/ 1.0 n))
14.0ms
(pow (+ x 1.0) (/ 1.0 n))
87.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series1.1s

Counts
4 → 12
Calls
4 calls:
103.0ms
(pow x (/ 1.0 n))
184.0ms
(pow (+ x 1.0) (/ 1.0 n))
239.0ms
(pow (+ x 1.0) (/ 1.0 n))
558.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify1.1s

Counts
127 → 127
Iterations
IterNodes
done5000
22196
1576
0203

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow x (/ 1.0 n))
0.3b
(pow x (/ 1.0 n))
1.1b
(pow (+ 1.0 x) (/ 1.0 n))
3.8b
(- (pow (+ 1.0 x) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
30×add-sqr-sqrt *-un-lft-identity
28×add-cube-cbrt
27×times-frac
11×unpow-prod-down
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube sqr-pow
3×pow-to-exp pow-pow pow-exp div-inv difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out
Counts
4 → 97
Calls
4 calls:
7.0ms
(pow x (/ 1.0 n))
7.0ms
(pow x (/ 1.0 n))
16.0ms
(pow (+ 1.0 x) (/ 1.0 n))
99.0ms
(- (pow (+ 1.0 x) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

series850.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(pow x (/ 1.0 n))
91.0ms
(pow x (/ 1.0 n))
213.0ms
(pow (+ 1.0 x) (/ 1.0 n))
457.0ms
(- (pow (+ 1.0 x) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

simplify996.0ms

Counts
109 → 109
Iterations
IterNodes
done5001
22134
1538
0180

prune800.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 22.2b

localize90.0ms

Local error

Found 4 expressions with local error:

1.1b
(pow (+ x 1.0) (/ 1.0 n))
1.5b
(* (+ (sqrt (pow x (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (- (- (/ 0.5 (* n x)) (* (/ 0.25 n) (/ (/ (- (log x)) x) n))) (/ (/ 0.25 (* x x)) n)))
3.0b
(- (/ 0.5 (* n x)) (* (/ 0.25 n) (/ (/ (- (log x)) x) n)))
9.5b
(/ (/ 0.25 (* x x)) n)

rewrite645.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
43×*-un-lft-identity
40×add-sqr-sqrt
30×add-cube-cbrt
27×frac-sub
18×frac-times
16×add-exp-log
15×add-cbrt-cube
13×pow-unpow
11×associate-*r/
8×unpow-prod-down flip3-+ flip-+
7×pow1 flip3-- associate-*r* associate-*l* flip-- associate-/l*
6×associate-*l/ sqrt-prod div-inv distribute-lft-out add-log-exp
5×cbrt-undiv sub-neg div-exp
4×distribute-rgt-in distribute-lft-in associate--l+
3×associate-/r* difference-of-squares
2×prod-exp cbrt-unprod
1×pow-to-exp clear-num pow-pow frac-2neg diff-log pow-prod-down pow-exp *-commutative distribute-lft-out-- unswap-sqr sqr-pow associate-/l/
Counts
4 → 148
Calls
4 calls:
14.0ms
(pow (+ x 1.0) (/ 1.0 n))
567.0ms
(* (+ (sqrt (pow x (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (- (- (/ 0.5 (* n x)) (* (/ 0.25 n) (/ (/ (- (log x)) x) n))) (/ (/ 0.25 (* x x)) n)))
32.0ms
(- (/ 0.5 (* n x)) (* (/ 0.25 n) (/ (/ (- (log x)) x) n)))
22.0ms
(/ (/ 0.25 (* x x)) n)

series976.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(pow (+ x 1.0) (/ 1.0 n))
652.0ms
(* (+ (sqrt (pow x (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n)))) (- (- (/ 0.5 (* n x)) (* (/ 0.25 n) (/ (/ (- (log x)) x) n))) (/ (/ 0.25 (* x x)) n)))
87.0ms
(- (/ 0.5 (* n x)) (* (/ 0.25 n) (/ (/ (- (log x)) x) n)))
42.0ms
(/ (/ 0.25 (* x x)) n)

simplify590.0ms

Counts
160 → 160
Iterations
IterNodes
done5001
11198
0394

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 22.1b

regimes1.0s

Accuracy

79.6% (1.8b remaining)

Error of 22.4b against oracle of 20.6b and baseline of 29.3b

bsearch274.0ms

Steps
ItersRangePoint
7
5787.9300826946865
383123.6636286385
251407.49747499867
9
-2.8555728020291845e+22
-83422883652835.42
-1111966062034791.0

simplify27.0ms

Iterations
IterNodes
done77
577
475
372
267
161
046

end0.0ms

sample8.3s

Algorithm
intervals
Results
2.9s3177×body1280valid
1.5s1663×body640valid
866.0ms1190×body10240exit
652.0ms698×body1280nan
459.0ms639×body640nan
419.0ms4583×body80valid
340.0ms5086×body80nan
332.0ms827×body320valid
150.0ms346×body320nan
95.0ms447×body160valid
35.0ms189×body160nan