Details

Time bar (total: 23.5s)

sample178.0ms

Algorithm
intervals
Results
58.0ms109×body1280valid
19.0ms50×body640valid
18.0ms164×body80valid
13.0ms35×body10240exit
12.0ms22×body1280nan
9.0ms20×body640nan
9.0ms165×body80nan
7.0ms26×body320valid
2.0ms11×body320nan
2.0ms13×body160valid
0.0ms2×body160nan

simplify1.1s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize15.0ms

Local error

Found 2 expressions with local error:

1.1b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b
(pow (+ x 1.0) (/ 1.0 n))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×*-un-lft-identity
14×unpow-prod-down
13×pow-unpow
10×add-cube-cbrt
9×times-frac difference-of-squares
7×sqr-pow
4×add-log-exp
3×pow1 add-exp-log distribute-lft-out--
2×add-cbrt-cube distribute-lft-out
1×pow-to-exp sub-neg pow-pow flip3-- diff-log pow-exp div-inv flip--
Counts
2 → 52
Calls
2 calls:
85.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms
(pow (+ x 1.0) (/ 1.0 n))

series643.0ms

Counts
2 → 6
Calls
2 calls:
428.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
215.0ms
(pow (+ x 1.0) (/ 1.0 n))

simplify881.0ms

Counts
58 → 58
Iterations
IterNodes
done5001
21423
1401
0148

prune421.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (pow (+ 1.0 x) (/ 1.0 n)))
0.0b
(log (exp (pow (+ 1.0 x) (/ 1.0 n))))
1.1b
(- (log (exp (pow (+ 1.0 x) (/ 1.0 n)))) (pow x (/ 1.0 n)))
1.7b
(pow (+ 1.0 x) (/ 1.0 n))

rewrite344.0ms

Algorithm
rewrite-expression-head
Rules
27×*-un-lft-identity
23×add-sqr-sqrt
18×add-cube-cbrt
16×exp-prod
13×pow-unpow unpow-prod-down
10×log-pow
9×times-frac
7×pow1
6×log-prod add-log-exp
5×add-exp-log
4×add-cbrt-cube sqr-pow
3×associate--l+ distribute-lft-out difference-of-squares
2×distribute-lft-out--
1×pow-to-exp sub-neg pow-pow flip3-- diff-log rem-log-exp pow-exp div-inv flip-- rem-exp-log
Counts
4 → 84
Calls
4 calls:
29.0ms
(exp (pow (+ 1.0 x) (/ 1.0 n)))
42.0ms
(log (exp (pow (+ 1.0 x) (/ 1.0 n))))
256.0ms
(- (log (exp (pow (+ 1.0 x) (/ 1.0 n)))) (pow x (/ 1.0 n)))
13.0ms
(pow (+ 1.0 x) (/ 1.0 n))

series1.1s

Counts
4 → 12
Calls
4 calls:
395.0ms
(exp (pow (+ 1.0 x) (/ 1.0 n)))
186.0ms
(log (exp (pow (+ 1.0 x) (/ 1.0 n))))
339.0ms
(- (log (exp (pow (+ 1.0 x) (/ 1.0 n)))) (pow x (/ 1.0 n)))
212.0ms
(pow (+ 1.0 x) (/ 1.0 n))

simplify894.0ms

Counts
96 → 96
Iterations
IterNodes
done5000
21748
1485
0188

prune551.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize41.0ms

Local error

Found 4 expressions with local error:

1.7b
(pow (+ x 1.0) (/ 1.0 n))
1.7b
(pow (+ x 1.0) (/ 1.0 n))
1.7b
(pow (+ x 1.0) (/ 1.0 n))
35.5b
(- (log (* (* (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))) (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

rewrite988.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow *-un-lft-identity
33×add-sqr-sqrt
28×add-cube-cbrt
27×times-frac
13×pow1 unpow-prod-down
7×add-exp-log
5×add-log-exp
4×add-cbrt-cube distribute-lft-out-- sqr-pow
3×pow-to-exp pow-pow pow-prod-down pow-exp log-pow div-inv distribute-lft-out difference-of-squares
1×log-prod sub-neg flip3-- diff-log associate--l+ flip--
Counts
4 → 104
Calls
4 calls:
16.0ms
(pow (+ x 1.0) (/ 1.0 n))
9.0ms
(pow (+ x 1.0) (/ 1.0 n))
9.0ms
(pow (+ x 1.0) (/ 1.0 n))
944.0ms
(- (log (* (* (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))) (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

series1.0s

Counts
4 → 12
Calls
4 calls:
247.0ms
(pow (+ x 1.0) (/ 1.0 n))
230.0ms
(pow (+ x 1.0) (/ 1.0 n))
227.0ms
(pow (+ x 1.0) (/ 1.0 n))
322.0ms
(- (log (* (* (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))) (cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))) (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

simplify871.0ms

Counts
116 → 116
Iterations
IterNodes
done5001
21438
1395
0144

prune818.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (* 1.0 (log x)) (* (pow n 2) x))
2.3b
(+ (/ (/ 1.0 n) x) (/ (* 1.0 (log x)) (* (pow n 2) x)))
9.1b
(/ (/ 0.5 n) (* x x))
9.5b
(* (pow n 2) x)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log
32×times-frac
30×add-cbrt-cube
27×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
15×prod-exp
14×div-exp associate-/l*
10×cbrt-undiv
8×associate-*l*
7×cbrt-unprod
6×add-log-exp
4×pow1 unpow-prod-down div-inv unswap-sqr
3×pow-to-exp associate-*r* pow-exp
2×clear-num associate-/r* frac-2neg unpow2 sqr-pow
1×+-commutative sum-log flip3-+ frac-add *-commutative flip-+ distribute-lft-out associate-/l/
Counts
4 → 111
Calls
4 calls:
13.0ms
(/ (* 1.0 (log x)) (* (pow n 2) x))
50.0ms
(+ (/ (/ 1.0 n) x) (/ (* 1.0 (log x)) (* (pow n 2) x)))
21.0ms
(/ (/ 0.5 n) (* x x))
11.0ms
(* (pow n 2) x)

series305.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ (* 1.0 (log x)) (* (pow n 2) x))
108.0ms
(+ (/ (/ 1.0 n) x) (/ (* 1.0 (log x)) (* (pow n 2) x)))
47.0ms
(/ (/ 0.5 n) (* x x))
30.0ms
(* (pow n 2) x)

simplify3.0s

Counts
123 → 123
Iterations
IterNodes
done5001
24488
1669
0240

prune737.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.4b

regimes448.0ms

Accuracy

90.8% (1.7b remaining)

Error of 21.8b against oracle of 20.1b and baseline of 38.7b

bsearch297.0ms

Steps
ItersRangePoint
8
11826.435389185313
20118063.614914328
18355886.857708633
10
-1399252.2602825884
-1.2609713053774054e-13
-981129.0977466904

simplify9.0ms

Iterations
IterNodes
done59
259
158
047

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.9s3114×body1280valid
1.3s1155×body10240exit
943.0ms1633×body640valid
546.0ms4699×body80valid
509.0ms592×body1280nan
480.0ms653×body640nan
403.0ms5042×body80nan
389.0ms836×body320valid
158.0ms471×body160valid
110.0ms323×body320nan
40.0ms208×body160nan