Details

Time bar (total: 26.4s)

sample227.0ms

Algorithm
intervals
Results
104.0ms115×body1280valid
24.0ms34×body10240exit
17.0ms37×body640valid
14.0ms38×body320valid
10.0ms131×body80valid
9.0ms146×body80nan
7.0ms17×body640nan
5.0ms12×body1280nan
3.0ms11×body320nan
3.0ms15×body160valid
0.0ms3×body160nan

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11713
23413
38113
423813
5122413
done500013

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.2b
(pow x (/ 1.0 n))
0.5b
(pow (+ x 1.0) (/ 1.0 n))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite173.0ms

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:
5.0ms
(pow x (/ 1.0 n))
11.0ms
(pow (+ x 1.0) (/ 1.0 n))
154.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series639.0ms

Counts
3 → 9
Calls
3 calls:
77.0ms
(pow x (/ 1.0 n))
188.0ms
(pow (+ x 1.0) (/ 1.0 n))
374.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01901337
15461246
221001206
done50001204

prune371.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow x (/ (/ 1.0 n) 2))
0.5b
(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.5b
(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.5b
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
129×pow-unpow
124×add-sqr-sqrt
123×*-un-lft-identity
112×add-cube-cbrt
21×unpow-prod-down
12×div-inv
9×difference-of-squares sqr-pow
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube
3×pow-to-exp pow-pow pow-exp distribute-lft-out distribute-lft-out--
1×sub-neg flip3-- diff-log flip--
Counts
4 → 197
Calls
4 calls:
11.0ms
(pow x (/ (/ 1.0 n) 2))
15.0ms
(pow (+ x 1.0) (/ (/ 1.0 n) 2))
15.0ms
(pow (+ x 1.0) (/ (/ 1.0 n) 2))
92.0ms
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series851.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow x (/ (/ 1.0 n) 2))
206.0ms
(pow (+ x 1.0) (/ (/ 1.0 n) 2))
187.0ms
(pow (+ x 1.0) (/ (/ 1.0 n) 2))
351.0ms
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify2.2s

Counts
209 → 209
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02973215
19602903
237272847
done50012843

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 21.6b

localize36.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (- (log x))) (* x (pow n 2)))))
3.3b
(- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n)))
7.1b
(* x (pow n 2))
9.6b
(* (pow x 2) n)

rewrite968.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
26×*-un-lft-identity
17×associate-*r* associate-*l*
16×add-exp-log
13×frac-sub
12×add-cube-cbrt unpow-prod-down
10×frac-times add-cbrt-cube
9×unswap-sqr
7×flip3-- prod-exp flip--
6×pow1 flip3-+ flip-+ add-log-exp
5×sub-neg associate-*r/
4×distribute-rgt-in distribute-lft-in associate--l+ distribute-lft-out distribute-lft-out-- unpow2 sqr-pow
3×*-commutative cbrt-unprod
2×pow-to-exp associate-*l/ pow-exp difference-of-squares
1×diff-log pow-prod-down
Counts
4 → 118
Calls
4 calls:
875.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (- (log x))) (* x (pow n 2)))))
46.0ms
(- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n)))
19.0ms
(* x (pow n 2))
21.0ms
(* (pow x 2) n)

series664.0ms

Counts
4 → 12
Calls
4 calls:
513.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (- (log x))) (* x (pow n 2)))))
84.0ms
(- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n)))
42.0ms
(* x (pow n 2))
24.0ms
(* (pow x 2) n)

simplify2.8s

Counts
130 → 130
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02824661
18434346
249874033
done50014033

prune915.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.3b

localize61.0ms

Local error

Found 4 expressions with local error:

2.4b
(* (sqrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (+ (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (log x)) (* x (pow n 2)))))
3.3b
(- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n)))
7.1b
(* x (pow n 2))
9.6b
(* (pow x 2) n)

rewrite905.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×*-un-lft-identity
20×associate-*l*
16×add-exp-log associate-*r*
13×add-cube-cbrt
12×unpow-prod-down sqrt-div
10×frac-times add-cbrt-cube unswap-sqr
9×flip3-+ frac-add flip-+
7×prod-exp sqrt-prod
6×pow1 distribute-lft-out add-log-exp
5×associate-*r/
4×flip3-- frac-sub flip-- unpow2 sqr-pow
3×*-commutative cbrt-unprod
2×pow-to-exp associate-*l/ pow-exp distribute-lft-out--
1×distribute-rgt-in sub-neg distribute-lft-in diff-log pow-prod-down difference-of-squares
Counts
4 → 115
Calls
4 calls:
806.0ms
(* (sqrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (+ (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (log x)) (* x (pow n 2)))))
37.0ms
(- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n)))
25.0ms
(* x (pow n 2))
33.0ms
(* (pow x 2) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
894.0ms
(* (sqrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (+ (- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n))) (/ (* 0.25 (log x)) (* x (pow n 2)))))
63.0ms
(- (/ 0.5 (* x n)) (/ 0.25 (* (pow x 2) n)))
35.0ms
(* x (pow n 2))
20.0ms
(* (pow x 2) n)

simplify507.0ms

Counts
127 → 127
Iterations

Useful iterations: done (502.0ms)

IterNodesCost
02894508
19054177
done50003949

prune894.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.3b

regimes307.0ms

Accuracy

81.6% (1.6b remaining)

Error of 22.2b against oracle of 20.7b and baseline of 29.2b

bsearch268.0ms

Steps
ItersRangePoint
8
2.4606182776879063e+18
2.1483055298205296e+21
2.504539914490965e+18
6
-55910705190.40923
-5850708151.804642
-17527377755.617737

simplify21.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
036133
14989
25589
35689
done5689

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.8s3137×body1280valid
1.1s658×body1280nan
982.0ms1544×body640valid
817.0ms1192×body10240exit
543.0ms4763×body80valid
472.0ms692×body640nan
348.0ms4986×body80nan
337.0ms831×body320valid
160.0ms375×body320nan
149.0ms449×body160valid
82.0ms181×body160nan