Details

Time bar (total: 29.3s)

sample283.0ms

Algorithm
intervals
Results
98.0ms104×body1280valid
33.0ms53×body640valid
31.0ms33×body10240exit
15.0ms17×body1280nan
14.0ms22×body640nan
14.0ms130×body80valid
13.0ms173×body80nan
10.0ms24×body320valid
5.0ms13×body320nan
4.0ms15×body160valid
1.0ms7×body160nan

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0813
11713
23413
38113
423813
5122413
done500013

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.5b
(pow x (/ 1.0 n))
1.0b
(pow (+ x 1.0) (/ 1.0 n))
2.0b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite215.0ms

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:
9.0ms
(pow x (/ 1.0 n))
26.0ms
(pow (+ x 1.0) (/ 1.0 n))
174.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series959.0ms

Counts
3 → 9
Calls
3 calls:
111.0ms
(pow x (/ 1.0 n))
290.0ms
(pow (+ x 1.0) (/ 1.0 n))
557.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.3s

Counts
88 → 88
Iterations

Useful iterations: done (2.3s)

IterNodesCost
01901337
15461246
221001206
done50001204

prune696.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
0.5b
(pow x (/ 1.0 n))
1.0b
(pow (+ x 1.0) (/ 1.0 n))
2.0b
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite413.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
47×unpow-prod-down
33×*-un-lft-identity
29×pow-unpow
27×difference-of-squares
25×add-cube-cbrt
24×cbrt-prod
23×sqr-pow
18×times-frac
17×cube-prod
8×add-exp-log
6×pow1 pow-exp add-log-exp
5×add-cbrt-cube
4×pow-to-exp
3×pow-pow distribute-lft-out
2×div-inv
1×cube-mult sub-neg flip3-- diff-log unpow3 flip-- distribute-lft-out-- rem-cube-cbrt
Counts
4 → 130
Calls
4 calls:
32.0ms
(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
11.0ms
(pow x (/ 1.0 n))
25.0ms
(pow (+ x 1.0) (/ 1.0 n))
333.0ms
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series1.3s

Counts
4 → 12
Calls
4 calls:
417.0ms
(pow (pow (+ x 1.0) (/ 1.0 n)) 3)
105.0ms
(pow x (/ 1.0 n))
261.0ms
(pow (+ x 1.0) (/ 1.0 n))
489.0ms
(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify2.9s

Counts
142 → 142
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02542695
17552341
231722259
done50002256

prune951.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 0.5 (* (pow x 2) n))
1.8b
(- (/ 1.0 (* x n)) (/ 0.5 (* (pow x 2) n)))
8.1b
(* (pow x 2) n)
8.6b
(* x (pow n 2))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×add-exp-log
14×*-un-lft-identity
13×add-cbrt-cube
12×add-cube-cbrt
11×associate-*r* associate-*l*
9×prod-exp
8×unpow-prod-down unswap-sqr
6×add-log-exp
4×pow1 div-exp unpow2 sqr-pow
3×pow-to-exp times-frac pow-exp cbrt-unprod associate-/l*
2×cbrt-undiv *-commutative
1×sub-neg flip3-- frac-2neg diff-log clear-num associate-/r* frac-sub flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 92
Calls
4 calls:
21.0ms
(/ 0.5 (* (pow x 2) n))
63.0ms
(- (/ 1.0 (* x n)) (/ 0.5 (* (pow x 2) n)))
23.0ms
(* (pow x 2) n)
32.0ms
(* x (pow n 2))

series224.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 0.5 (* (pow x 2) n))
91.0ms
(- (/ 1.0 (* x n)) (/ 0.5 (* (pow x 2) n)))
34.0ms
(* (pow x 2) n)
53.0ms
(* x (pow n 2))

simplify2.1s

Counts
104 → 104
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01531113
13741033
22073907
done5001905

prune749.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.7b

localize80.0ms

Local error

Found 4 expressions with local error:

1.8b
(- (/ 1.0 (* x n)) (/ 0.5 (log (exp (* (pow x 2) n)))))
2.5b
(log (exp (* (pow x 2) n)))
8.1b
(* (pow x 2) n)
8.6b
(* x (pow n 2))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
14×add-exp-log
13×*-un-lft-identity
11×add-cube-cbrt associate-*r* associate-*l*
8×unpow-prod-down add-cbrt-cube unswap-sqr
7×add-log-exp
6×prod-exp
5×pow1
4×unpow2 sqr-pow
3×log-prod log-pow
2×pow-to-exp pow-exp *-commutative cbrt-unprod difference-of-squares
1×sub-neg exp-prod flip3-- exp-to-pow times-frac diff-log rem-log-exp frac-sub flip-- distribute-lft-out--
Counts
4 → 84
Calls
4 calls:
72.0ms
(- (/ 1.0 (* x n)) (/ 0.5 (log (exp (* (pow x 2) n)))))
8.0ms
(log (exp (* (pow x 2) n)))
25.0ms
(* (pow x 2) n)
24.0ms
(* x (pow n 2))

series218.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(- (/ 1.0 (* x n)) (/ 0.5 (log (exp (* (pow x 2) n)))))
35.0ms
(log (exp (* (pow x 2) n)))
34.0ms
(* (pow x 2) n)
53.0ms
(* x (pow n 2))

simplify1.7s

Counts
96 → 96
Iterations

Useful iterations: 2 (486.0ms)

IterNodesCost
01471093
1339955
21668841
done5001841

prune748.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.7b

regimes593.0ms

Accuracy

75.9% (2.1b remaining)

Error of 22.7b against oracle of 20.6b and baseline of 29.3b

bsearch2.0ms

simplify27.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
04086
14986
25386
35686
done5686

end0.0ms

sample11.0s

Algorithm
intervals
Results
3.7s3186×body1280valid
1.2s1552×body640valid
1.2s1166×body10240exit
874.0ms865×body320valid
855.0ms653×body1280nan
616.0ms4757×body80valid
505.0ms4952×body80nan
494.0ms680×body640nan
216.0ms438×body160valid
206.0ms364×body320nan
47.0ms191×body160nan