Details

Time bar (total: 38.3s)

sample261.0ms

Algorithm
intervals
Results
109.0ms114×body1280valid
40.0ms31×body10240exit
29.0ms47×body640valid
15.0ms120×body80valid
13.0ms139×body80nan
13.0ms13×body1280nan
12.0ms28×body320valid
10.0ms16×body640nan
3.0ms7×body320nan
1.0ms6×body160valid
1.0ms4×body160nan

simplify14.0ms

Calls
1 calls:
Slowest
13.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize17.0ms

Local error

Found 3 expressions with local error:

1.2b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.5b
(pow x (/ 1 n))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow-unpow *-un-lft-identity
6×add-cube-cbrt
5×add-log-exp
4×pow1 unpow-prod-down add-exp-log
3×add-cbrt-cube insert-posit16
2×pow-to-exp div-inv difference-of-squares
1×sub-neg pow-pow flip3-- diff-log pow-exp flip-- distribute-lft-out--
Calls
3 calls:
Slowest
19.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms
(pow (+ x 1) (/ 1 n))
2.0ms
(pow x (/ 1 n))

series359.0ms

Calls
3 calls:
Slowest
213.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
82.0ms
(pow (+ x 1) (/ 1 n))
65.0ms
(pow x (/ 1 n))

simplify1.6s

Calls
28 calls:
Slowest
362.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
252.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
237.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
184.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
177.0ms
(- (+ (/ (log -1) n) (+ (* 1/2 (/ (pow (log -1) 2) (pow n 2))) (+ (* 1/2 (/ (pow (log (/ -1 x)) 2) (pow n 2))) 1))) (+ (/ (log (/ -1 x)) n) (/ (* (log (/ -1 x)) (log -1)) (pow n 2))))

prune572.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 21.9b

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(/ 1 (* n x))
0.8b
(/ (log x) (* n (* n x)))
0.2b
(* n (* n x))
0.1b
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-cube-cbrt
7×pow1
5×associate-*r*
4×insert-posit16 add-log-exp
3×times-frac associate-*l* div-inv associate-/l*
2×frac-times rec-exp clear-num associate-/r* frac-2neg flip3-+ associate-*l/ prod-exp *-commutative flip-+
1×cbrt-undiv div-exp pow-prod-down associate-*r/ un-div-inv cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
12.0ms
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
4.0ms
(/ (log x) (* n (* n x)))
1.0ms
(* n (* n x))
1.0ms
(/ 1 (* n x))

series144.0ms

Calls
4 calls:
Slowest
91.0ms
(/ (log x) (* n (* n x)))
29.0ms
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
14.0ms
(* n (* n x))
10.0ms
(/ 1 (* n x))

simplify3.8s

Calls
42 calls:
Slowest
678.0ms
(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
245.0ms
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
234.0ms
(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) 1)
223.0ms
(* (* (* (+ (/ -1/2 x) 1) (+ (/ -1/2 x) 1)) (+ (/ -1/2 x) 1)) (* (* (/ 1 (* n x)) (/ 1 (* n x))) (/ 1 (* n x))))
217.0ms
(/ (* (* (log x) (log x)) (log x)) (* (* (* n (* n x)) (* n (* n x))) (* n (* n x))))

prune885.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ (log x) (* n (* n x)))
0.2b
(/ (/ 1 n) x)
0.2b
(* n (* n x))
0.1b
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×associate-/l*
6×pow1
5×associate-*r*
4×insert-posit16 div-inv add-log-exp
3×times-frac associate-*l*
2×frac-times clear-num frac-2neg flip3-+ associate-*l/ *-commutative flip-+
1×cbrt-undiv associate-/r* div-exp pow-prod-down prod-exp associate-*r/ cbrt-unprod associate-/l/
Calls
4 calls:
Slowest
9.0ms
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
6.0ms
(/ (/ 1 n) x)
4.0ms
(/ (log x) (* n (* n x)))
1.0ms
(* n (* n x))

series152.0ms

Calls
4 calls:
Slowest
97.0ms
(/ (log x) (* n (* n x)))
28.0ms
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
16.0ms
(* n (* n x))
11.0ms
(/ (/ 1 n) x)

simplify4.3s

Calls
40 calls:
Slowest
770.0ms
(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
493.0ms
(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ (/ 1 n) x))
348.0ms
(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ 1 n))
297.0ms
(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) (/ 1 n))
276.0ms
(* (+ (* (/ -1/2 x) (/ -1/2 x)) (- (* 1 1) (* (/ -1/2 x) 1))) x)

prune1.3s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 21.0b

localize40.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n) (- (/ -1/2 x) 1))
3.9b
(/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n)
0.8b
(/ (log x) (* n (* n x)))
0.3b
(* (/ -1/2 x) (/ -1/2 x))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
11×div-inv associate-/l*
10×add-cbrt-cube add-exp-log
9×pow1
5×associate-/r* difference-of-sqr-1 div-sub
4×associate-*r* associate-*l* insert-posit16 add-log-exp
3×clear-num frac-2neg
2×cbrt-undiv div-exp associate-/r/ associate-/l/
1×pow2 frac-times pow-plus flip3-- pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
4 calls:
Slowest
27.0ms
(/ (/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n) (- (/ -1/2 x) 1))
10.0ms
(/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n)
4.0ms
(/ (log x) (* n (* n x)))
4.0ms
(* (/ -1/2 x) (/ -1/2 x))

series166.0ms

Calls
4 calls:
Slowest
75.0ms
(/ (log x) (* n (* n x)))
53.0ms
(/ (/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n) (- (/ -1/2 x) 1))
26.0ms
(/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n)
11.0ms
(* (/ -1/2 x) (/ -1/2 x))

simplify12.4s

Calls
88 calls:
Slowest
737.0ms
(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
402.0ms
(/ (/ (/ (* (/ -1/2 x) (/ -1/2 x)) x) n) (- (/ -1/2 x) 1))
384.0ms
(/ (sqrt (/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n)) (sqrt (- (/ -1/2 x) 1)))
376.0ms
(/ (* (cbrt (/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n)) (cbrt (/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) n))) (* (cbrt (- (/ -1/2 x) 1)) (cbrt (- (/ -1/2 x) 1))))
359.0ms
(/ (/ (- (* (/ -1/2 x) (/ -1/2 x)) 1) x) 1)

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 20.0b

regimes313.0ms

Accuracy

84.2% (1.5b remaining)

Error of 21.5b against oracle of 20.0b and baseline of 29.3b

bsearch11.0ms

end0.0ms

sample10.6s

Algorithm
intervals
Results
3.5s3178×body1280valid
1.4s1638×body640valid
1.3s1086×body10240exit
1.1s4690×body80valid
855.0ms867×body320valid
654.0ms603×body1280nan
594.0ms5049×body80nan
499.0ms594×body640nan
174.0ms292×body320nan
134.0ms432×body160valid
54.0ms186×body160nan