Details

Time bar (total: 29.5s)

sample323.0ms

Algorithm
intervals
Results
93.0ms90×body1280valid
73.0ms68×body640valid
31.0ms29×body1280nan
25.0ms31×body10240exit
23.0ms151×body80valid
19.0ms173×body80nan
15.0ms31×body320valid
13.0ms15×body640nan
4.0ms8×body320nan
3.0ms10×body160valid
2.0ms5×body160nan

simplify13.0ms

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: 31.6b

localize41.0ms

Local error

Found 3 expressions with local error:

1.2b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b
(pow (+ x 1) (/ 1 n))
0.2b
(pow x (/ 1 n))

rewrite26.0ms

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
20.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms
(pow (+ x 1) (/ 1 n))
1.0ms
(pow x (/ 1 n))

series912.0ms

Calls
3 calls:
Slowest
732.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
111.0ms
(pow (+ x 1) (/ 1 n))
69.0ms
(pow x (/ 1 n))

simplify1.6s

Calls
28 calls:
Slowest
328.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
253.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
217.0ms
(- (+ (/ (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))))
193.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
184.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune583.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.9b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b
(pow (+ x 1) (/ 1 n))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity
10×add-log-exp
6×unpow-prod-down add-cube-cbrt difference-of-squares
5×pow1 add-exp-log
4×pow-unpow add-cbrt-cube insert-posit16
3×sub-neg flip3-- diff-log flip-- distribute-lft-out--
1×pow-to-exp pow-pow pow-exp div-inv
Calls
4 calls:
Slowest
14.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
11.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
10.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
2.0ms
(pow (+ x 1) (/ 1 n))

series774.0ms

Calls
4 calls:
Slowest
250.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
211.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
211.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
101.0ms
(pow (+ x 1) (/ 1 n))

simplify2.5s

Calls
39 calls:
Slowest
358.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
296.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
275.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
262.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
240.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 22.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (* n x))
0.4b
(/ (log x) (* n (* n x)))
0.1b
(* n (* n x))
0.1b
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))

rewrite15.0ms

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
8.0ms
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
4.0ms
(/ (log x) (* n (* n x)))
1.0ms
(* n (* n x))
1.0ms
(/ 1 (* n x))

series189.0ms

Calls
4 calls:
Slowest
80.0ms
(/ (log x) (* n (* n x)))
68.0ms
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
29.0ms
(* n (* n x))
11.0ms
(/ 1 (* n x))

simplify3.8s

Calls
42 calls:
Slowest
710.0ms
(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
282.0ms
(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) 1)
282.0ms
(* (+ (/ -1/2 x) 1) (/ 1 (* n x)))
225.0ms
(/ (* (* (log x) (log x)) (log x)) (* (* (* n (* n x)) (* n (* n x))) (* n (* n x))))
199.0ms
(- (/ 1 (* x n)) (* 1/2 (/ 1 (* (pow x 2) n))))

prune925.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (log x) (* n (* n x)))
0.2b
(/ (/ 1 n) x)
0.1b
(* n (* n x))
0.1b
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))

rewrite32.0ms

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
18.0ms
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
7.0ms
(/ (log x) (* n (* n x)))
5.0ms
(/ (/ 1 n) x)
2.0ms
(* n (* n x))

series202.0ms

Calls
4 calls:
Slowest
85.0ms
(/ (log x) (* n (* n x)))
60.0ms
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
31.0ms
(* n (* n x))
26.0ms
(/ (/ 1 n) x)

simplify4.3s

Calls
40 calls:
Slowest
678.0ms
(* -1 (/ (log (/ 1 x)) (* x (pow n 2))))
443.0ms
(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ (/ 1 n) x))
403.0ms
(* (- (* (/ -1/2 x) (/ -1/2 x)) (* 1 1)) (/ 1 n))
289.0ms
(* (+ (/ -1/2 x) 1) (/ (/ 1 n) x))
283.0ms
(* (+ (pow (/ -1/2 x) 3) (pow 1 3)) (/ 1 n))

prune826.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 22.4b

regimes450.0ms

Accuracy

85.9% (1.2b remaining)

Error of 22.1b against oracle of 20.9b and baseline of 29.4b

bsearch362.0ms

end0.0ms

sample10.5s

Algorithm
intervals
Results
3.2s3149×body1280valid
1.6s1158×body10240exit
1.3s1685×body640valid
1.2s4675×body80valid
787.0ms664×body1280nan
577.0ms4932×body80nan
570.0ms614×body640nan
437.0ms823×body320valid
203.0ms319×body320nan
153.0ms383×body160valid
49.0ms184×body160nan