Details

Time bar (total: 1.1m)

sample279.0ms

Algorithm
intervals
Results
108.0ms114×body1280valid
40.0ms28×body320valid
29.0ms47×body640valid
23.0ms31×body10240exit
17.0ms13×body1280nan
15.0ms120×body80valid
14.0ms139×body80nan
11.0ms16×body640nan
3.0ms7×body320nan
2.0ms6×body160valid
1.0ms4×body160nan

simplify17.0ms

Calls
1 calls:
Slowest
17.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize30.0ms

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))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
16×unpow-prod-down
8×pow-unpow
6×fma-neg
5×add-log-exp
4×pow1 add-exp-log
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
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
41.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
5.0ms
(pow (+ x 1) (/ 1 n))
2.0ms
(pow x (/ 1 n))

series394.0ms

Calls
3 calls:
Slowest
236.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
89.0ms
(pow (+ x 1) (/ 1 n))
69.0ms
(pow x (/ 1 n))

simplify4.1s

Calls
69 calls:
Slowest
806.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
281.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
278.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
235.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
234.0ms
(- (+ (/ (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))))

prune835.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
0.5b
(pow x (/ 1 n))
0.1b
(/ (log1p x) n)
0.0b
(exp (/ (log1p x) n))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
9×prod-diff
7×add-log-exp
4×expm1-log1p-u pow1 pow-unpow exp-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×fma-neg div-inv associate-/l*
1×pow-to-exp clear-num sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares rem-exp-log
Calls
4 calls:
Slowest
30.0ms
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
5.0ms
(/ (log1p x) n)
4.0ms
(exp (/ (log1p x) n))
1.0ms
(pow x (/ 1 n))

series394.0ms

Calls
4 calls:
Slowest
205.0ms
(- (exp (/ (log1p x) n)) (pow x (/ 1 n)))
72.0ms
(exp (/ (log1p x) n))
64.0ms
(/ (log1p x) n)
53.0ms
(pow x (/ 1 n))

simplify3.8s

Calls
47 calls:
Slowest
466.0ms
(- (+ (/ x n) (* 1/3 (/ (pow x 3) n))) (* 1/2 (/ (pow x 2) n)))
383.0ms
(- (+ (/ (log -1) n) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) n)))
374.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
336.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
264.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune849.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 19.5b

localize8.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (pow E (/ (log1p x) n)) (pow x (/ 1 n)))
0.5b
(pow x (/ 1 n))
0.1b
(/ (log1p x) n)
0.0b
(pow E (/ (log1p x) n))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
9×prod-diff
8×pow-unpow
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×fma-neg div-inv associate-/l*
2×pow-to-exp
1×clear-num sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Calls
4 calls:
Slowest
10.0ms
(- (pow E (/ (log1p x) n)) (pow x (/ 1 n)))
3.0ms
(/ (log1p x) n)
1.0ms
(pow E (/ (log1p x) n))
1.0ms
(pow x (/ 1 n))

series482.0ms

Calls
4 calls:
Slowest
238.0ms
(- (pow E (/ (log1p x) n)) (pow x (/ 1 n)))
91.0ms
(pow E (/ (log1p x) n))
90.0ms
(/ (log1p x) n)
64.0ms
(pow x (/ 1 n))

simplify3.7s

Calls
46 calls:
Slowest
454.0ms
(- (+ (/ x n) (* 1/3 (/ (pow x 3) n))) (* 1/2 (/ (pow x 2) n)))
416.0ms
(- (+ (/ (log -1) n) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) n)))
315.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
304.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
255.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune977.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 19.5b

localize34.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (/ 1 (* n x)) (/ (- (log x)) (* n (* n x))))
1.1b
(/ 1 (* n x))
1.1b
(/ 1 (* n x))
0.8b
(/ (- (log x)) (* n (* n x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
56×prod-diff
50×times-frac
44×*-un-lft-identity
43×add-sqr-sqrt
41×add-cube-cbrt
23×div-inv
18×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/l*
8×add-exp-log
6×pow1 neg-mul-1 add-cbrt-cube add-log-exp
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
3×clear-num associate-/r* frac-2neg
2×neg-sub0 rec-exp div-sub pow-flip distribute-lft-out-- inv-pow
1×cbrt-undiv sub-neg flip3-- diff-log div-exp distribute-frac-neg frac-sub flip-- associate--r- difference-of-squares
Calls
4 calls:
Slowest
11.0ms
(- (/ 1 (* n x)) (/ (- (log x)) (* n (* n x))))
11.0ms
(/ (- (log x)) (* n (* n x)))
2.0ms
(/ 1 (* n x))
1.0ms
(/ 1 (* n x))

series184.0ms

Calls
4 calls:
Slowest
112.0ms
(/ (- (log x)) (* n (* n x)))
57.0ms
(- (/ 1 (* n x)) (/ (- (log x)) (* n (* n x))))
8.0ms
(/ 1 (* n x))
7.0ms
(/ 1 (* n x))

simplify33.1s

Calls
168 calls:
Slowest
635.0ms
(fma (- (/ (- (log x)) (* n x))) (/ 1 n) (* (/ (- (log x)) (* n x)) (/ 1 n)))
613.0ms
(fma (- (/ (- (log x)) (* n x))) (/ 1 n) (* (/ (- (log x)) (* n x)) (/ 1 n)))
587.0ms
(fma (- (/ (- (log x)) (* n x))) (/ 1 n) (* (/ (- (log x)) (* n x)) (/ 1 n)))
581.0ms
(fma (- (/ (- (log x)) (* n x))) (/ 1 n) (* (/ (- (log x)) (* n x)) (/ 1 n)))
578.0ms
(fma (- (/ (cbrt (log x)) (* n x))) (/ (- (* (cbrt (log x)) (cbrt (log x)))) n) (* (/ (cbrt (log x)) (* n x)) (/ (- (* (cbrt (log x)) (cbrt (log x)))) n)))

prune1.9s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 18.5b

regimes343.0ms

Accuracy

85.5% (1.7b remaining)

Error of 19.3b against oracle of 17.6b and baseline of 29.3b

bsearch1.2s

end0.0ms

sample10.8s

Algorithm
intervals
Results
3.5s3178×body1280valid
1.7s1086×body10240exit
1.5s1638×body640valid
710.0ms4690×body80valid
663.0ms603×body1280nan
619.0ms5049×body80nan
587.0ms432×body160valid
482.0ms867×body320valid
451.0ms594×body640nan
147.0ms292×body320nan
57.0ms186×body160nan