Details

Time bar (total: 2.4m)

sample318.0ms

Algorithm
intervals
Results
134.0ms103×body1280valid
36.0ms46×body10240exit
32.0ms49×body640valid
26.0ms27×body1280nan
22.0ms169×body80valid
15.0ms22×body640nan
15.0ms148×body80nan
14.0ms31×body320valid
4.0ms9×body320nan
3.0ms10×body160valid
2.0ms8×body160nan

simplify733.0ms

Calls
1 calls:
Slowest
733.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize34.0ms

Local error

Found 3 expressions with local error:

1.6b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.8b
(pow x (/ 1 n))
0.7b
(pow (+ x 1) (/ 1 n))

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×unpow-prod-down
63×add-sqr-sqrt
56×prod-diff
51×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
5×pow1 add-exp-log add-log-exp
3×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Calls
3 calls:
Slowest
115.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
13.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))

series435.0ms

Calls
3 calls:
Slowest
250.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
106.0ms
(pow (+ x 1) (/ 1 n))
78.0ms
(pow x (/ 1 n))

simplify40.5s

Calls
188 calls:
Slowest
700.0ms
(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
659.0ms
(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
561.0ms
(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
556.0ms
(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
550.0ms
(+ (sqrt (pow (+ x 1) (/ 1 n))) (pow (sqrt x) (/ 1 n)))

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (pow x (/ 1 n)))
1.6b
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
0.8b
(pow x (/ 1 n))
0.7b
(pow (+ x 1) (/ 1 n))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity
85×add-sqr-sqrt unpow-prod-down
80×prod-diff
72×log-prod
68×add-cube-cbrt
65×exp-sum
29×sqr-pow
26×pow-unpow
18×times-frac
12×distribute-lft-out difference-of-squares
8×fma-neg add-exp-log
6×pow1 add-log-exp
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u
3×pow-to-exp rem-log-exp pow-exp
2×pow-pow div-inv
1×sub-neg flip3-- diff-log log-pow flip-- distribute-lft-out--
Calls
4 calls:
Slowest
82.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
14.0ms
(pow (+ x 1) (/ 1 n))
5.0ms
(pow x (/ 1 n))
3.0ms
(log (pow x (/ 1 n)))

series574.0ms

Calls
4 calls:
Slowest
246.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
132.0ms
(log (pow x (/ 1 n)))
120.0ms
(pow (+ x 1) (/ 1 n))
76.0ms
(pow x (/ 1 n))

simplify1.0m

Calls
252 calls:
Slowest
782.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (exp (log (pow (sqrt x) (/ 1 n)))))
727.0ms
(fma (- (exp (log (sqrt (pow x (/ 1 n)))))) (exp (log (sqrt (pow x (/ 1 n))))) (* (exp (log (sqrt (pow x (/ 1 n))))) (exp (log (sqrt (pow x (/ 1 n)))))))
632.0ms
(fma (pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n)) (pow (cbrt (+ x 1)) (/ 1 n)) (- (* (cbrt (exp (log (pow x (/ 1 n))))) (* (cbrt (exp (log (pow x (/ 1 n))))) (cbrt (exp (log (pow x (/ 1 n)))))))))
593.0ms
(- (pow (+ x 1) (/ (/ 1 n) 2)) (exp (log (pow (sqrt x) (/ 1 n)))))
591.0ms
(- (pow (sqrt (+ x 1)) (/ 1 n)) (exp (log (sqrt (pow x (/ 1 n))))))

prune2.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.7b

localize38.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (pow x (/ (/ 1 n) 2)))
2.6b
(log (pow x (/ (/ 1 n) 2)))
1.9b
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (exp (log (pow x (/ (/ 1 n) 2)))) (exp (log (pow x (/ (/ 1 n) 2)))))))
0.8b
(pow x (/ (/ 1 n) 2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
44×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
43×pow-unpow
14×log-prod
9×unpow-prod-down add-exp-log
6×rem-log-exp
5×pow1
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-to-exp pow-exp sqr-pow
2×log-pow
1×pow-pow fma-udef
Calls
4 calls:
Slowest
7.0ms
(log (pow x (/ (/ 1 n) 2)))
7.0ms
(pow x (/ (/ 1 n) 2))
7.0ms
(log (pow x (/ (/ 1 n) 2)))
0.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (exp (log (pow x (/ (/ 1 n) 2)))) (exp (log (pow x (/ (/ 1 n) 2)))))))

series652.0ms

Calls
4 calls:
Slowest
343.0ms
(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (exp (log (pow x (/ (/ 1 n) 2)))) (exp (log (pow x (/ (/ 1 n) 2)))))))
137.0ms
(log (pow x (/ (/ 1 n) 2)))
105.0ms
(log (pow x (/ (/ 1 n) 2)))
67.0ms
(pow x (/ (/ 1 n) 2))

simplify8.7s

Calls
81 calls:
Slowest
629.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
501.0ms
(log (sqrt (pow x (/ (/ 1 n) 2))))
468.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
467.0ms
(log (pow (* (cbrt x) (cbrt x)) (/ (/ 1 n) 2)))
456.0ms
(log (sqrt (pow x (/ (/ 1 n) 2))))

prune2.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.7b

localize64.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (pow x (/ (/ 1 n) 2)))
2.6b
(log (pow x (/ (/ 1 n) 2)))
2.6b
(log (pow x (/ (/ 1 n) 2)))
2.6b
(log (pow x (/ (/ 1 n) 2)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
28×log-prod
12×add-sqr-sqrt unpow-prod-down *-un-lft-identity rem-log-exp add-exp-log add-cube-cbrt
4×expm1-log1p-u pow-to-exp pow1 add-cbrt-cube pow-exp log-pow insert-posit16 log1p-expm1-u add-log-exp sqr-pow
Calls
4 calls:
Slowest
4.0ms
(log (pow x (/ (/ 1 n) 2)))
4.0ms
(log (pow x (/ (/ 1 n) 2)))
3.0ms
(log (pow x (/ (/ 1 n) 2)))
3.0ms
(log (pow x (/ (/ 1 n) 2)))

series797.0ms

Calls
4 calls:
Slowest
460.0ms
(log (pow x (/ (/ 1 n) 2)))
128.0ms
(log (pow x (/ (/ 1 n) 2)))
110.0ms
(log (pow x (/ (/ 1 n) 2)))
99.0ms
(log (pow x (/ (/ 1 n) 2)))

simplify11.6s

Calls
56 calls:
Slowest
638.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
609.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
571.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
551.0ms
(* -1 (/ (- (* 1/2 (log (/ -1 x))) (* 1/2 (log -1))) n))
503.0ms
(log (pow (* (cbrt x) (cbrt x)) (/ (/ 1 n) 2)))

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.7b

regimes271.0ms

Accuracy

79.8% (2.3b remaining)

Error of 20.6b against oracle of 18.3b and baseline of 29.9b

bsearch317.0ms

end0.0ms

sample10.1s

Algorithm
intervals
Results
3.2s3106×body1280valid
1.9s1146×body10240exit
1.3s1621×body640valid
747.0ms618×body1280nan
718.0ms4867×body80valid
657.0ms5100×body80nan
490.0ms673×body640nan
412.0ms862×body320valid
183.0ms345×body320nan
124.0ms426×body160valid
49.0ms184×body160nan