Average Error: 29.5 → 21.4
Time: 23.7s
Precision: 64
Internal Precision: 128
\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{n} \le -0.6517347580237447:\\ \;\;\;\;\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right)}\\ \mathbf{elif}\;\frac{1}{n} \le 2.242242130232908 \cdot 10^{-09}:\\ \;\;\;\;\frac{\log x}{n \cdot \left(x \cdot n\right)} + \left(\frac{1}{x \cdot n} + \frac{\frac{\frac{-1}{2}}{x}}{x \cdot n}\right)\\ \mathbf{elif}\;\frac{1}{n} \le 2.1870911623611415 \cdot 10^{+170}:\\ \;\;\;\;\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - 1} \cdot \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right)\\ \end{array}\]

Error

Bits error versus x

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ 1 n) < -0.6517347580237447 or 2.242242130232908e-09 < (/ 1 n) < 2.1870911623611415e+170

    1. Initial program 3.1

      \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
    2. Using strategy rm

    3. Applied add-exp-log3.1

      \[\leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt3.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}}\]
    6. Using strategy rm

    7. Applied add-cube-cbrt3.1

      \[\leadsto \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}}}\]
    8. Using strategy rm

    9. Applied add-cube-cbrt3.2

      \[\leadsto \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \color{blue}{\left(\left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}}\]

    10. Applied log-prod3.2

      \[\leadsto \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\color{blue}{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}}}\right) \cdot \sqrt[3]{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}}\]

    if -0.6517347580237447 < (/ 1 n) < 2.242242130232908e-09

    1. Initial program 44.8

      \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
    2. Using strategy rm

    3. Applied add-exp-log44.8

      \[\leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\]

    4. Taylor expanded around inf 33.0

      \[\leadsto \color{blue}{\frac{1}{x \cdot n} - \left(\frac{\log \left(\frac{1}{x}\right)}{x \cdot {n}^{2}} + \frac{1}{2} \cdot \frac{1}{{x}^{2} \cdot n}\right)}\]

    5. Simplified32.9

      \[\leadsto \color{blue}{\frac{\log x}{n \cdot \left(n \cdot x\right)} + \left(\frac{\frac{\frac{-1}{2}}{x}}{n \cdot x} + \frac{1}{n \cdot x}\right)}\]

    if 2.1870911623611415e+170 < (/ 1 n)

    1. Initial program 40.7

      \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
    2. Using strategy rm

    3. Applied add-exp-log40.7

      \[\leadsto {\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\]
    4. Using strategy rm

    5. Applied add-cube-cbrt40.7

      \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}}\]

    6. Taylor expanded around 0 18.8

      \[\leadsto \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\color{blue}{0}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification21.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{n} \le -0.6517347580237447:\\ \;\;\;\;\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right)}\\ \mathbf{elif}\;\frac{1}{n} \le 2.242242130232908 \cdot 10^{-09}:\\ \;\;\;\;\frac{\log x}{n \cdot \left(x \cdot n\right)} + \left(\frac{1}{x \cdot n} + \frac{\frac{\frac{-1}{2}}{x}}{x \cdot n}\right)\\ \mathbf{elif}\;\frac{1}{n} \le 2.1870911623611415 \cdot 10^{+170}:\\ \;\;\;\;\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - 1} \cdot \left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}} \cdot \sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019021 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))

Details

Time bar (total: 22.4s)Debug log

sample393.0ms

Algorithm
intervals
Results
94.0ms101×body1280valid
66.0ms26×body640nan
52.0ms59×body640valid
49.0ms39×body10240exit
34.0ms36×body1280nan
23.0ms151×body80valid
18.0ms169×body80nan
15.0ms29×body320valid
6.0ms13×body320nan
4.0ms14×body160valid
0.0ms1×body160nan

simplify7.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
7.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize32.0ms

Local error

Found 3 expressions with local error:

1.3b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.2b
(pow (+ x 1) (/ 1 n))
0.5b
(pow x (/ 1 n))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
8×pow-unpow
6×add-cube-cbrt
5×add-log-exp
4×add-exp-log
4×unpow-prod-down
4×pow1
3×add-cbrt-cube
2×difference-of-squares
2×div-inv
2×pow-to-exp
1×distribute-lft-out--
1×flip--
1×pow-exp
1×diff-log
1×flip3--
1×pow-pow
1×sub-neg
Counts
3 → 44
Calls
3 calls:
Slowest
16.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms
(pow (+ x 1) (/ 1 n))
1.0ms
(pow x (/ 1 n))

series357.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
194.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
84.0ms
(pow (+ x 1) (/ 1 n))
78.0ms
(pow x (/ 1 n))

simplify1.6s

Counts
28 → 53
Calls
28 calls:
Slowest
559.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
298.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
285.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
204.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
107.0ms
(- (+ (/ (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))))

prune532.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.6b

localize9.0ms

Local error

Found 4 expressions with local error:

5.0b
(log (pow x (/ 1 n)))
1.3b
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
1.2b
(pow (+ x 1) (/ 1 n))
0.5b
(pow x (/ 1 n))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt
8×pow-unpow
6×add-log-exp
6×add-exp-log
5×unpow-prod-down
5×log-prod
5×pow1
4×difference-of-squares
4×add-cbrt-cube
3×pow-to-exp
2×div-inv
2×exp-sum
2×rem-log-exp
1×distribute-lft-out--
1×flip--
1×log-pow
1×pow-exp
1×diff-log
1×flip3--
1×pow-pow
1×sub-neg
Counts
4 → 59
Calls
4 calls:
Slowest
18.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
3.0ms
(pow (+ x 1) (/ 1 n))
2.0ms
(pow x (/ 1 n))
1.0ms
(log (pow x (/ 1 n)))

series472.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
212.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
114.0ms
(log (pow x (/ 1 n)))
79.0ms
(pow (+ x 1) (/ 1 n))
67.0ms
(pow x (/ 1 n))

simplify1.8s

Counts
41 → 71
Calls
41 calls:
Slowest
509.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
229.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
228.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
178.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
139.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))

prune791.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.2b

localize24.0ms

Local error

Found 4 expressions with local error:

5.0b
(log (pow x (/ 1 n)))
5.0b
(log (pow x (/ 1 n)))
5.0b
(log (pow x (/ 1 n)))
1.3b
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
11×log-prod
9×*-un-lft-identity
7×add-cube-cbrt
7×add-exp-log
6×add-log-exp
6×rem-log-exp
4×difference-of-squares
4×add-cbrt-cube
4×pow1
3×log-pow
3×pow-to-exp
2×exp-sum
2×unpow-prod-down
1×distribute-lft-out--
1×flip--
1×diff-log
1×flip3--
1×sub-neg
Counts
4 → 56
Calls
4 calls:
Slowest
15.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
3.0ms
(log (pow x (/ 1 n)))
2.0ms
(log (pow x (/ 1 n)))
2.0ms
(log (pow x (/ 1 n)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
195.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
83.0ms
(log (pow x (/ 1 n)))
78.0ms
(log (pow x (/ 1 n)))
71.0ms
(log (pow x (/ 1 n)))

simplify1.4s

Counts
40 → 68
Calls
40 calls:
Slowest
267.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
218.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
139.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
133.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
116.0ms
(* -1 (/ (log (/ 1 x)) n))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.2b

localize16.0ms

Local error

Found 4 expressions with local error:

5.0b
(log (pow x (/ 1 n)))
5.0b
(log (pow x (/ 1 n)))
5.0b
(log (pow x (/ 1 n)))
5.0b
(log (pow x (/ 1 n)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod
8×add-cube-cbrt
8×add-exp-log
8×rem-log-exp
8×*-un-lft-identity
8×add-sqr-sqrt
4×add-log-exp
4×log-pow
4×add-cbrt-cube
4×pow1
4×pow-to-exp
Counts
4 → 52
Calls
4 calls:
Slowest
2.0ms
(log (pow x (/ 1 n)))
1.0ms
(log (pow x (/ 1 n)))
1.0ms
(log (pow x (/ 1 n)))
1.0ms
(log (pow x (/ 1 n)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(log (pow x (/ 1 n)))
85.0ms
(log (pow x (/ 1 n)))
84.0ms
(log (pow x (/ 1 n)))
81.0ms
(log (pow x (/ 1 n)))

simplify843.0ms

Counts
36 → 64
Calls
36 calls:
Slowest
158.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
124.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
102.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
97.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
86.0ms
(* -1 (/ (log (/ 1 x)) n))

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 18.2b

regimes398.0ms

Accuracy

74.4% (2.8b remaining)

Error of 21.4b against oracle of 18.6b and baseline of 29.5b

bsearch7.0ms

end0.0ms

sample10.5s

Algorithm
intervals
Results
3.3s3222×body1280valid
1.3s1191×body10240exit
1.3s4676×body80valid
1.2s1595×body640valid
712.0ms658×body1280nan
593.0ms4850×body80nan
561.0ms665×body640nan
547.0ms330×body320nan
477.0ms845×body320valid
156.0ms428×body160valid
54.0ms185×body160nan