Average Error: 29.3 → 20.8
Time: 25.4s
Precision: 64
Internal Precision: 128
\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{n} \le -0.012152689055358101:\\ \;\;\;\;\sqrt[3]{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right)\right)}\\ \mathbf{elif}\;\frac{1}{n} \le 5.162294537707631 \cdot 10^{-17}:\\ \;\;\;\;\frac{\log x}{n \cdot \left(x \cdot n\right)} + \left(\frac{1}{x \cdot n} + \frac{\frac{\frac{-1}{2}}{x}}{x \cdot n}\right)\\ \mathbf{elif}\;\frac{1}{n} \le 1.2106355415914036 \cdot 10^{+198}:\\ \;\;\;\;\sqrt[3]{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - 1\right) \cdot \left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right)\right)}\\ \end{array}\]

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 4 regimes

  2. if (/ 1 n) < -0.012152689055358101

    1. Initial program 0.1

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

    3. Applied add-exp-log0.2

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

    5. Applied add-cbrt-cube0.1

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

    7. Applied add-log-exp0.3

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

    9. Applied rem-log-exp0.1

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

    if -0.012152689055358101 < (/ 1 n) < 5.162294537707631e-17

    1. Initial program 45.2

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

    3. Applied add-exp-log45.2

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

    4. Taylor expanded around inf 32.5

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

    5. Simplified32.5

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

    if 5.162294537707631e-17 < (/ 1 n) < 1.2106355415914036e+198

    1. Initial program 17.1

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

    3. Applied add-exp-log17.1

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

    5. Applied add-cbrt-cube17.1

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

    7. Applied add-log-exp17.2

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

    9. Applied add-cube-cbrt17.2

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

    10. Applied log-prod17.2

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

    if 1.2106355415914036e+198 < (/ 1 n)

    1. Initial program 47.8

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

    3. Applied add-exp-log47.8

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

    5. Applied add-cbrt-cube47.8

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

    6. Taylor expanded around 0 13.4

      \[\leadsto \sqrt[3]{\left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right)\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\color{blue}{0}}\right)}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification20.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{n} \le -0.012152689055358101:\\ \;\;\;\;\sqrt[3]{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right)\right)}\\ \mathbf{elif}\;\frac{1}{n} \le 5.162294537707631 \cdot 10^{-17}:\\ \;\;\;\;\frac{\log x}{n \cdot \left(x \cdot n\right)} + \left(\frac{1}{x \cdot n} + \frac{\frac{\frac{-1}{2}}{x}}{x \cdot n}\right)\\ \mathbf{elif}\;\frac{1}{n} \le 1.2106355415914036 \cdot 10^{+198}:\\ \;\;\;\;\sqrt[3]{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}}\right) \cdot \left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right) + \log \left(\sqrt[3]{{x}^{\left(\frac{1}{n}\right)}} \cdot \sqrt[3]{{x}^{\left(\frac{1}{n}\right)}}\right)}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - 1\right) \cdot \left(\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right) \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - e^{\log \left({x}^{\left(\frac{1}{n}\right)}\right)}\right)\right)}\\ \end{array}\]

Reproduce

herbie shell --seed 2019010 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))

Details

Time bar (total: 24.0s)Debug log

sample382.0ms

Algorithm
intervals

simplify10.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
10.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize32.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.7b
(pow (+ x 1) (/ 1 n))
1.0b
(pow x (/ 1 n))

rewrite35.0ms

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
15.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.0ms
(pow (+ x 1) (/ 1 n))
1.0ms
(pow x (/ 1 n))

series391.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
216.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
92.0ms
(pow (+ x 1) (/ 1 n))
82.0ms
(pow x (/ 1 n))

simplify1.8s

Counts
28 → 53
Calls
28 calls:
Slowest
656.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
300.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
273.0ms
(- (/ 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))
77.0ms
(- (+ (/ (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))))

prune533.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.8b

localize8.0ms

Local error

Found 4 expressions with local error:

5.2b
(log (pow x (/ 1 n)))
2.4b
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
1.7b
(pow (+ x 1) (/ 1 n))
1.0b
(pow x (/ 1 n))

rewrite15.0ms

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
9.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
2.0ms
(pow (+ x 1) (/ 1 n))
1.0ms
(pow x (/ 1 n))
1.0ms
(log (pow x (/ 1 n)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
121.0ms
(log (pow x (/ 1 n)))
75.0ms
(pow x (/ 1 n))
60.0ms
(pow (+ x 1) (/ 1 n))

simplify2.1s

Counts
41 → 71
Calls
41 calls:
Slowest
586.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
283.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
260.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
249.0ms
(- (+ (* 1/2 (/ (pow (log (/ 1 x)) 2) (pow n 2))) 1) (/ (log (/ 1 x)) n))
149.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))

prune820.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.2b

localize13.0ms

Local error

Found 4 expressions with local error:

5.2b
(log (pow x (/ 1 n)))
5.2b
(log (pow x (/ 1 n)))
5.2b
(log (pow x (/ 1 n)))
2.4b
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))

rewrite22.0ms

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
17.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (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)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
228.0ms
(- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))
112.0ms
(log (pow x (/ 1 n)))
83.0ms
(log (pow x (/ 1 n)))
83.0ms
(log (pow x (/ 1 n)))

simplify1.7s

Counts
40 → 68
Calls
40 calls:
Slowest
345.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
295.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
161.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
133.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
124.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.2b

localize15.0ms

Local error

Found 4 expressions with local error:

5.2b
(log (pow x (/ 1 n)))
5.2b
(log (pow x (/ 1 n)))
5.2b
(log (pow x (/ 1 n)))
2.5b
(log (exp (- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
16×log-prod
12×log-pow
11×*-un-lft-identity
9×add-cube-cbrt
8×exp-prod
7×add-exp-log
7×rem-log-exp
5×pow1
4×difference-of-squares
4×add-log-exp
4×exp-sum
4×add-cbrt-cube
3×pow-to-exp
2×unpow-prod-down
1×distribute-lft-out--
1×exp-diff
1×sub-neg
1×log-div
Counts
4 → 62
Calls
4 calls:
Slowest
31.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (exp (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)))

series506.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
196.0ms
(log (exp (- (pow (+ x 1) (/ 1 n)) (exp (log (pow x (/ 1 n)))))))
113.0ms
(log (pow x (/ 1 n)))
101.0ms
(log (pow x (/ 1 n)))
97.0ms
(log (pow x (/ 1 n)))

simplify1.7s

Counts
45 → 74
Calls
45 calls:
Slowest
272.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
248.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
161.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
161.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))
155.0ms
(* -1 (/ (- (log (/ -1 x)) (log -1)) n))

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.2b

regimes362.0ms

Accuracy

76.1% (2.7b remaining)

Error of 20.8b against oracle of 18.0b and baseline of 29.4b

bsearch8.0ms

end0.0ms

sample10.5s

Algorithm
intervals