Average Error: 29.1 → 22.3
Time: 29.8s
Precision: 64
Internal Precision: 128
\[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{1}{n} \le -8.938998699431754 \cdot 10^{-05}:\\ \;\;\;\;\left(\log \left(\sqrt[3]{\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}}\right) + \log \left(\sqrt[3]{\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}} \cdot \sqrt[3]{\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}}\right)\right) + \left(\log \left(\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}\right) - \log \left(\sqrt{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)\right)\\ \mathbf{elif}\;\frac{1}{n} \le 1.0591236119246845 \cdot 10^{-05}:\\ \;\;\;\;\frac{\log x}{n \cdot \left(x \cdot n\right)} + \left(\frac{\frac{\frac{-1}{2}}{x}}{x \cdot n} + \frac{1}{x \cdot n}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}\right) + \left(\left(\log \left(\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}\right) - \log \left(\sqrt{\sqrt{e^{{x}^{\left(\frac{1}{n}\right)}}}}\right)\right) - \log \left(\sqrt{\sqrt{e^{{x}^{\left(\frac{1}{n}\right)}}}}\right)\right)\\ \end{array}\]

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) < -8.938998699431754e-05

    1. Initial program 0.3

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

    3. Applied add-log-exp0.4

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

    4. Applied add-log-exp0.4

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

    5. Applied diff-log0.4

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

    6. Simplified0.4

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

    8. Applied add-sqr-sqrt0.4

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

    9. Applied log-prod0.4

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

    11. Applied exp-diff0.4

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

    12. Applied sqrt-div0.4

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

    13. Applied log-div0.4

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

    15. Applied add-cube-cbrt0.4

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

    16. Applied log-prod0.4

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

    if -8.938998699431754e-05 < (/ 1 n) < 1.0591236119246845e-05

    1. Initial program 44.2

      \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]

    2. Taylor expanded around inf 32.6

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

    3. 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 1.0591236119246845e-05 < (/ 1 n)

    1. Initial program 24.2

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

    3. Applied add-log-exp24.2

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

    4. Applied add-log-exp24.2

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

    5. Applied diff-log24.2

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

    6. Simplified24.2

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

    8. Applied add-sqr-sqrt24.2

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

    9. Applied log-prod24.2

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

    11. Applied exp-diff24.2

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

    12. Applied sqrt-div24.2

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

    13. Applied log-div24.2

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

    15. Applied add-sqr-sqrt24.3

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

    16. Applied log-prod24.2

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

    17. Applied associate--r+24.3

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

  4. Final simplification22.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{1}{n} \le -8.938998699431754 \cdot 10^{-05}:\\ \;\;\;\;\left(\log \left(\sqrt[3]{\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}}\right) + \log \left(\sqrt[3]{\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}} \cdot \sqrt[3]{\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}}\right)\right) + \left(\log \left(\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}\right) - \log \left(\sqrt{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)\right)\\ \mathbf{elif}\;\frac{1}{n} \le 1.0591236119246845 \cdot 10^{-05}:\\ \;\;\;\;\frac{\log x}{n \cdot \left(x \cdot n\right)} + \left(\frac{\frac{\frac{-1}{2}}{x}}{x \cdot n} + \frac{1}{x \cdot n}\right)\\ \mathbf{else}:\\ \;\;\;\;\log \left(\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}\right) + \left(\left(\log \left(\sqrt{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}\right) - \log \left(\sqrt{\sqrt{e^{{x}^{\left(\frac{1}{n}\right)}}}}\right)\right) - \log \left(\sqrt{\sqrt{e^{{x}^{\left(\frac{1}{n}\right)}}}}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019007 
(FPCore (x n)
  :name "2nthrt (problem 3.4.6)"
  (- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n))))

Details

Time bar (total: 28.3s)Debug log

sample319.0ms

Algorithm
intervals

simplify5.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

5.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize28.0ms

Local error

Found 3 expressions with local error:

1.5b
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0b
(pow (+ x 1) (/ 1 n))
0.3b
(pow x (/ 1 n))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
3 → 44
Calls

3 calls. Slowest were:

14.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
1.0ms
(pow (+ x 1) (/ 1 n))
1.0ms
(pow x (/ 1 n))

series347.0ms

Counts
3 → 9
Calls

3 calls. Slowest were:

197.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
79.0ms
(pow (+ x 1) (/ 1 n))
72.0ms
(pow x (/ 1 n))

simplify1.7s

Counts
28 → 53
Calls

28 calls. Slowest were:

598.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
326.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
269.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))

prune547.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.5b
(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
1.0b
(pow (+ 1 x) (/ 1 n))
0.3b
(pow x (/ 1 n))

rewrite57.0ms

Algorithm
rewrite-expression-head
Counts
4 → 65
Calls

4 calls. Slowest were:

35.0ms
(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
17.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
3.0ms
(pow (+ 1 x) (/ 1 n))

series568.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

223.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
183.0ms
(log (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))))
83.0ms
(pow x (/ 1 n))
79.0ms
(pow (+ 1 x) (/ 1 n))

simplify2.0s

Counts
44 → 77
Calls

44 calls. Slowest were:

513.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
245.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
235.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))

prune865.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.4b

localize9.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.5b
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.5b
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
1.5b
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Counts
4 → 68
Calls

4 calls. Slowest were:

15.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
8.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
7.0ms
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))

series988.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

320.0ms
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
275.0ms
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
218.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
174.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))

simplify2.5s

Counts
44 → 80
Calls

44 calls. Slowest were:

355.0ms
(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
334.0ms
(- (/ 1 (* x n)) (+ (/ (log (/ 1 x)) (* x (pow n 2))) (* 1/2 (/ 1 (* (pow x 2) n)))))
312.0ms
(- (+ (* 1/2 (/ (log -1) (* x (pow n 2)))) (* 1/2 (/ 1 (* x n)))) (+ (* 1/4 (/ 1 (* (pow x 2) n))) (* 1/2 (/ (log (/ -1 x)) (* x (pow n 2))))))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.3b

localize27.0ms

Local error

Found 4 expressions with local error:

1.5b
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
1.5b
(- (log (sqrt (exp (pow (+ 1 x) (/ 1 n))))) (log (sqrt (exp (pow x (/ 1 n))))))
1.5b
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
1.0b
(pow (+ 1 x) (/ 1 n))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
4 → 81
Calls

4 calls. Slowest were:

10.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
9.0ms
(- (log (sqrt (exp (pow (+ 1 x) (/ 1 n))))) (log (sqrt (exp (pow x (/ 1 n))))))
7.0ms
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))

series959.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

392.0ms
(- (log (sqrt (exp (pow (+ 1 x) (/ 1 n))))) (log (sqrt (exp (pow x (/ 1 n))))))
320.0ms
(log (sqrt (exp (- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n))))))
188.0ms
(- (pow (+ 1 x) (/ 1 n)) (pow x (/ 1 n)))
60.0ms
(pow (+ 1 x) (/ 1 n))

simplify2.4s

Counts
57 → 93
Calls

57 calls. Slowest were:

556.0ms
(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))
331.0ms
(- (+ (* 1/2 (/ (log -1) (* x (pow n 2)))) (* 1/2 (/ 1 (* x n)))) (+ (* 1/4 (/ 1 (* (pow x 2) n))) (* 1/2 (/ (log (/ -1 x)) (* x (pow n 2))))))
279.0ms
(- (+ (* 1/2 (/ (log -1) (* x (pow n 2)))) (* 1/2 (/ 1 (* x n)))) (+ (* 1/4 (/ 1 (* (pow x 2) n))) (* 1/2 (/ (log (/ -1 x)) (* x (pow n 2))))))

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.1b

regimes307.0ms

Accuracy

83.1% (1.4b remaining)

Error of 22.3b against oracle of 20.9b and baseline of 29.3b

bsearch16.0ms

end0.0ms

sample11.1s

Algorithm
intervals