Average Error: 31.3 → 19.4
Time: 1.0m
Precision: 64
Internal Precision: 128
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
↓
\[\begin{array}{l} \mathbf{if}\;im \le -2.562518015156732 \cdot 10^{+119}:\\ \;\;\;\;\left(\sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right) \cdot \left(\frac{-1}{\log base} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right) + \frac{-1}{\log base} \cdot \log \left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right)\\ \mathbf{elif}\;im \le -3.0031008952659085 \cdot 10^{+25}:\\ \;\;\;\;\frac{\log \left(\sqrt{im \cdot im + re \cdot re}\right)}{\log base}\\ \mathbf{elif}\;im \le -3.503887784193748 \cdot 10^{-67}:\\ \;\;\;\;\sqrt[3]{{\left(\log \left(\frac{-1}{re}\right)\right)}^{3} \cdot \frac{\frac{-1}{\log base}}{\log base \cdot \log base}}\\ \mathbf{elif}\;im \le -5.1953225150642786 \cdot 10^{-158}:\\ \;\;\;\;\frac{\sqrt[3]{\left(\left(\log base \cdot \log \left(\sqrt{im \cdot im + re \cdot re}\right)\right) \cdot \left(\log base \cdot \log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)\right) \cdot \left(\log base \cdot \log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)}}{\log base \cdot \log base}\\ \mathbf{elif}\;im \le 8.620660951623408 \cdot 10^{-151}:\\ \;\;\;\;\frac{\log \left(\frac{-1}{re}\right)}{\frac{\log base}{\frac{-2}{3}}} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}\\ \mathbf{elif}\;im \le 8.608873861029687 \cdot 10^{-16}:\\ \;\;\;\;\frac{\log \left(\sqrt{im \cdot im + re \cdot re}\right)}{\log base}\\ \mathbf{elif}\;im \le 2.4019107055312503 \cdot 10^{+32}:\\ \;\;\;\;\log \left(e^{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\log base \cdot \log im}{\log base \cdot \log base}\\ \end{array}\]

Error

Bits error versus re

Bits error versus im

Bits error versus base

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 7 regimes

  2. if im < -2.562518015156732e+119

    1. Initial program 53.3

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified53.3

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]

    3. Taylor expanded around -inf 62.7

      \[\leadsto \color{blue}{-1 \cdot \frac{\log \left(\frac{-1}{re}\right)}{\log -1 - \log \left(\frac{-1}{base}\right)}}\]

    4. Simplified49.3

      \[\leadsto \color{blue}{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt49.3

      \[\leadsto \frac{-1}{\log base} \cdot \log \color{blue}{\left(\left(\sqrt[3]{\frac{-1}{re}} \cdot \sqrt[3]{\frac{-1}{re}}\right) \cdot \sqrt[3]{\frac{-1}{re}}\right)}\]

    7. Applied log-prod49.3

      \[\leadsto \frac{-1}{\log base} \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{-1}{re}} \cdot \sqrt[3]{\frac{-1}{re}}\right) + \log \left(\sqrt[3]{\frac{-1}{re}}\right)\right)}\]

    8. Applied distribute-rgt-in49.3

      \[\leadsto \color{blue}{\log \left(\sqrt[3]{\frac{-1}{re}} \cdot \sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}}\]

    9. Taylor expanded around -inf 49.3

      \[\leadsto \log \color{blue}{\left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right)} \cdot \frac{-1}{\log base} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}\]
    10. Using strategy rm

    11. Applied add-cube-cbrt49.3

      \[\leadsto \log \left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right) \cdot \frac{-1}{\log base} + \color{blue}{\left(\left(\sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right) \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right)} \cdot \frac{-1}{\log base}\]

    12. Applied associate-*l*49.3

      \[\leadsto \log \left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right) \cdot \frac{-1}{\log base} + \color{blue}{\left(\sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right) \cdot \left(\sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)} \cdot \frac{-1}{\log base}\right)}\]

    if -2.562518015156732e+119 < im < -3.0031008952659085e+25 or 8.620660951623408e-151 < im < 8.608873861029687e-16

    1. Initial program 15.3

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified15.3

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]
    3. Using strategy rm

    4. Applied times-frac15.2

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log base} \cdot \frac{\log base}{\log base}}\]

    5. Simplified15.2

      \[\leadsto \frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log base} \cdot \color{blue}{1}\]

    if -3.0031008952659085e+25 < im < -3.503887784193748e-67

    1. Initial program 19.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified19.4

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]

    3. Taylor expanded around -inf 62.8

      \[\leadsto \color{blue}{-1 \cdot \frac{\log \left(\frac{-1}{re}\right)}{\log -1 - \log \left(\frac{-1}{base}\right)}}\]

    4. Simplified24.3

      \[\leadsto \color{blue}{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\]
    5. Using strategy rm

    6. Applied add-cbrt-cube24.5

      \[\leadsto \frac{-1}{\log base} \cdot \color{blue}{\sqrt[3]{\left(\log \left(\frac{-1}{re}\right) \cdot \log \left(\frac{-1}{re}\right)\right) \cdot \log \left(\frac{-1}{re}\right)}}\]

    7. Applied add-cbrt-cube24.5

      \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{-1}{\log base} \cdot \frac{-1}{\log base}\right) \cdot \frac{-1}{\log base}}} \cdot \sqrt[3]{\left(\log \left(\frac{-1}{re}\right) \cdot \log \left(\frac{-1}{re}\right)\right) \cdot \log \left(\frac{-1}{re}\right)}\]

    8. Applied cbrt-unprod24.5

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{-1}{\log base} \cdot \frac{-1}{\log base}\right) \cdot \frac{-1}{\log base}\right) \cdot \left(\left(\log \left(\frac{-1}{re}\right) \cdot \log \left(\frac{-1}{re}\right)\right) \cdot \log \left(\frac{-1}{re}\right)\right)}}\]

    9. Simplified24.5

      \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{-1}{\log base}}{\log base \cdot \log base} \cdot {\left(\log \left(\frac{-1}{re}\right)\right)}^{3}}}\]

    if -3.503887784193748e-67 < im < -5.1953225150642786e-158

    1. Initial program 17.5

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified17.5

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]
    3. Using strategy rm

    4. Applied add-cbrt-cube17.6

      \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right) \cdot \left(\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right)\right) \cdot \left(\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base\right)}}}{\log base \cdot \log base}\]

    if -5.1953225150642786e-158 < im < 8.620660951623408e-151

    1. Initial program 29.4

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified29.4

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]

    3. Taylor expanded around -inf 62.8

      \[\leadsto \color{blue}{-1 \cdot \frac{\log \left(\frac{-1}{re}\right)}{\log -1 - \log \left(\frac{-1}{base}\right)}}\]

    4. Simplified6.9

      \[\leadsto \color{blue}{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\]
    5. Using strategy rm

    6. Applied add-cube-cbrt6.9

      \[\leadsto \frac{-1}{\log base} \cdot \log \color{blue}{\left(\left(\sqrt[3]{\frac{-1}{re}} \cdot \sqrt[3]{\frac{-1}{re}}\right) \cdot \sqrt[3]{\frac{-1}{re}}\right)}\]

    7. Applied log-prod6.9

      \[\leadsto \frac{-1}{\log base} \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{-1}{re}} \cdot \sqrt[3]{\frac{-1}{re}}\right) + \log \left(\sqrt[3]{\frac{-1}{re}}\right)\right)}\]

    8. Applied distribute-rgt-in6.9

      \[\leadsto \color{blue}{\log \left(\sqrt[3]{\frac{-1}{re}} \cdot \sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}}\]

    9. Taylor expanded around -inf 6.9

      \[\leadsto \log \color{blue}{\left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right)} \cdot \frac{-1}{\log base} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}\]

    10. Taylor expanded around -inf 62.8

      \[\leadsto \color{blue}{-1 \cdot \frac{\log \left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right)}{\log -1 - \log \left(\frac{-1}{base}\right)}} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}\]

    11. Simplified6.9

      \[\leadsto \color{blue}{\frac{\log \left(\frac{-1}{re}\right)}{\frac{\log base}{\frac{-2}{3}}}} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}\]

    if 8.608873861029687e-16 < im < 2.4019107055312503e+32

    1. Initial program 14.2

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified14.2

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]

    3. Taylor expanded around -inf 62.8

      \[\leadsto \color{blue}{-1 \cdot \frac{\log \left(\frac{-1}{re}\right)}{\log -1 - \log \left(\frac{-1}{base}\right)}}\]

    4. Simplified31.1

      \[\leadsto \color{blue}{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\]
    5. Using strategy rm

    6. Applied add-log-exp31.2

      \[\leadsto \color{blue}{\log \left(e^{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\right)}\]

    if 2.4019107055312503e+32 < im

    1. Initial program 42.0

      \[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]

    2. Simplified42.0

      \[\leadsto \color{blue}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base}{\log base \cdot \log base}}\]

    3. Taylor expanded around 0 12.0

      \[\leadsto \frac{\color{blue}{\log base \cdot \log im}}{\log base \cdot \log base}\]
  3. Recombined 7 regimes into one program.

  4. Final simplification19.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;im \le -2.562518015156732 \cdot 10^{+119}:\\ \;\;\;\;\left(\sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right) \cdot \left(\frac{-1}{\log base} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{-1}{re}}\right)}\right) + \frac{-1}{\log base} \cdot \log \left({\left(\frac{-1}{re}\right)}^{\frac{2}{3}}\right)\\ \mathbf{elif}\;im \le -3.0031008952659085 \cdot 10^{+25}:\\ \;\;\;\;\frac{\log \left(\sqrt{im \cdot im + re \cdot re}\right)}{\log base}\\ \mathbf{elif}\;im \le -3.503887784193748 \cdot 10^{-67}:\\ \;\;\;\;\sqrt[3]{{\left(\log \left(\frac{-1}{re}\right)\right)}^{3} \cdot \frac{\frac{-1}{\log base}}{\log base \cdot \log base}}\\ \mathbf{elif}\;im \le -5.1953225150642786 \cdot 10^{-158}:\\ \;\;\;\;\frac{\sqrt[3]{\left(\left(\log base \cdot \log \left(\sqrt{im \cdot im + re \cdot re}\right)\right) \cdot \left(\log base \cdot \log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)\right) \cdot \left(\log base \cdot \log \left(\sqrt{im \cdot im + re \cdot re}\right)\right)}}{\log base \cdot \log base}\\ \mathbf{elif}\;im \le 8.620660951623408 \cdot 10^{-151}:\\ \;\;\;\;\frac{\log \left(\frac{-1}{re}\right)}{\frac{\log base}{\frac{-2}{3}}} + \log \left(\sqrt[3]{\frac{-1}{re}}\right) \cdot \frac{-1}{\log base}\\ \mathbf{elif}\;im \le 8.608873861029687 \cdot 10^{-16}:\\ \;\;\;\;\frac{\log \left(\sqrt{im \cdot im + re \cdot re}\right)}{\log base}\\ \mathbf{elif}\;im \le 2.4019107055312503 \cdot 10^{+32}:\\ \;\;\;\;\log \left(e^{\frac{-1}{\log base} \cdot \log \left(\frac{-1}{re}\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\log base \cdot \log im}{\log base \cdot \log base}\\ \end{array}\]

Reproduce

herbie shell --seed 2019007 
(FPCore (re im base)
  :name "math.log/2 on complex, real part"
  (/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0))))

Details

Time bar (total: 58.0s)Debug log

sample1.5s

Algorithm
intervals

simplify13.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

13.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0)) (+ (* (log base) (log base)) (* 0 0)))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize53.0ms

Local error

Found 4 expressions with local error:

29.9b
(sqrt (+ (* re re) (* im im)))
0.5b
(* (log base) (log base))
0.4b
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
0.3b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))

rewrite53.0ms

Algorithm
rewrite-expression-head
Counts
4 → 74
Calls

4 calls. Slowest were:

30.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
10.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
8.0ms
(* (log base) (log base))

series373.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

188.0ms
(* (log base) (log base))
78.0ms
(/ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (log base) (log base)))
74.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
32.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.0s

Counts
49 → 86
Calls

49 calls. Slowest were:

398.0ms
(* -1 (* (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
364.0ms
(- (+ (log (log (sqrt (+ (* re re) (* im im))))) (log (log base))) (log (* (log base) (log base))))
363.0ms
(- (+ (log (log (sqrt (+ (* re re) (* im im))))) (log (log base))) (+ (log (log base)) (log (log base))))

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b
(* (/ -1 (log base)) (log (/ -1 re)))
0.3b
(/ -1 (log base))

rewrite11.0ms

Algorithm
rewrite-expression-head
Counts
2 → 41
Calls

2 calls. Slowest were:

9.0ms
(* (/ -1 (log base)) (log (/ -1 re)))
1.0ms
(/ -1 (log base))

series369.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

220.0ms
(/ -1 (log base))
148.0ms
(* (/ -1 (log base)) (log (/ -1 re)))

simplify1.2s

Counts
27 → 47
Calls

27 calls. Slowest were:

504.0ms
(* (* (* (/ -1 (log base)) (/ -1 (log base))) (/ -1 (log base))) (* (* (log (/ -1 re)) (log (/ -1 re))) (log (/ -1 re))))
158.0ms
(* -1 (/ (log (/ -1 re)) (- (log -1) (log (/ -1 base)))))
84.0ms
(* -1 (/ (- (log -1) (log re)) (log base)))

prune568.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.9b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ -1 re))
0.6b
(cbrt (/ -1 re))
0.6b
(cbrt (/ -1 re))
0.5b
(* (cbrt (/ -1 re)) (cbrt (/ -1 re)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Counts
4 → 72
Calls

4 calls. Slowest were:

4.0ms
(* (cbrt (/ -1 re)) (cbrt (/ -1 re)))
1.0ms
(cbrt (/ -1 re))
0.0ms
(cbrt (/ -1 re))

series1.3s

Counts
4 → 12
Calls

4 calls. Slowest were:

333.0ms
(cbrt (/ -1 re))
330.0ms
(cbrt (/ -1 re))
323.0ms
(* (cbrt (/ -1 re)) (cbrt (/ -1 re)))
297.0ms
(cbrt (/ -1 re))

simplify159.0ms

Counts
53 → 84
Calls

53 calls. Slowest were:

22.0ms
(* (pow (/ 1 (pow re 2)) 1/3) (pow (cbrt -1) 2))
21.0ms
(* (pow (/ 1 (pow re 2)) 1/3) (pow (cbrt -1) 2))
13.0ms
(* (/ -1 re) (/ -1 re))

prune1.2s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 6.9b

localize19.0ms

Local error

Found 4 expressions with local error:

5.9b
(pow (/ -1 re) 2/3)
0.6b
(cbrt (/ -1 re))
0.3b
(* (log (cbrt (/ -1 re))) (/ -1 (log base)))
0.3b
(* (log (pow (/ -1 re) 2/3)) (/ -1 (log base)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Counts
4 → 68
Calls

4 calls. Slowest were:

10.0ms
(* (log (cbrt (/ -1 re))) (/ -1 (log base)))
8.0ms
(* (log (pow (/ -1 re) 2/3)) (/ -1 (log base)))
1.0ms
(pow (/ -1 re) 2/3)

series943.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

317.0ms
(cbrt (/ -1 re))
267.0ms
(pow (/ -1 re) 2/3)
202.0ms
(* (log (cbrt (/ -1 re))) (/ -1 (log base)))
156.0ms
(* (log (pow (/ -1 re) 2/3)) (/ -1 (log base)))

simplify2.1s

Counts
43 → 80
Calls

43 calls. Slowest were:

636.0ms
(* (* (* (log (pow (/ -1 re) 2/3)) (log (pow (/ -1 re) 2/3))) (log (pow (/ -1 re) 2/3))) (* (* (/ -1 (log base)) (/ -1 (log base))) (/ -1 (log base))))
314.0ms
(* -1 (/ (log (pow (/ -1 re) 2/3)) (- (log -1) (log (/ -1 base)))))
254.0ms
(* -1 (/ (log (pow (/ -1 re) 1/3)) (- (log -1) (log (/ -1 base)))))

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 6.9b

regimes1.1s

Accuracy

45.2% (12.0b remaining)

Error of 19.4b against oracle of 7.4b and baseline of 29.3b

bsearch5.8s

end0.0ms

sample35.7s

Algorithm
intervals