Simple math results in an Emacs org-mode file with babel

Question

I'd like to embed simple math expressions in an org-mode file, such as:

sqrt(p * (1-p) * N)

where p=0.8, N=10,000 and the answer according to a simple desk calculator is 40. I'm having no luck get org-babel give me this answer... Here's an org file:

Some weird rounding errors with Python:

#+begin_src python :var N=100000 :var p=0.8
from math import sqrt
return sqrt(p * (1 - p) * N)
#+end_src

#+results:
: 126.491106407


Some other weird rounding errors, this time with Emacs lisp:

#+begin_src elisp :var N=100000 :var p=0.8
(sqrt (* p (- 1 p) N))
#+end_src

#+results:
: 126.49110640673517


Note sure which number calc is unhappy with:

#+begin_src calc :var N=100000 :var p=0.8
sqrt(p * (1 - p) * N)
#+end_src

#+results:
| 5 | Expected a number |


Yet more weird rounding errors, using bc in the shell:

#+begin_src sh :var N=100000 :var p=0.8
echo "sqrt($p * (1 - $p) * $N)" | bc
#+end_src

#+results:
: 100.0


A different set of rounding errors with bc without using variables:

#+begin_src sh
echo "sqrt(0.8 * (1 - 0.8) * 10000)" | bc
#+end_src

#+results:
: 31.6


Looks like the variables are being substituted OK:

#+begin_src sh :var N=100000 :var p=0.8
echo "sqrt($p * (1 - $p) * $N)"
#+end_src

#+results:
: sqrt(0.8 * (1 - 0.8) * 100000)


Using extra precision directly gives the correct result:

#+begin_src sh
echo "sqrt(0.80 * (1 - 0.80) * 10000)" | bc
#+end_src

#+results:
: 40.0


So, just use extra precision in the p variable, eh:

#+begin_src sh :var N=100000 :var p=0.80
echo "sqrt($p * (1 - $p) * $N)" | bc
#+end_src

#+results:
: 100.0


No! Because it get stripped out:

#+begin_src sh :var N=100000 :var p=0.80
echo "sqrt($p * (1 - $p) * $N)"
#+end_src

#+results:
: sqrt(0.8 * (1 - 0.8) * 100000)


Please God, kill me now...

I'm just looking for a convenient way to embed some math in an org file.

(org-mode 7.8.03 from a recent git checkout, emacs 24.0.93.1 from a recent git chekout)

Answer 1

You say:

sqrt(p * (1-p) * N)

where p=0.8, N=10,000 and the answer according to a simple desk calculator is 40. 

This is correct, but in many of your codes you use

:var N=100000

instead, i.e. off by a factor of 10.

>>> from math import sqrt 
>>> p = 0.8
>>> sqrt(p*(1-p)*10000)
40.0
>>> sqrt(p*(1-p)*100000)
126.49110640673517

Answer 2

Don't kill yourself over a typo:)

(sqrt (* p (- 1 p)))
0.39999999999999997

Add the missing N..

(let ((p 0.8) (N 10000))
  (sqrt (* p (- 1 p) N)))

40.0

For bc, try with

scale=10